Statistics and types of statistics .docx
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This document discusses different types of statistics. It defines descriptive statistics as summarizing and describing data, while inferential statistics use samples to make inferences about populations. Measures of central tendency like mean, median and mode are described as well as measures of variability such as range, standard deviation and variance. Specific types of each are defined and explained, such as weighted mean, interquartile range, and harmonic mean. Tables and figures are included to illustrate the differences between descriptive and inferential statistics and examples of various statistical measures.
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- 1. 1 | P a g e L F U First Stage - Group ( A )Faculty of Business and Economics Department of Business Administration First Stage - Group ( A ) ReportFirst Stage - Group ( A )Faculty of Business and Economics Department of Business Administration First Stage - Group ( A )Faculty of Statistics and types of statistics Supervised by: Dlshad Mahmood SalehStatistics and types of statistics Supervised by: Dlshad Mahmood Saleh Prepared by: Hawre Idrees KareemSupervised by: Dlshad Mahmood SalehStatistics and types of Supervised by: Prepared by: Hawre Idrees KareemSupervised by: Dlshad Mahmood Saleh Prepared by: Hawre Idrees Kareem Prepared by: Prepared by: Hawre Idrees Kareem Prepared by: Hawre Idrees Kareem (2022–2023) Figure 1 types of statis tics( 202 2– ReportFirst Stage - Group ( A ) Report ReportFirst Stage - Group ( A ) Faculty of Business and EconomicsLebanese French University Faculty of Business and Economics Department of Business Administration First Stage - Group ( A )Faculty of Business and EconomicsLebanese French University Faculty of Business and EconomicsLebanese Report Report Report
- 2. 2 | P a g e Contents Introduction ............................................................................................................................................3 types of statistics ................................................................................................................................3 what are Descriptive Statistics and Inferential Statistics....................................................................4 difference between Descriptive statistics and Inferential statistics...............................................4 Types of Descriptive Statistics.............................................................................................................6 Types of Measure of Central Tendency ..............................................................................................7 Types of mean.....................................................................................................................................8 Types of Measure of Variability........................................................................................................10 Measure of Variability.......................................................................................................................10 Figure 1 types of statistics....................................................................................................................3 Figure 2 Inferential Vs Descriptive Statistics........................................................................................6 Figure 3 data-variability........................................................................................................................9 Table 1 Inferential Vs Descriptive Statistics - The Difference..............................................................5 Table 2 Types of Measure of Central Tendency..................................................................................7 Table 3 Types of mean ........................................................................................................................8 Table 4 Types of Measure of Variability............................................................................................10
- 3. 3 | P a g e Figure 1 types of statistics Introduction Statistics is a branch of mathematics that deals with collecting, organizing, analyzing, presenting, and interpreting data. Statistics can help us understand patterns, trends, and relationships in the world, and make informed decisions based on data. Statistics can be divided into two main types: descriptive and inferential. types of statistics
- 4. 4 | P a g e what are Descriptive Statistics and Inferential Statistics Descriptive Statistics: and Inferential Statistics are two broad categories in the field of statistics that have different purposes and methods. Descriptive statistics summarize and display the characteristics of a data set, such as the mean, median, mode, frequency, and distribution of the values. Descriptive statistics can precisely describe the data that is collected from a sample or a population. Inferential statistics, on the other hand, use the data from a sample to make estimates and test hypotheses about a larger population. Inferential statistics: on the other hand, use the data from a sample to make estimates and test hypotheses about a larger population. Inferential statistics allow researchers to draw conclusions and make predictions based on their data. However, inferential statistics also involve uncertainty and sampling error, so they cannot guarantee the accuracy or generalizability of the results. difference between Descriptive statistics and Inferential statistics Descriptive statistics and inferential statistics are two branches of statistics that have different purposes and methods. Descriptive statistics summarize and display the data in a meaningful way, such as using tables, charts, graphs, or measures of central tendency and variability. Descriptive statistics do not make any assumptions or draw any conclusions about the population from which the data are obtained. They only describe what is seen in the sample. Inferential statistics use the data from a sample to make inferences or predictions about the population that the sample stands for. Inferential statistics rely on probability theory and hypothesis testing to decide how likely it is that the results obtained from the sample are generalizable to the population. Inferential statistics can also estimate the parameters of the population, such as the mean, proportion, or correlation coefficient, based on the sample statistics.
- 5. 5 | P a g e Table 1 Inferential Vs Descriptive Statistics - The Difference Inferential Vs Descriptive Statistics - The Difference DESCRIPTIVE STATISTICS INFERENTIAL STATISTICS The utilization of descriptive statis- tics researchers has total crude populace data. The vast majority of the researchers take the help of inferential statistics when the crude populace data is in huge amounts and can't be Assam- bled or gathered. The utilization of descriptive statis- tics is when inspecting isn't re- quired. Here testing measure is required as the analysis depends on test boundaries. Properties of the crude populace are Mean, median and mode are known as descriptivestatistics pa- riometers. Properties of the examining data in the inferential statistics are not named as boundaries fairly pro- nouned as statistics. This kind of statistics has certain constraints. One can possibly apply this while having really estimated data. It tends to be applied to a huge populace of data when the example data is a delegate of the populace. The descriptive type of statistics is quite often 100% precise as there are no suspicions being made for the crude populace data Whereas, inferential statistics depend on the theories or conclusions dependent on samples. That is the reason one can't locate a 100% precision in inferential statis- tics.
- 6. 6 | P a g e Figure 2 Inferential Vs Descriptive Statistics Types of Descriptive Statistics 1. Measure of Central Tendency: A measure of central tendency is a single value that describes the way in which a group of data cluster around a central value. In other words, it is a way to summarize the average or typical value of a dataset. there are three main measures of central tendency, mean, the median, and the mode. the mean is the sum of all the data values divided by the number of values in the dataset, It is also known as the arithmetic average, mean is sensitive to outliers, which are extreme values that are much higher or lower than the rest of the data, median is the middle value of a dataset that has been arranged in ascending or descending order, It divides the dataset into two equal halves. Outliers do not affect the median, so it is a more robust measure of central tendency than the mean, the mode is the most often occurring value in a dataset, There can be more than one mode if two or more values have the same frequency, or no mode if all values have different frequencies, mode can be used for any type of data, including nominal data that have no numerical value.
- 7. 7 | P a g e Table 2 Types of Measure of Central Tendency Types of Measure of Central Tendency Mean: The mean is the average of a set of numbers. It is calculated by adding up all the numbers and dividing by the number of values. The mean is a useful measure of central tendency when the data is symmetric and has no outliers. Median: The median is the middle value of a set of numbers when they are arranged in ascending or descending order. If there is an odd number of values, the median is the middle one. If there is an even number of values, the median is the average of the middle two. The median is a useful measure of central tendency when the data is skewed or has outliers. Mode: The mode is the most frequent value in a set of numbers. There can be more than one mode if two or more values have the same frequency. The mode is a useful measure of central tendency when the data is categorical or discrete. Central Tendency Mode Mean Median
- 8. 8 | P a g e Table 3Types of mean Types of mean Geometric: The geometric mean of n positive numbers is the n-the root of their product. It is often used to calculate average rates of change or growth, such as population growth or compound interest. Harmonic: The harmonic mean of n positive numbers is the reciprocal of the arithmetic mean of their reciprocals. It is often used to calculate average rates when dealing with ratios or fractions, such as speed, density, or harmonic frequency. Weighted: The weighted mean of n numbers is the sum of their products with their corresponding weights divided by the sum of the weights. It is often used to calculate average values when some data values have more importance or influence than others, such as grades, test scores, or survey responses. Mean Weighted Geometric Harmonic
- 9. 9 | P a g e Figure 3 data-variability 2. Measure of Variability: A measure of variability is a single value that describes the spread or dispersion of a dataset. In other words, it is a way to summarize how much the data values differ from each other, there are several measures of variability, such as the range, the interquartile range, the standard deviation, and the variance, range is the difference between the maximum and minimum values in a dataset, It gives an estimate of how large the spread of the data is, but it does not consider how the data are distributed, interquartile range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3) of a dataset, first quartile is the median of the lower half of the data, and the third quartile is the median of the upper half of the data, IQR shows how much variation there is in the middle 50% of the data, and it is not affected by outliers, standard deviation (SD) is a measure of how much each data value deviates from the mean, It is calculated by taking the square root of the variance, standard deviation tells us how closely clustered or widely dispersed the data values are around the mean, variance (V) is a measure of how much each data value deviates from the mean squared. It is calculated by taking the average of the squared differences between each data value and the mean, variance gives an idea of how much variation there is in the entire dataset, but it is not easy to interpret because it has different units than the original data.
- 10. 10 | P a g e Table 4 Types of Measure of Variability Types of Measure of Variability Range: is the difference between the highest and lowest values in the data set. It is the simplest measure of variability to calculate, but it is influenced by outliers and does not give any information about the distribution of values. Variance: is the average of squared distances from the mean. It measures how far each value is from the mean on average. Squaring the distances ensures that positive and negative deviations do not cancel out. However, variance is not in the same unit as the original data and can be difficult to interpret. Dispersion: are the three commonly used measures of dispersion. 1. Interquartile range (IQR): the difference between the third quartile (Q3) and the first quartile (Q1) of the data set. It is the range of the middle 50% of the data, and it is less affected by outliers than the range. It is a good measure of variability dispersion for skewed distributions. 2. Variance: the average of the squared distances of each value from the mean of the data set. It is a measure of how much the values deviate from the center of the distribution. It is always positive, and it has a different unit than the original data. 3. Standard deviation: the square root of the variance. It is a measure of how much the values deviate from the center of the distribution. It has the same unit as the original data, and it is easier to interpret than the variance. These measures of variability dispersion can help us compare different data sets or different aspects of the same data set. For example, we can use them to assess how reliable a sample mean is as an estimate of a population mean, or how homogeneous or heterogeneous a population is. Measure of Variability Dispersion Range Variance