To measure variability, why is the standard deviation usually preferred over the range? Give an example of a data sets to illustrate your answer. (Data sets should have the same range but very different standard deviations.)

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section11.1: Measures Of Center And Variation
Problem 32E
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To measure variability, why is the standard deviation usually preferred over
the range? Give an example of a data sets to illustrate your answer. (Data sets should
have the same range but very different standard deviations.)
a)
b)
Would outliers affect the standard deviation or the IQR? Explain your answer.
Transcribed Image Text:To measure variability, why is the standard deviation usually preferred over the range? Give an example of a data sets to illustrate your answer. (Data sets should have the same range but very different standard deviations.) a) b) Would outliers affect the standard deviation or the IQR? Explain your answer.
Expert Solution
Step 1

(a)

The standard deviation is used to calculate the variability of the data set. It tells us about the spread of the data points from the mean value. The standard deviation is the square root of the average squared differences of each value from the mean value.  To calculate the standard deviation, one should know the mean value. The standard deviation of the data depends on the center of the dataset.

The difference between the maximum and minimum values of the data is called the range of the data. As a measure of dispersion, the range has some limitations. The range is not dependent on the exact value of every measurement because the range uses the maximum and minimum values to find the variability.

 

consider two data sets:

A: 8, 2,4,6,7,9,4, 3, 6, 5

B: 12,7,8,9,10,11,5,6, 10,9

 

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