Business statistics ( Methods of variablity measurement))

Apr 11, 2020Download as pptx, pdf1 like18 views

This document discusses various methods used to measure variability or dispersion in a dataset. It defines range, variance, standard deviation, interquartile range, percentiles, deciles, and coefficient of variation. It also discusses how to represent data distribution through a five number summary and boxplot. The five number summary consists of the minimum, first quartile, median, third quartile, and maximum values arranged in order. A boxplot is a graphical representation of the five number summary.

Business statistics ( Methods of variablity measurement))

Methods of Variability Measurement
Commonly used methods: Range, Variance,
Standard deviation, Interquartile Range, Coefficient
of Variation etc.
Range: The difference between the largest and the smallest
observations. The range of 10, 5, 2, 100 is (100-2)=98.
It’s a crude measure of variability.
Variability (or Dispersion) measures the
amount of scatter in a dataset.
2

Methods of Variability Measurement
Variance: The variance of a set of observations is the average of the
squares of the deviations of the observations from their mean.
In symbols, the variance of the n observations x1, x2,…xn is
Variance of 5, 7, 3? Mean is (5+7+3)/3 = 5 and the variance is 4
4
13
)57()53()55( 222



1
)(....)( 22
12



n
xxxx
S n
Standard Deviation: Square root of the variance. The standard
deviation of the above example is 2.
>
3

Methods of Variability Measurement
Quartiles: Data can be divided into four regions that cover the
total range of observed values. Cut points for these regions are
known as quartiles.
The first quartile (Q1) is the first 25% of the data.
The second quartile (Q2) is between the 25th and 50th percentage
points in the data. The upper bound of Q2 is the median.
The third quartile (Q3) is the 25% of the data lying between the median
and the 75% cut point in the data.
Q1 is the median of the first half of the ordered observations and Q3 is
the median of the second half of the ordered observations.
In notations, quartiles of a data is the ((n+1)/4)qth observation of the
data, where q is the desired quartile and n is the number of
observations of data.
4

Methods of Variability Measurement
An example with 15 numbers
3 6 7 11 13 22 30 40 44 50 52 61 68 80 94
Q1 Q2 Q3
The first quartile is Q1=11.
The second quartile is Q2=40= (2(15+1)/4)=8th Observation (This is
also called the Median.)
The third quartile is Q3=61= (3(15+1)/4)=12th Observation is 61
Inter-quartile Range: Difference between Q3 and Q1. Inter-
quartile range of the previous example is 61- 40=21.
The middle half of the ordered data lie between 40 and 61.
In the following example Q1= ((15+1)/4)1 =4th observation of
the data. The 4th observation is 11. So Q1 of this data set is 11.
5

Deciles and Percentiles
Percentiles: If data is ordered and divided into 100 parts, then cut
points are called Percentiles. 25th percentile is the Q1, 50th
percentile is the Median (Q2) and the 75th percentile of the data is
Q3.
Deciles: If data is ordered and divided into 10 parts, then cut points
are called Deciles
In notations, percentiles of a data is the ((n+1)/100)p th observation
of the data, where p is the desired percentile and n is the number of
observations of data.
Coefficient of Variation: The standard deviation of data divided by it’s
mean. It is usually expressed in percent.
100
x

Coefficient of Variation =
6

Five Number Summary
Five Number Summary: The five number summary of a distribution
consists of the smallest (Minimum) observation, the first quartile (Q1),
The median(Q2), the third quartile, and the largest (Maximum)
observation written in order from smallest to largest.
Box Plot: A box plot is a graph of the five number summary. The
central box spans the quartiles. A line within the box marks the
median. Lines extending above and below the box mark the
smallest and the largest observations (i.e., the range).
Outlying samples may be additionally plotted outside the range.
7

Boxplot
0
20
40
60
80
100
120
140
160
1
q1
min
median
max
q3
Distribution of Age in Month
8

This document discusses various measures of dispersion used to quantify how spread out or varied values in a data set are. It defines dispersion as the difference or deviation of values from the central value. Measures of dispersion described include range, standard deviation, quartile deviation, mean deviation, variance, and coefficient of variation. Both absolute measures, which use numerical variations, and relative measures, which use statistical variations based on percentages, are examined. Relative measures allow for comparison between different data sets.

Measure of Dispersionsonia gupta

This document defines and explains various measures of dispersion used in statistics, including range, quartile deviation, mean deviation, standard deviation, and Lorenz curve. It provides formulas for calculating each measure and includes examples to demonstrate how to apply the formulas. The key measures discussed are standard deviation, which is considered the most useful and popular, and measures of skewness, which quantify the symmetry of a distribution based on comparing the mean and third central moment.

Measure of variabilityHaneza Farcasa

This document discusses two measures of variability: quartile deviation and average deviation. Quartile deviation indicates the distance above and below the median needed to include the middle 50% of scores. It is calculated by taking the difference between the third (Q3) and first (Q1) quartiles and dividing by 2. Average deviation is the mean of the absolute deviations from the mean. It is calculated by taking the sum of the absolute value of each score's deviation from the mean and dividing by the total number of scores. The document provides examples of calculating both measures using sample data sets.

Measure of dispersionAtiq Rehman

This document provides information about measures of dispersion used in business statistics. It discusses variance and standard deviation, which are commonly used to quantify how spread out values are from the mean in a data set. The document includes an example calculating the variance (0.378) and standard deviation (0.615) of a data set with 27 observations of IT department graduate levels. Variance is defined as the average of the squared differences from the mean, while standard deviation is the square root of the variance.

Measures of dispersion.. Statistics& Library and information scienceharshaec

This document discusses various measures of dispersion, including range, quartile deviation, mean deviation, standard deviation, and the Lorenz curve. Range is the difference between the largest and smallest values. Quartile deviation is based on the first and third quartiles. Mean deviation is the average amount of deviation from the mean. Standard deviation is the most widely used measure, calculated as the square root of the average squared deviation from the mean. The Lorenz curve is a graphical measure that compares variability between distributions. Each measure has merits and limitations in understanding and calculating dispersion.

Measures of dispersion Self-employed

This document defines and compares several common measures of statistical dispersion, or variation within a data set from the average value. It explains that measures of dispersion include range, interquartile range, variance, standard deviation, and others. Each measure is defined and their advantages and disadvantages for describing how spread out numbers are in a data set are discussed. For example, the range is simple to calculate but influenced by outliers, while the standard deviation takes all values into account but can also be impacted by outliers.

Measures of dispersionMayuri Joshi

This document discusses measures of dispersion, which indicate how spread out or variable a set of data is. There are three main measures: the range, which is the difference between the highest and lowest values; the semi-interquartile range (SIR), which is the difference between the first and third quartiles divided by two; and variance/standard deviation. Variance is the average of the squared deviations from the mean, while standard deviation is the square root of the variance. These measures provide summaries of how concentrated or dispersed the observed values are from the average or expected value.

Measure of DispersionRyan Pineda

Measures of dispersion describe how spread out or clustered the data is. The range is the difference between the highest and lowest values. Standard deviation measures how far each value deviates from the mean by finding the deviations, squaring them, summing them, dividing by n-1, and taking the square root. It accounts for all data points unlike the range. To calculate standard deviation, first find the mean, then deviations from it, square those values, sum them, and divide the sum by n-1 before taking the square root.

Measures of dispersion or variationRaj Teotia

This document discusses various measures of dispersion used to describe how varied or spread out a set of data values are from the average. It describes range, interquartile range, mean deviation, standard deviation, and the Lorenz curve. Standard deviation is highlighted as the most important measure, being easy to calculate, taking all data points into account equally, and indicating how far values typically are from the average in a normal distribution. The document provides formulas and explains properties and limitations of each measure.

Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari

This document discusses measures of dispersion used in statistics. It defines measures such as range, quartile deviation, mean deviation, variance, and standard deviation. It provides formulas to calculate these measures and examples showing how to apply the formulas. The key points are: - Measures of dispersion quantify how spread out or varied the values in a data set are. They help identify variation, compare data sets, and enable other statistical techniques. - Common absolute measures include range, quartile deviation, and mean deviation. Common relative measures include coefficient of range, coefficient of quartile deviation, and coefficient of variation. - Variance and standard deviation are calculated using all data points. Variance is the average of squared deviations

quartile deviation: An introductionDr Rajesh Verma

Measures of dispersionyogesh ingle

This document defines and explains several common measures of dispersion used in statistics including range, mean absolute deviation, variance, standard deviation, and coefficient of variation. Range is the difference between the highest and lowest values. Mean absolute deviation measures the average distance between values and the mean. Variance and standard deviation both measure how spread out numbers are by taking the average of the squared distances from the mean, with standard deviation being the square root of variance. Coefficient of variation expresses standard deviation as a percentage of the mean to allow comparison between data sets with different means.

Measures of variabilityjennytuazon01630

This document defines and provides examples of key statistical concepts used to describe and analyze variability in data sets, including range, variance, standard deviation, coefficient of variation, quartiles, and percentiles. It explains that range is the difference between the highest and lowest values, variance is the average squared deviation from the mean, and standard deviation describes how distant scores are from the mean on average. Examples are provided to demonstrate calculating these measures from data sets and interpreting what they indicate about the spread of scores.

Standard deviation quartile deviationRekha Yadav

This document discusses measures of dispersion, specifically standard deviation and quartile deviation. It defines standard deviation as a measure of how closely values are clustered around the mean. Standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. Quartile deviation is defined as half the difference between the third quartile (Q3) and first quartile (Q1), which divide a data set into four equal parts. The document provides examples of calculating standard deviation and quartile deviation for both individual and grouped data sets. It also discusses the merits, demerits, and uses of these statistical measures.

Mean DeviationCarlo Luna

This document defines and provides the formula for calculating mean deviation, which is a measure of variation that uses all the scores in a distribution. It is more reliable than range. Mean deviation is calculated by finding the absolute difference between each score and the mean, summing the absolute differences, and dividing by the number of observations. Two examples of calculating mean deviation for sets of data are provided, along with exercises asking students to find the mean deviation of additional data sets and define standard deviation.

QUARTILE DEVIATIONMARIA KATRINA MACAPAZ

This document discusses various statistical measures including the coefficient of variation, quartile deviation, and box and whisker plots. It defines the coefficient of variation as the ratio of the standard deviation to the mean. Formulas for calculating the coefficient of variation by hand and in Excel are provided. Quartile deviation is defined as the semi-variation between the upper and lower quartiles, or the interquartile range. Steps for calculating quartile deviation from a data set are outlined. Finally, box and whisker plots are introduced as a way to visually represent the minimum, maximum, median, quartiles and interquartile range of a data set.

Absolute Measures of dispersionAyushi Jain

Measures of dispersionSachin Shekde

This document provides an overview of measures of dispersion, including range, quartile deviation, mean deviation, standard deviation, and variance. It defines dispersion as a measure of how scattered data values are around a central value like the mean. Different measures of dispersion are described and formulas are provided. The standard deviation is identified as the most useful measure as it considers all data values and is not overly influenced by outliers. Examples are included to demonstrate calculating measures of dispersion.

Measures of variability to grading and reportingApril Gealene Alera

The document discusses various measures of variability and statistical analysis that can be used to analyze data, including range, standard deviation, z-scores, quartile deviation, and correlation. It also provides examples of how to calculate these measures, such as calculating the range by subtracting the lowest score from the highest, and how to interpret the results, like higher standard deviation indicating more variation in the data. The document also covers topics like grades, grading systems, and guidelines for effective grading.

Measure of dispersionSana butt

Mean deviation is a measure of dispersion that calculates the average distance of data points from the central value (usually the mean). It is calculated by taking the absolute value of differences between each data point and the mean, then finding the average of those absolute differences. For a sample of data, the formula is the sum of the absolute values of (x - x-bar) divided by n. Mean deviation indicates how far data points typically are from the central value. It is useful for business applications but can be affected by outliers and does not retain positive and negative signs.

Variabilityguest0a8c96

This document discusses measures of variability used to describe how spread out data values are from the mean or average. It defines and provides formulas for calculating range, variance, standard deviation, sample variance, sample standard deviation, population variance, population standard deviation, estimated population variance, and estimated population standard deviation. These measures are important in statistical analysis to understand the distribution of data values.

Standard deviation by nikitaNikita Dewangan

Dr. R.K. Rao presented a seminar on standard deviation. The seminar covered the definition of standard deviation as the positive square root of the arithmetic mean of the squared deviations from the mean. It discussed various methods for calculating standard deviation for individual data series, discrete series, and grouped series. The seminar also reviewed the uses and merits of standard deviation as a statistical measure of dispersion.

Properties of Standard DeviationRizwan Sharif

The document discusses standard deviation and its properties. Standard deviation is a measure of how spread out numbers are from the average (mean) value. It is always non-negative and can be impacted by outliers. A low standard deviation means values are close to the mean, while a high standard deviation means values are more spread out. Standard deviation can be used to calculate what percentage of data falls within certain intervals from the mean when data is normally distributed.

Measures of SpreadDanica Joy Aquino

The document discusses various statistical concepts including range, mean deviation, variance, and standard deviation. It provides formulas and steps to calculate each measure. The range is the distance between the highest and lowest values. Mean deviation measures the average deviation from the mean. Variance is the average of the squared deviations from the mean and standard deviation is the square root of the variance, representing the average distance from the mean. Examples are given to demonstrate calculating each measure for both ungrouped and grouped data.

Unit iii measures of dispersion (2)Sanoj Fernando

Measures of dispersion describe how similar or spread out scores in a data set are. The three main measures are: 1) The range, which is the difference between the highest and lowest scores. 2) The semi-interquartile range, which is the difference between the first and third quartiles divided by two. 3) Variance and standard deviation, which measure how far scores deviate from the mean on average, with larger values indicating more spread out data. Variance is the average of the squared deviations from the mean.

Measures of DispersionMohit Mahajan

Standard deviationAbdelrahman Alkilani

Standard deviation measures how dispersed data values are from the average. It is the most reliable measure of dispersion and shows the average distance of each data point from the mean. While it is more difficult to calculate than other measures, standard deviation provides important information about how concentrated or spread out the data is. The presentation defines standard deviation, lists its merits and demerits, and shows how to calculate it for both populations and samples.

Describing Distributions with Numbersnszakir

The document discusses various methods for describing data distributions numerically, including measures of center (mean, median), measures of spread (standard deviation, interquartile range), and graphical representations (boxplots). It explains how to calculate and interpret the mean, median, quartiles, five-number summary, standard deviation, and identifies outliers. Choosing an appropriate measure of center and spread depends on the symmetry of the distribution and presence of outliers. Changing the measurement units affects the calculated values but not the underlying shape of the distribution.

Measures of Variability By Dr. Vikramjit SinghVikramjit Singh

More Related Content

What's hot (20)

Measure of DispersionRyan Pineda

Measures of dispersion or variationRaj Teotia

Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari

quartile deviation: An introductionDr Rajesh Verma

Measures of dispersionyogesh ingle

Measures of variabilityjennytuazon01630

Standard deviation quartile deviationRekha Yadav

Mean DeviationCarlo Luna

QUARTILE DEVIATIONMARIA KATRINA MACAPAZ

Absolute Measures of dispersionAyushi Jain

Measures of dispersionSachin Shekde

Measures of variability to grading and reportingApril Gealene Alera

Measure of dispersionSana butt

Variabilityguest0a8c96

Standard deviation by nikitaNikita Dewangan

Properties of Standard DeviationRizwan Sharif

Measures of SpreadDanica Joy Aquino

Unit iii measures of dispersion (2)Sanoj Fernando

Measures of DispersionMohit Mahajan

Standard deviationAbdelrahman Alkilani

Measure of DispersionRyan Pineda

Measures of dispersion or variationRaj Teotia

Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari

quartile deviation: An introductionDr Rajesh Verma

Measures of dispersionyogesh ingle

Measures of variabilityjennytuazon01630

Standard deviation quartile deviationRekha Yadav

Mean DeviationCarlo Luna

QUARTILE DEVIATIONMARIA KATRINA MACAPAZ

Absolute Measures of dispersionAyushi Jain

Measures of dispersionSachin Shekde

Measures of variability to grading and reportingApril Gealene Alera

Measure of dispersionSana butt

Variabilityguest0a8c96

Standard deviation by nikitaNikita Dewangan

Properties of Standard DeviationRizwan Sharif

Measures of SpreadDanica Joy Aquino

Unit iii measures of dispersion (2)Sanoj Fernando

Measures of DispersionMohit Mahajan

Standard deviationAbdelrahman Alkilani

Similar to Business statistics ( Methods of variablity measurement)) (20)

Describing Distributions with Numbersnszakir

Measures of Variability By Dr. Vikramjit SinghVikramjit Singh

Basics of statistics by Arup Nama DasArup8

This document provides an overview of biostatistics, including definitions, concepts, and methods. It defines statistics as the science of collecting, organizing, summarizing, analyzing, and interpreting data. Various statistical concepts are explained, such as variables, distributions, frequency distributions, measures of center and variability. Graphical and numerical methods for presenting data are described, including histograms, box plots, mean, median, and standard deviation. Methods for summarizing categorical and numerical variable data are also outlined.

Measures of Position (For Ungrouped Data)Joey Fontanilla Valdriz

local_media4419196206087945469 (1).pptxJayArRodriguez2

This document discusses various statistical measures used to summarize and describe data distributions, including measures of central tendency (mean, median, mode), measures of dispersion (range, interquartile range, standard deviation), and measures of relative position (percentiles, quartiles, z-scores). It provides definitions, formulas, and examples for calculating each measure and interpreting the results.

3. Descriptive statistics.pdfYomifDeksisaHerpa

This document provides an overview of descriptive statistics and numerical summary measures. It discusses measures of central tendency including the mean, median, and mode. It also covers measures of relative standing such as percentiles and quartiles. Additionally, the document outlines measures of dispersion like variance, standard deviation, coefficient of variation, range, and interquartile range. Graphs and charts are presented as ways to describe data using these numerical summary measures.

presentationPwalmiki

This document provides an overview of basic statistics concepts. It defines statistics as the science of collecting, analyzing, and interpreting data. There are two main types of statistics: descriptive statistics which summarize data, and inferential statistics which make predictions from data. Key concepts discussed include variables, frequency distributions, measures of center such as mean and median, measures of variability such as range and standard deviation, and methods of presenting data graphically and numerically.

Student’s presentationPwalmiki

Measures of dispersion are statistical tools that show how spread out a set o...Abhishek Job

Statistical Method for engineers and scienceusaproductservices

Statisticsdineshmeena53

This document discusses measures of dispersion and the normal distribution. It defines measures of dispersion as ways to quantify the variability in a data set beyond measures of central tendency like mean, median, and mode. The key measures discussed are range, quartile deviation, mean deviation, and standard deviation. It provides formulas and examples for calculating each measure. The document then explains the normal distribution as a theoretical probability distribution important in statistics. It outlines the characteristics of the normal curve and provides examples of using the normal distribution and calculating z-scores.

variance ShahwarKhan16

Measures of Central Tendency, Variability and ShapesScholarsPoint1

DispersionVimarsh Padha

Measures of dispersion describe how similar or spread out scores in a data set are. The three main measures are range, semi-interquartile range (SIR), and variance/standard deviation. Range is the difference between the highest and lowest scores. SIR is less affected by outliers than range. Variance/standard deviation quantify the average squared distance of scores from the mean, with larger numbers indicating more spread out data. Skew and kurtosis further describe the shape of distributions.

Chapter 3 Ken Black 2.pptNurinaSWGotami

This document provides an overview of descriptive statistics concepts including measures of central tendency (mean, median, mode), measures of variability (range, standard deviation, variance), and how to compute them from both ungrouped and grouped data. It defines key terms like mean, median, mode, percentiles, quartiles, range, standard deviation, variance, and coefficient of variation. It also discusses how standard deviation can be used to measure financial risk and the empirical rule and Chebyshev's theorem for interpreting standard deviation.

Unit 1 - Measures of Dispersion - 18MAB303T - PPT - Part 2.pdfAravindS199

The document discusses various measures of dispersion, which describe how data values are spread around the mean. It describes absolute measures like range, interquartile range, mean deviation, and standard deviation. Range is the difference between highest and lowest values. Standard deviation calculates the average distance of all values from the mean. It is the most robust measure as it considers all data points. The document also provides examples of calculating different dispersion measures and their merits and limitations.

variancestandarddeviation-170416111818.pptxAsimaNoreen2

Descriptive statistics: Mean, Mode, Medianabidasultana86

Measures of Dispersion.pptxVanmala Buchke

The document discusses measures of dispersion, which describe how varied or spread out a data set is around the average value. It defines several measures of dispersion, including range, interquartile range, mean deviation, and standard deviation. The standard deviation is described as the most important measure, as it takes into account all values in the data set and is not overly influenced by outliers. The document provides a detailed example of calculating the standard deviation, which involves finding the differences from the mean, squaring those values, summing them, and taking the square root.

Describing Distributions with Numbersnszakir

Measures of Variability By Dr. Vikramjit SinghVikramjit Singh

Basics of statistics by Arup Nama DasArup8

Measures of Position (For Ungrouped Data)Joey Fontanilla Valdriz

local_media4419196206087945469 (1).pptxJayArRodriguez2

3. Descriptive statistics.pdfYomifDeksisaHerpa

presentationPwalmiki

Student’s presentationPwalmiki

Measures of dispersion are statistical tools that show how spread out a set o...Abhishek Job

Statistical Method for engineers and scienceusaproductservices

Statisticsdineshmeena53

variance ShahwarKhan16

Measures of Central Tendency, Variability and ShapesScholarsPoint1

DispersionVimarsh Padha

Chapter 3 Ken Black 2.pptNurinaSWGotami

Unit 1 - Measures of Dispersion - 18MAB303T - PPT - Part 2.pdfAravindS199

variancestandarddeviation-170416111818.pptxAsimaNoreen2

Descriptive statistics: Mean, Mode, Medianabidasultana86

Measures of Dispersion.pptxVanmala Buchke

More from AhmedToheed3 (6)

Computer Programming (C++)Pointers and ArraysAhmedToheed3

Pointers allow programs to dynamically allocate memory during runtime. There are two types of memory allocation: static and dynamic. Static allocation is done by the compiler at compile time, for variables declared within a function or globally. Dynamic allocation occurs at runtime using pointers, returning unnamed memory on the heap that is referenced indirectly. Pointers can either be constant pointers, where the pointer value cannot change but the referenced object can, or pointers to constant, where the pointer can change but the referenced object cannot.

Business statistics (Basic concepts of Index Numbers)AhmedToheed3

Index numbers are used to measure percentage changes in economic variables like prices, production, and exports over time. They show changes relative to a base time period or location. There are different types of index numbers including price, quantity, and value indexes. A price index measures changes in prices over time by taking the price of commodities in the current year and expressing them as a percentage of prices in the base year.

Business statistics (Shape of data)AhmedToheed3

Skewness and kurtosis are used to measure the shape of data. Skewness measures the asymmetry of data, whether the distribution has a longer tail on the right or left side. Kurtosis measures the peakedness of a distribution, with a normal distribution having a kurtosis of 0. Both skewness and kurtosis are calculated using formulas involving the sum of the cubed and squared deviations of the data from the mean.

Business statistics (Methods of Centre Measurement)AhmedToheed3

This document discusses different methods of measuring the central tendency of a dataset, including the mean, median, and mode. The mean is calculated by summing all observations and dividing by the total number of observations. The median is the middle value of an ordered dataset. The mode is the most frequently occurring value. For skewed distributions, the median is a better measure than the mean because it is less influenced by outliers.

Business statistics (Basics)AhmedToheed3

This document provides an overview of basic statistics concepts. It defines statistics as the science of collecting, presenting, analyzing, and reasonably interpreting data. Descriptive statistics are used to summarize and organize data through methods like tables, graphs, and descriptive values, while inferential statistics allow researchers to make general conclusions about populations based on sample data. Variables can be either categorical or quantitative, and their distributions and presentations are discussed.

Business statistics (Introduction)AhmedToheed3

This document introduces the concepts of data analysis. It defines key terms like individuals, variables, categorical vs. quantitative variables, and distribution. It explains that the goal of data analysis is to organize, display, summarize and ask questions about data in order to make inferences about populations based on samples. The next sections will cover analyzing categorical data with graphs and tables, as well as describing quantitative data with numerical summaries.

Computer Programming (C++)Pointers and ArraysAhmedToheed3

Business statistics (Basic concepts of Index Numbers)AhmedToheed3

Business statistics (Shape of data)AhmedToheed3

Business statistics (Methods of Centre Measurement)AhmedToheed3

Business statistics (Basics)AhmedToheed3

Business statistics (Introduction)AhmedToheed3

Recently uploaded (20)

vMix Pro Crack + Serial Number Torrent free Downloadeyeskye547

文凭证书美国SDSU文凭圣地亚哥州立大学学生证学历认证查询Taqyea

保密服务圣地亚哥州立大学英文毕业证书影本美国成绩单圣地亚哥州立大学文凭【q微1954292140】办理圣地亚哥州立大学学位证(SDSU毕业证书)毕业证书购买【q微1954292140】帮您解决在美国圣地亚哥州立大学未毕业难题（San Diego State University）文凭购买、毕业证购买、大学文凭购买、大学毕业证购买、买文凭、日韩文凭、英国大学文凭、美国大学文凭、澳洲大学文凭、加拿大大学文凭（q微1954292140）新加坡大学文凭、新西兰大学文凭、爱尔兰文凭、西班牙文凭、德国文凭、教育部认证，买毕业证，毕业证购买，买大学文凭，购买日韩毕业证、英国大学毕业证、美国大学毕业证、澳洲大学毕业证、加拿大大学毕业证（q微1954292140）新加坡大学毕业证、新西兰大学毕业证、爱尔兰毕业证、西班牙毕业证、德国毕业证，回国证明，留信网认证，留信认证办理，学历认证。从而完成就业。圣地亚哥州立大学毕业证办理，圣地亚哥州立大学文凭办理，圣地亚哥州立大学成绩单办理和真实留信认证、留服认证、圣地亚哥州立大学学历认证。学院文凭定制，圣地亚哥州立大学原版文凭补办，扫描件文凭定做，100%文凭复刻。特殊原因导致无法毕业，也可以联系我们帮您办理相关材料：１：在圣地亚哥州立大学挂科了，不想读了，成绩不理想怎么办？？？ 2：打算回国了，找工作的时候，需要提供认证《SDSU成绩单购买办理圣地亚哥州立大学毕业证书范本》【Q/WeChat：1954292140】Buy San Diego State University Diploma《正式成绩单论文没过》有文凭却得不到认证。又该怎么办？？？美国毕业证购买，美国文凭购买，【q微1954292140】美国文凭购买，美国文凭定制，美国文凭补办。专业在线定制美国大学文凭，定做美国本科文凭，【q微1954292140】复制美国San Diego State University completion letter。在线快速补办美国本科毕业证、硕士文凭证书，购买美国学位证、圣地亚哥州立大学Offer，美国大学文凭在线购买。美国文凭圣地亚哥州立大学成绩单，SDSU毕业证【q微1954292140】办理美国圣地亚哥州立大学毕业证(SDSU毕业证书)【q微1954292140】录取通知书offer在线制作圣地亚哥州立大学offer/学位证毕业证书样本、留信官方学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作。帮你解决圣地亚哥州立大学学历学位认证难题。主营项目： 1、真实教育部国外学历学位认证《美国毕业文凭证书快速办理圣地亚哥州立大学办留服认证》【q微1954292140】《论文没过圣地亚哥州立大学正式成绩单》，教育部存档，教育部留服网站100%可查. 2、办理SDSU毕业证，改成绩单《SDSU毕业证明办理圣地亚哥州立大学成绩单购买》【Q/WeChat：1954292140】Buy San Diego State University Certificates《正式成绩单论文没过》，圣地亚哥州立大学Offer、在读证明、学生卡、信封、证明信等全套材料，从防伪到印刷，从水印到钢印烫金，高精仿度跟学校原版100%相同. 3、真实使馆认证（即留学人员回国证明），使馆存档可通过大使馆查询确认. 4、留信网认证，国家专业人才认证中心颁发入库证书，留信网存档可查. 《圣地亚哥州立大学学位证书的英文美国毕业证书办理SDSU办理学历认证书》【q微1954292140】学位证1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。高仿真还原美国文凭证书和外壳，定制美国圣地亚哥州立大学成绩单和信封。毕业证网上可查学历信息SDSU毕业证【q微1954292140】办理美国圣地亚哥州立大学毕业证(SDSU毕业证书)【q微1954292140】学历认证生成授权声明圣地亚哥州立大学offer/学位证文凭购买、留信官方学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作。帮你解决圣地亚哥州立大学学历学位认证难题。圣地亚哥州立大学offer/学位证、留信官方学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作【q微1954292140】Buy San Diego State University Diploma购买美国毕业证，购买英国毕业证，购买澳洲毕业证，购买加拿大毕业证，以及德国毕业证，购买法国毕业证（q微1954292140）购买荷兰毕业证、购买瑞士毕业证、购买日本毕业证、购买韩国毕业证、购买新西兰毕业证、购买新加坡毕业证、购买西班牙毕业证、购买马来西亚毕业证等。包括了本科毕业证，硕士毕业证。

2024-Media-Literacy-Index-Of-Ukrainians-ENG-SHORT.pdfOlhaTatokhina1

How to regulate and control your it-outsourcing provider with process miningProcess mining Evangelist

Oliver Wildenstein is an IT process manager at MLP. As in many other IT departments, he works together with external companies who perform supporting IT processes for his organization. With process mining he found a way to monitor these outsourcing providers. Rather than having to believe the self-reports from the provider, process mining gives him a controlling mechanism for the outsourced process. Because such analyses are usually not foreseen in the initial outsourcing contract, companies often have to pay extra to get access to the data for their own process.

定制(意大利Rimini毕业证)布鲁诺马代尔纳嘉雷迪米音乐学院学历认证Taqyea

2025年新版意大利毕业证布鲁诺马代尔纳嘉雷迪米音乐学院文凭【q微1954292140】办理布鲁诺马代尔纳嘉雷迪米音乐学院毕业证(Rimini毕业证书)2025年新版毕业证书【q微1954292140】布鲁诺马代尔纳嘉雷迪米音乐学院offer/学位证、留信官方学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作【q微1954292140】Buy Conservatorio di Musica "B.Maderna G.Lettimi" Diploma购买美国毕业证，购买英国毕业证，购买澳洲毕业证，购买加拿大毕业证，以及德国毕业证，购买法国毕业证（q微1954292140）购买荷兰毕业证、购买瑞士毕业证、购买日本毕业证、购买韩国毕业证、购买新西兰毕业证、购买新加坡毕业证、购买西班牙毕业证、购买马来西亚毕业证等。包括了本科毕业证，硕士毕业证。主营项目： 1、真实教育部国外学历学位认证《意大利毕业文凭证书快速办理布鲁诺马代尔纳嘉雷迪米音乐学院毕业证定购》【q微1954292140】《论文没过布鲁诺马代尔纳嘉雷迪米音乐学院正式成绩单》，教育部存档，教育部留服网站100%可查. 2、办理Rimini毕业证，改成绩单《Rimini毕业证明办理布鲁诺马代尔纳嘉雷迪米音乐学院办理文凭》【Q/WeChat：1954292140】Buy Conservatorio di Musica "B.Maderna G.Lettimi" Certificates《正式成绩单论文没过》，布鲁诺马代尔纳嘉雷迪米音乐学院Offer、在读证明、学生卡、信封、证明信等全套材料，从防伪到印刷，从水印到钢印烫金，高精仿度跟学校原版100%相同. 3、真实使馆认证（即留学人员回国证明），使馆存档可通过大使馆查询确认. 4、留信网认证，国家专业人才认证中心颁发入库证书，留信网存档可查. 《布鲁诺马代尔纳嘉雷迪米音乐学院留服认证意大利毕业证书办理Rimini文凭不见了怎么办》【q微1954292140】学位证1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。高仿真还原意大利文凭证书和外壳，定制意大利布鲁诺马代尔纳嘉雷迪米音乐学院成绩单和信封。毕业证定制Rimini毕业证【q微1954292140】办理意大利布鲁诺马代尔纳嘉雷迪米音乐学院毕业证(Rimini毕业证书)【q微1954292140】学位证书制作代办流程布鲁诺马代尔纳嘉雷迪米音乐学院offer/学位证成绩单激光标、留信官方学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作。帮你解决布鲁诺马代尔纳嘉雷迪米音乐学院学历学位认证难题。意大利文凭布鲁诺马代尔纳嘉雷迪米音乐学院成绩单，Rimini毕业证【q微1954292140】办理意大利布鲁诺马代尔纳嘉雷迪米音乐学院毕业证(Rimini毕业证书)【q微1954292140】安全可靠的布鲁诺马代尔纳嘉雷迪米音乐学院offer/学位证办理原版成绩单、留信官方学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作。帮你解决布鲁诺马代尔纳嘉雷迪米音乐学院学历学位认证难题。意大利文凭购买，意大利文凭定制，意大利文凭补办。专业在线定制意大利大学文凭，定做意大利本科文凭，【q微1954292140】复制意大利Conservatorio di Musica "B.Maderna G.Lettimi" completion letter。在线快速补办意大利本科毕业证、硕士文凭证书，购买意大利学位证、布鲁诺马代尔纳嘉雷迪米音乐学院Offer，意大利大学文凭在线购买。如果您在英、加、美、澳、欧洲等留学过程中或回国后： 1、在校期间因各种原因未能顺利毕业《Rimini成绩单工艺详解》【Q/WeChat：1954292140】《Buy Conservatorio di Musica "B.Maderna G.Lettimi" Transcript快速办理布鲁诺马代尔纳嘉雷迪米音乐学院教育部学历认证书毕业文凭证书》，拿不到官方毕业证； 2、面对父母的压力，希望尽快拿到； 3、不清楚认证流程以及材料该如何准备； 4、回国时间很长，忘记办理； 5、回国马上就要找工作《正式成绩单布鲁诺马代尔纳嘉雷迪米音乐学院文凭详解细节》【q微1954292140】《研究生文凭Rimini毕业证详解细节》办给用人单位看；　　 6、企事业单位必须要求办理的； 7、需要报考公务员、购买免税车、落转户口、申请留学生创业基金。【q微1954292140】帮您解决在意大利布鲁诺马代尔纳嘉雷迪米音乐学院未毕业难题（Conservatorio di Musica "B.Maderna G.Lettimi" ）文凭购买、毕业证购买、大学文凭购买、大学毕业证购买、买文凭、日韩文凭、英国大学文凭、美国大学文凭、澳洲大学文凭、加拿大大学文凭（q微1954292140）新加坡大学文凭、新西兰大学文凭、爱尔兰文凭、西班牙文凭、德国文凭、教育部认证，买毕业证，毕业证购买，买大学文凭，购买日韩毕业证、英国大学毕业证、美国大学毕业证、澳洲大学毕业证、加拿大大学毕业证（q微1954292140）新加坡大学毕业证、新西兰大学毕业证、爱尔兰毕业证、西班牙毕业证、德国毕业证，回国证明，留信网认证，留信认证办理，学历认证。从而完成就业。布鲁诺马代尔纳嘉雷迪米音乐学院毕业证办理，布鲁诺马代尔纳嘉雷迪米音乐学院文凭办理，布鲁诺马代尔纳嘉雷迪米音乐学院成绩单办理和真实留信认证、留服认证、布鲁诺马代尔纳嘉雷迪米音乐学院学历认证。学院文凭定制，布鲁诺马代尔纳嘉雷迪米音乐学院原版文凭补办，扫描件文凭定做，100%文凭复刻。特殊原因导致无法毕业，也可以联系我们帮您办理相关材料：１：在布鲁诺马代尔纳嘉雷迪米音乐学院挂科了，不想读了，成绩不理想怎么办？？？ 2：打算回国了，找工作的时候，需要提供认证《Rimini成绩单购买办理布鲁诺马代尔纳嘉雷迪米音乐学院毕业证书范本》【Q/WeChat：1954292140】Buy Conservatorio di Musica "B.Maderna G.Lettimi" Diploma《正式成绩单论文没过》有文凭却得不到认证。又该怎么办？？？意大利毕业证购买，意大利文凭购买， 3：回国了找工作没有布鲁诺马代尔纳嘉雷迪米音乐学院文凭怎么办？有本科却要求硕士又怎么办？

indonesia-gen-z-report-2024 Gen Z (born between 1997 and 2012) is currently t...disnakertransjabarda

录取通知书加拿大TMU毕业证多伦多都会大学电子版毕业证成绩单Taqyea

保密服务多伦多都会大学英文毕业证书影本加拿大成绩单多伦多都会大学文凭【q微1954292140】办理多伦多都会大学学位证(TMU毕业证书)成绩单VOID底纹防伪【q微1954292140】帮您解决在加拿大多伦多都会大学未毕业难题（Toronto Metropolitan University）文凭购买、毕业证购买、大学文凭购买、大学毕业证购买、买文凭、日韩文凭、英国大学文凭、美国大学文凭、澳洲大学文凭、加拿大大学文凭（q微1954292140）新加坡大学文凭、新西兰大学文凭、爱尔兰文凭、西班牙文凭、德国文凭、教育部认证，买毕业证，毕业证购买，买大学文凭，购买日韩毕业证、英国大学毕业证、美国大学毕业证、澳洲大学毕业证、加拿大大学毕业证（q微1954292140）新加坡大学毕业证、新西兰大学毕业证、爱尔兰毕业证、西班牙毕业证、德国毕业证，回国证明，留信网认证，留信认证办理，学历认证。从而完成就业。多伦多都会大学毕业证办理，多伦多都会大学文凭办理，多伦多都会大学成绩单办理和真实留信认证、留服认证、多伦多都会大学学历认证。学院文凭定制，多伦多都会大学原版文凭补办，扫描件文凭定做，100%文凭复刻。特殊原因导致无法毕业，也可以联系我们帮您办理相关材料：１：在多伦多都会大学挂科了，不想读了，成绩不理想怎么办？？？ 2：打算回国了，找工作的时候，需要提供认证《TMU成绩单购买办理多伦多都会大学毕业证书范本》【Q/WeChat：1954292140】Buy Toronto Metropolitan University Diploma《正式成绩单论文没过》有文凭却得不到认证。又该怎么办？？？加拿大毕业证购买，加拿大文凭购买，【q微1954292140】加拿大文凭购买，加拿大文凭定制，加拿大文凭补办。专业在线定制加拿大大学文凭，定做加拿大本科文凭，【q微1954292140】复制加拿大Toronto Metropolitan University completion letter。在线快速补办加拿大本科毕业证、硕士文凭证书，购买加拿大学位证、多伦多都会大学Offer，加拿大大学文凭在线购买。加拿大文凭多伦多都会大学成绩单，TMU毕业证【q微1954292140】办理加拿大多伦多都会大学毕业证(TMU毕业证书)【q微1954292140】学位证书电子图在线定制服务多伦多都会大学offer/学位证offer办理、留信官方学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作。帮你解决多伦多都会大学学历学位认证难题。主营项目： 1、真实教育部国外学历学位认证《加拿大毕业文凭证书快速办理多伦多都会大学毕业证书不见了怎么办》【q微1954292140】《论文没过多伦多都会大学正式成绩单》，教育部存档，教育部留服网站100%可查. 2、办理TMU毕业证，改成绩单《TMU毕业证明办理多伦多都会大学学历认证定制》【Q/WeChat：1954292140】Buy Toronto Metropolitan University Certificates《正式成绩单论文没过》，多伦多都会大学Offer、在读证明、学生卡、信封、证明信等全套材料，从防伪到印刷，从水印到钢印烫金，高精仿度跟学校原版100%相同. 3、真实使馆认证（即留学人员回国证明），使馆存档可通过大使馆查询确认. 4、留信网认证，国家专业人才认证中心颁发入库证书，留信网存档可查. 《多伦多都会大学学位证购买加拿大毕业证书办理TMU假学历认证》【q微1954292140】学位证1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。高仿真还原加拿大文凭证书和外壳，定制加拿大多伦多都会大学成绩单和信封。学历认证证书电子版TMU毕业证【q微1954292140】办理加拿大多伦多都会大学毕业证(TMU毕业证书)【q微1954292140】毕业证书样本多伦多都会大学offer/学位证学历本科证书、留信官方学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作。帮你解决多伦多都会大学学历学位认证难题。多伦多都会大学offer/学位证、留信官方学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作【q微1954292140】Buy Toronto Metropolitan University Diploma购买美国毕业证，购买英国毕业证，购买澳洲毕业证，购买加拿大毕业证，以及德国毕业证，购买法国毕业证（q微1954292140）购买荷兰毕业证、购买瑞士毕业证、购买日本毕业证、购买韩国毕业证、购买新西兰毕业证、购买新加坡毕业证、购买西班牙毕业证、购买马来西亚毕业证等。包括了本科毕业证，硕士毕业证。

Just-In-Timeasdfffffffghhhhhhhhhhj Systems.pptssuser5f8f49

Automation Platforms and Process Mining - success storyProcess mining Evangelist

Zig Websoftware creates process management software for housing associations. Their workflow solution is used by the housing associations to, for instance, manage the process of finding and on-boarding a new tenant once the old tenant has moved out of an apartment. Paul Kooij shows how they could help their customer WoonFriesland to improve the housing allocation process by analyzing the data from Zig's platform. Every day that a rental property is vacant costs the housing association money. But why does it take so long to find new tenants? For WoonFriesland this was a black box. Paul explains how he used process mining to uncover hidden opportunities to reduce the vacancy time by 4,000 days within just the first six months.

hersh's midterm project.pdf music retail and distributionhershtara1

Oral Malodor.pptx jsjshdhushehsidjjeiejdhfjmaitripatel5301

717239550-Hotel-Management-Ppt-Final.pptxdharmendrasingh31102

iydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyfgyyyyyyyyyyyyyyyyyyyyyyyiydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyfgyyyyyyyyyyyyyyyyyyyyyyyiydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyfgyyyyyyyyyyyyyyyyyyyyyyyiydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyfgyyyyyyyyyyyyyyyyyyyyyyyiydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyfgyyyyyyyyyyyyyyyyyyyyyyyiydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyfgyyyyyyyyyyyyyyyyyyyyyyyiydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyfgyyyyyyyyyyyyyyyyyyyyyyyiydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyfgyyyyyyyyyyyyyyyyyyyyyyyiydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyfgyyyyyyyyyyyyyyyyyyyyyyyiydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyfgyyyyyyyyyyyyyyyyyyyyyyyiydqgdutauybdibafyvseufvsVhsjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjvCSUYEVkSJekiyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

Lagos School of Programming Final Project Updated.pdfbenuju2016

chapter 4 Variability statistical research .pptxjustinebandajbn

50_questions_full.pptxddddddddddddddddddemir73065

Decision Trees in Artificial-Intelligence.pdfSaikat Basu

FPET_Implementation_2_MA to 360 Engage Direct.pptxssuser4ef83d

Process Mining at AE - Key success factorsProcess mining Evangelist

Bram Vanschoenwinkel is a Business Architect at AE. Bram first heard about process mining in 2008 or 2009, when he was searching for new techniques with a quantitative approach to process analysis. By now he has completed several projects in payroll accounting, public administration, and postal services. The discovered AS IS process models are based on facts rather than opinions and, therefore, serve as the ideal starting point for change. Bram uses process mining not as a standalone technique but complementary and in combination with other techniques to focus on what is really important: Actually improving the process.

spssworksho9035530-lva1-app6891 (1).pptxclarkraal

Collibra DQ Installation setup and debugkarthikprince20

vMix Pro Crack + Serial Number Torrent free Downloadeyeskye547

文凭证书美国SDSU文凭圣地亚哥州立大学学生证学历认证查询Taqyea

2024-Media-Literacy-Index-Of-Ukrainians-ENG-SHORT.pdfOlhaTatokhina1

How to regulate and control your it-outsourcing provider with process miningProcess mining Evangelist

定制(意大利Rimini毕业证)布鲁诺马代尔纳嘉雷迪米音乐学院学历认证Taqyea

indonesia-gen-z-report-2024 Gen Z (born between 1997 and 2012) is currently t...disnakertransjabarda

录取通知书加拿大TMU毕业证多伦多都会大学电子版毕业证成绩单Taqyea

Just-In-Timeasdfffffffghhhhhhhhhhj Systems.pptssuser5f8f49

Automation Platforms and Process Mining - success storyProcess mining Evangelist

hersh's midterm project.pdf music retail and distributionhershtara1

Oral Malodor.pptx jsjshdhushehsidjjeiejdhfjmaitripatel5301

717239550-Hotel-Management-Ppt-Final.pptxdharmendrasingh31102

Lagos School of Programming Final Project Updated.pdfbenuju2016

chapter 4 Variability statistical research .pptxjustinebandajbn

50_questions_full.pptxddddddddddddddddddemir73065

Decision Trees in Artificial-Intelligence.pdfSaikat Basu

FPET_Implementation_2_MA to 360 Engage Direct.pptxssuser4ef83d

Process Mining at AE - Key success factorsProcess mining Evangelist

spssworksho9035530-lva1-app6891 (1).pptxclarkraal

Collibra DQ Installation setup and debugkarthikprince20

Business statistics ( Methods of variablity measurement))

2. Methods of Variability Measurement Commonly used methods: Range, Variance, Standard deviation, Interquartile Range, Coefficient of Variation etc. Range: The difference between the largest and the smallest observations. The range of 10, 5, 2, 100 is (100-2)=98. It’s a crude measure of variability. Variability (or Dispersion) measures the amount of scatter in a dataset. 2

3. Methods of Variability Measurement Variance: The variance of a set of observations is the average of the squares of the deviations of the observations from their mean. In symbols, the variance of the n observations x1, x2,…xn is Variance of 5, 7, 3? Mean is (5+7+3)/3 = 5 and the variance is 4 4 13 )57()53()55( 222    1 )(....)( 22 12    n xxxx S n Standard Deviation: Square root of the variance. The standard deviation of the above example is 2. > 3

4. Methods of Variability Measurement Quartiles: Data can be divided into four regions that cover the total range of observed values. Cut points for these regions are known as quartiles. The first quartile (Q1) is the first 25% of the data. The second quartile (Q2) is between the 25th and 50th percentage points in the data. The upper bound of Q2 is the median. The third quartile (Q3) is the 25% of the data lying between the median and the 75% cut point in the data. Q1 is the median of the first half of the ordered observations and Q3 is the median of the second half of the ordered observations. In notations, quartiles of a data is the ((n+1)/4)qth observation of the data, where q is the desired quartile and n is the number of observations of data. 4

5. Methods of Variability Measurement An example with 15 numbers 3 6 7 11 13 22 30 40 44 50 52 61 68 80 94 Q1 Q2 Q3 The first quartile is Q1=11. The second quartile is Q2=40= (2(15+1)/4)=8th Observation (This is also called the Median.) The third quartile is Q3=61= (3(15+1)/4)=12th Observation is 61 Inter-quartile Range: Difference between Q3 and Q1. Inter- quartile range of the previous example is 61- 40=21. The middle half of the ordered data lie between 40 and 61. In the following example Q1= ((15+1)/4)1 =4th observation of the data. The 4th observation is 11. So Q1 of this data set is 11. 5

6. Deciles and Percentiles Percentiles: If data is ordered and divided into 100 parts, then cut points are called Percentiles. 25th percentile is the Q1, 50th percentile is the Median (Q2) and the 75th percentile of the data is Q3. Deciles: If data is ordered and divided into 10 parts, then cut points are called Deciles In notations, percentiles of a data is the ((n+1)/100)p th observation of the data, where p is the desired percentile and n is the number of observations of data. Coefficient of Variation: The standard deviation of data divided by it’s mean. It is usually expressed in percent. 100 x  Coefficient of Variation = 6

7. Five Number Summary Five Number Summary: The five number summary of a distribution consists of the smallest (Minimum) observation, the first quartile (Q1), The median(Q2), the third quartile, and the largest (Maximum) observation written in order from smallest to largest. Box Plot: A box plot is a graph of the five number summary. The central box spans the quartiles. A line within the box marks the median. Lines extending above and below the box mark the smallest and the largest observations (i.e., the range). Outlying samples may be additionally plotted outside the range. 7

8. Boxplot 0 20 40 60 80 100 120 140 160 1 q1 min median max q3 Distribution of Age in Month 8

Business statistics ( Methods of variablity measurement))

Recommended

More Related Content

What's hot (20)

Similar to Business statistics ( Methods of variablity measurement)) (20)

More from AhmedToheed3 (6)

Recently uploaded (20)

Business statistics ( Methods of variablity measurement))