Types of Statistical Analysis

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  • 0:03 Statistical Analysis
  • 1:28 Measures of Central Tendency
  • 2:32 Measures of Dispersion
  • 3:49 Tests of Difference
  • 5:08 Tests of Relationship
  • 6:00 Lesson Summary
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Lesson Transcript
Instructor: Usha Bhakuni

Usha has taught high school level Math and has master's degree in Finance

This lesson introduces the concept of statistical analysis and its uses. Then it explores the broad categories and various types of analysis that are used.

Statistical Analysis

In this modern world, we are surrounded by data everywhere, be it our shopping behavior, eating habits, sleeping patterns, education, or jobs. Data can be captured from almost anything. So how are these data used and what do they tell us? The data in itself does not tell much. In order to get meaningful information out of the data, certain analysis needs to be carried out on the data.

The science of analyzing large amounts of data to explore the underlying patterns, trends, and hidden insights from them is called statistical analysis. Broadly speaking, there are two categories of statistical analysis. Descriptive analysis helps in summarizing the available data. It analyzes the structure and distribution of either the entire data. This analysis generates limited insights that only presents a way to summarize the data. Inferential analysis is used to deduce some insights from the data that are not apparently visible. It can be used to make judgments and infer insights from the data.

Now we will look at the various types of analysis within each of these categories with the help of an example. Let's say Marie is a math teacher and teaches a class of 50 students. She wants to analyze the test scores of her students. We'll see what types of statistical analysis techniques she can use.

Measures of Central Tendency

Measures of central tendency are a type of descriptive analysis that are used to represent the central cluster or typical scenario depicted by the data. The most commonly used measures here are median, mean, and mode.

Median is calculated by arranging the data points in ascending order and then taking the middle number. In case of two middle numbers, their average is taken. Here we see a formula for a set of n data points:


In our example, if Marie finds out that the median test score in the class is 60, it means that half of the students scored higher than 60 and half scored below 60.

Mean represents the average of the data points. It is calculated by dividing the sum of all the data points by the number of data points, as shown here.

Formula of mean

Mode represents the most frequently occurring data point in the sample of data. In our example, Marie finds out that four students scored a perfect 100, and this was the most frequently occurring score. In such a case, 100 would be the mode.

Measures of Dispersion

Measures of dispersion are a type of descriptive analysis that are used to explain how far apart the data points are spread. The most commonly used measure is standard deviation.

Standard deviation is a measure of how far data might lie from the mean. Calculating standard deviation starts by taking the difference of each data point from the mean of the data, squaring them, then adding them up. Finally, square the sum by the number of data points and then taking the square root, as shown here.

Standard Deviation

If that sounds like a headache to calculate, one can use computer software to calculate the standard deviation. With big data sets, statisticians have no other choice.

Standard deviation is very useful in a normal distribution. A normal distribution is a variable that is distributed evenly about a mean. It is usually bell-shaped and symmetrical about the mean, like we see here.

Approximately 2/3 of all data are within one standard deviation above and below the mean in a normal distribution.
normal distribution

In a normal distribution, approximately two-third of the data points lie between one standard deviation above and below the mean. For example, if the scores in Marie's class are normally distributed, the mean score is 55 and the standard deviation is 15, then two-third of the students have scored between 40 and 70.

Tests of Difference

Test of difference are the type of inferential statistical analysis that help figuring out whether the difference between various groups in a data sample occurs randomly or due to another variable.

Two commonly used tests for this are:

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