BA 3rd , Sem. V, Course II (Theory) Program/Class: Degree /BA Year: Third Semester: Fifth Subject: Education Course Code: E010502T Course Title: Educational Statistics

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 Introduction to Statistics


History of Statistics

The history of statistics can be traced back to ancient times. For example, the Egyptians collected data on population and agricultural production. The Chinese used data to make decisions about government and military strategy.

The modern field of statistics began to develop in the 17th century. During this time, scholars such as Pierre de Fermat and Blaise Pascal developed new mathematical methods for analyzing data.

In the 19th century, statistics began to be used in a wider range of fields, such as economics, sociology, and medicine. During this time, scholars such as Francis Galton and Karl Pearson developed new statistical methods, such as correlation and regression analysis.

Definition and Need of Statistics

Statistics is the science of collecting, analyzing, and interpreting data. It is used in a wide range of fields to make informed decisions.

Statistics is needed because data can be complex and difficult to interpret. Statistical methods can help us to make sense of data and to draw meaningful conclusions.

Types of Statistics

There are two main types of statistics:

  • Descriptive statistics: Descriptive statistics are used to summarize and describe data. Examples of descriptive statistics include the mean, median, and mode.
  • Inferential statistics: Inferential statistics are used to draw conclusions about a population based on a sample. Examples of inferential statistics include t-tests, chi-square tests, and ANOVA tests.

Symbols in Statistics

There are a number of symbols that are commonly used in statistics. Some of the most common symbols include:

  • μ: Mean
  • M: Median
  • Mo: Mode
  • SD: Standard deviation
  • n: Sample size
  • σ: Population standard deviation
  • p: Population proportion
  • q: Population proportion

Presentation and Organization of Data

Organization of Data

There are three main ways to organize data:

  • Simple array: A simple array is a list of data values in order from least to greatest.
  • Frequency array: A frequency array is a table that shows the number of times each data value occurs.
  • Frequency distribution: A frequency distribution is a graph that shows the distribution of data values.

Class Interval

A class interval is a range of values. Class intervals are used to group data values together when there are a large number of data values or when the data values are spread out over a wide range.

Inclusive Class Interval

An inclusive class interval includes both the lower and upper limits of the interval.

Exclusive Class Interval

An exclusive class interval excludes both the lower and upper limits of the interval.

Graphical Representation of Data

Bar Diagram

A bar diagram is a graph that uses bars to represent data. Each bar represents a category. The height of each bar represents the frequency of the category.

Histogram

A histogram is a graph that uses bars to represent data. Each bar represents a class interval. The height of each bar represents the frequency of the class interval.

Pie Chart

A pie chart is a graph that uses slices of a circle to represent data. Each slice represents a category. The size of each slice is proportional to the frequency of the category.

Measures of Central Tendency

Mean

The mean is the average of all the data values.

Median

The median is the middle data value when the data values are ordered from least to greatest.

Mode

The mode is the most frequent data value.

Measures of Relative Position

Concept of Relative Position

Relative position is a measure of where a data value falls in relation to the other data values.

Percentile Rank

The percentile rank of a data value is the percentage of data values that are less than or equal to the data value.

Percentile

A percentile is a value that divides a distribution into 100 equal parts.

Measures of Variability

Range

The range is the difference between the largest and smallest data values.

Mean Deviation

The mean deviation is the average of the absolute deviations from the mean.

Standard Deviation

The standard deviation is a measure of the variability of the data values around the mean.

Unit IV: Correlation

Meaning

Correlation is a measure of the

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