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Statistics 101: Principles of Statistics
Course

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Summarizing Data
Chapter

Spread of Data Measures & Examples | What are Spread Statistics?

Understand what the spread of data is and how to find the spread of data. Discover the various measures of spread and practice calculating spread in statistics.

Updated: 02/13/2022

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Maximums, Minimums & Outliers in a Data Set

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0:03 The Spread in Data Sets

1:39 Range

2:32 Interquartile Range

3:48 Variance

5:14 Standard Deviation

5:36 Lesson Summary

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Spread Statistics Measures & Examples | What are Spread Statistics?

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Nuriye has been teaching mathematics and statistics for over 25 years. She mainly taught grades 9 to 12 with some middle school classes. She has a bachelor's degree in mathematics and a master's degree in education focusing on instructional technology. She coauthored a variety of mathematics textbooks. She also develops digital learning materials for students and teachers.

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

A data set is a collection of information. Data could be from surveys, measurements, observations, etc. When the data is only about one variable then it is called univariate data . Examples of univariate data could be SAT scores, heights, or salaries. When the data set is small, it is easier to understand the data; when there is a large data set, to understand the data better, analysis must be done to draw some inferences from the data.
Univariate data sets can be analyzed in two different ways:
Central tendency describes the center of the data. In Figure 1, two data sets x1 and x2 have the same mean which is 9. When you look at the spread of the data, however, it is quite different. While x1 has ten data points of 8 and one 19, x2 has a fairly even spread ranging from 4 to 14. If these two sets were to be compared by only using the mean, it could be assumed that they are about the same, when in fact they are different.
Figure 1 Data sets x1 and x2 have the same mean but their spread is very different
Consider the annual salaries of employees of company A, given below:
$20,000, $20,000, $20,000, $20,000, $400,000
The mean of this data set is $96,000, meaning the average annual salary in this company is $96,000. This is obviously misleading.
Figure 2 If data is skewed, central tendencies can be misleading
Now consider company B, again with 5 employees whose salaries are given below:
$10,000, $11,000, $50,000, $50,500, $50,600
The median of this data set is $50,000, but once again saying the median salary in this company is $50,000 per year is misleading.
Both measures, the mean and the median, only represent the center of the data and therefore they can lead to misleading conclusions. The mean is e
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