Practice Variability in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Variability is the degree to which data points in a set differ from each other and from the center of the distribution.

How spread out or bunched up the data is. No variability = everyone is the same.

Example 1

easy
Three measures of spread exist for the data \{5, 10, 15, 20, 25\}: range, IQR, and standard deviation. Calculate all three and compare what each captures.

Example 2

medium
Two data sets have the same mean of 50 but different standard deviations: Set A has \sigma=2, Set B has \sigma=15. Describe what this means and sketch what their distributions would look like.

Example 3

easy
Which data set has greater variability? Set A: \{48, 49, 50, 51, 52\} or Set B: \{10, 30, 50, 70, 90\}? Use range and explain.

Example 4

hard
A factory produces bolts. Machine A produces bolts with diameter mean 10 mm, SD = 0.1 mm. Machine B produces bolts with mean 10 mm, SD = 0.5 mm. The specification requires bolts between 9.8 mm and 10.2 mm. Explain which machine is preferable and why variability matters here.
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