STATISTICS.pptx

Introduction to Statistics
What is Statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.
Basic Concepts:
• Population: The entire group of individuals or objects that we are interested in studying.
• Sample: A subset of the population that is selected for analysis and study.
• Variable: A characteristic or attribute that can be measured or observed and can vary from one individual or object to another.
• Data: The values or observations that are collected for a variable.
Principles of Statistics
• Collecting Data: Gathering information through surveys, experiments, or observations.
• Organizing Data: Arranging the collected data in a meaningful and structured manner.
• Analyzing Data: Applying statistical techniques and methods to draw conclusions and make inferences from
• the data.
• Interpreting Data: Drawing meaningful insights and conclusions from the analyzed data.
• Presenting Data: Communicating the results and findings of the analysis in a clear and concise manner.
Sir Ronald
Aylmer

Collection Of Data
Observations
Observations involve directly watching and recording
data without interacting with the subjects. This
method is useful for collecting objective data.
Surveys
Surveys are a common method for
collecting data. They involve asking
questions to a sample of individuals or
groups to gather information.

Organization of Data
In statistics, data can be organized and represented in various ways depending on the nature of
the data and the purpose of analysis. Different methods of organization and representation
provide different insights and facilitate different types of analysis. Here are some common
ways to organize and represent data:
• Tabular Form: Data can be organized in a tabular form using rows and columns. This allows
for easy comparison and analysis of different variables. Tables can be used to present raw
data or summary statistics.
• Frequency Distribution: Data can be organized into frequency distributions, which group
data into intervals and show the frequency of data points in each interval or category.
Frequency distributions are useful for summarizing and analyzing large datasets.
• Pictorial Representation: Data can be represented using pictorial methods such as
pictographs, bar graphs, and pie charts. Pictorial representation makes it easier to
understand and interpret data, especially for visual learners.
• Statistical Measures: Data can be summarized using statistical measures such as measures
of central tendency (mean, median, mode) and measures of dispersion (range, variance,
standard deviation). These measures provide a concise summary of the data and help in
making inferences and conclusions.
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Presentation of Data
Methods and Techniques for Presenting Data
Visually
•Bar Graphs: Represent data using rectangular bars of different
lengths.
•Column Graphs: Similar to bar graphs, but the bars are
vertical.
•Pie Charts: Show the proportion of different categories in a
whole.
•Line Graphs: Display the relationship between two variables
over a continuous interval.
•Histograms: Present data in intervals or bins.
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Category 1 Category 2 Category 3 Category 4
Series 1 Series 2 Series 3

Measures of Central Tendency
Measures of central tendency are statistical measures used to identify the center or average value of a data set. They provide a single value that
represents the typical or central value of the data. There are three commonly used measures of central tendency: mean, median, and mode.
Measures of Central Tendency
Measure Calculation Description
Mean Sum of all values divided by the number of
values.
The arithmetic average of a set of
values.
Median If the number of values is odd, the middle
value. If the number of values is even, the
average of the two middle values.
The middle value in a sorted list of
values.
Mode The value(s) with the highest frequency. The value(s) that appear most
frequently in a data set.

Mean, Median and Mode
Mean, median, and mode are measures of central tendency used in statistics to describe a set of data. Each of these measures provides
different insights into the data and can be useful in different scenarios.
Mean
The mean is the average of a set of numbers. It is calculated by summing up all the values in the dataset and dividing it by the total number of
values. The mean is sensitive to extreme values, also known as outliers, and can be influenced by them.
Significance: The mean provides a measure of the central tendency of the data and is commonly used in various statistical analyses. It is
particularly useful when the dataset follows a normal distribution.
Limitation: The mean can be heavily influenced by outliers, skewing the value and not accurately representing the majority of the data.
Median
The median is the middle value in a dataset when it is arranged in ascending or descending order. If there is an even number of values, the
median is calculated as the average of the two middle values. The median is not affected by extreme values and provides a measure of the
central tendency that is more robust to outliers compared to the mean.
Significance: The median is useful when dealing with skewed distributions or datasets with outliers. It represents the middle value and gives a
better understanding of the central tendency of the data.
Limitation: The median does not take into account the actual values of the dataset, only their position. It may not provide a complete picture of
the data distribution.

Mode
The mode is the value that appears most frequently in a dataset. It can be used for both numerical and categorical data. In some cases, there may
be multiple modes or no mode at all.
Significance: The mode helps identify the most common value or category in the dataset. It is useful for understanding the distribution of
categorical data and can provide insights into the central tendency of numerical data.
Limitation: The mode does not consider the actual values of the dataset, only their frequency. It may not provide a comprehensive understanding
of the data distribution.
Some Examples of Mean, Median and Mode In Our Daily Life
• If we would like to know how many hours on average an employee spends at training in a year, we can find the mean training hours of a group
of employees.
• Insurance analysts often calculate the mean age of the individuals they provide insurance for so they can know the average age of their
customers. These were few examples how Mean is useful to us in our day-to-day activities.
• Similarly for the use of Median, Actuaries often calculate the median amount spend on healthcare each year by individuals so they can know
how much insurance they need to be able to provide to individuals.
• Actuaries also calculate the mode of their customers (the most commonly occurring age) so they can know which age group uses their
insurance the most.

Histograms and Ogives in Statistical Analysis
k
k
Histogram
A histogram is a graphical representation of the
distribution of a dataset. It is used to visualize the
frequency or probability of different values in a dataset.
The mode, which represents the most common value in
the dataset, can be depicted in a histogram.
Ogive
An ogive, also known as a cumulative frequency curve, is a
graph that represents the cumulative frequencies of
different values in a dataset. It is used to analyze the
distribution and cumulative behavior of a dataset. The
median, which represents the middle value in a dataset,
can be depicted in an ogive.

Mean Deviation
Mean deviation is a measure of the dispersion or spread of a set of data points around the mean. It provides insight
into how much the individual data points deviate from the average value.
Significance and Importance
Mean deviation is an important statistical measure as it
helps in understanding the variability within a data set. It
provides a more comprehensive view of the spread of
data points compared to other measures like range or
standard deviation.
Examples
Example 1: Stock Prices
Mean deviation can be used to analyze the volatility
of stock prices. By calculating the mean deviation of
daily price changes, investors can assess the stability
and risk associated with a particular stock.
Example 2: Customer Satisfaction
Mean deviation can also be applied to measure customer
satisfaction. By calculating the mean deviation of survey
responses, businesses can identify areas where customer
opinions vary significantly, allowing them to focus on
improving those aspects.
For Individual Data = ∑|xi−M|
n
For Discrete Data = ∑ f∣X−M∣
∑f
∑ = Summation
X = Observation / Values
M = Mean
f = frequency of observations

Correlation
Concept of Correlation
Correlation is a statistical measure that indicates the strength and
direction of the relationship between two or more variables. It is
used to determine how changes in one variable are related to
changes in another variable.
Use of Correlation
Correlation is widely used in analyzing relationships between
variables in various fields such as economics, psychology,
sociology, and finance. It helps in understanding the degree and
nature of the relationship between variables and can be used for
prediction and decision-making.

Sampling and Estimation
Sampling
Sampling is the process of selecting a subset of individuals
or items from a larger population to gather information or
make inferences about the population as a whole. It is
often impractical or impossible to collect data from every
member of a population, so sampling allows us to study a
smaller group that represents the larger population.
Estimation
Estimation is the process of using sample data to
make inferences or draw conclusions about a
population parameter. By analyzing the data from a
sample, we can estimate the value of a population
parameter, such as the mean or proportion.
POPULATION
SAMPLE

Statistical Inference
Concept of Statistical Inference
Statistical inference is the process of drawing conclusions about a population based on a sample of data. It involves making
inferences, predictions, or decisions about a population parameter based on sample statistics.
Hypothesis Testing
Hypothesis testing is a statistical method used to make
inferences about a population based on a sample of
data. It involves formulating a hypothesis, collecting
and analyzing data, and making a decision about the
hypothesis based on the evidence provided by the
data.

Conclusion For Statistics
In short, the widespread application of statistics in areas like
business, healthcare, and research underscores its
significance in shaping outcomes. By providing a
quantitative foundation, statistics enables professionals to
make data-driven decisions, fostering efficiency and
innovation. However, practitioners should remain vigilant
about the ethical implications of data use and
interpretation, ensuring responsible and unbiased
application in a rapidly evolving technological landscape.

STATISTICS.pptx

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