Practice Center vs Spread in Math

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

Quick Recap

Center versus spread describes two complementary aspects of any data distribution: center (mean, median) tells you where the typical value lies, while spread (range, IQR, standard deviation) tells you how much the values vary around that center.

Where is the data located? How spread out is it around that location?

Example 1

easy
For the data \{2, 4, 6, 8, 10\}: calculate the mean (center) and standard deviation (spread), then explain why both are needed to describe the data.

Example 2

medium
Three data sets all have mean = 10: Set A = \{10, 10, 10, 10\}, Set B = \{8, 9, 11, 12\}, Set C = \{1, 5, 15, 19\}. Calculate the SD of each and describe what the spread reveals.

Example 3

easy
A quality control manager says: 'Our bolts average 50 mm, which is the target.' Why might this still be a problem, and what additional information is needed?

Example 4

hard
For symmetric distributions, which pair (mean ± SD) or (median, IQR) is preferred? For skewed distributions? Justify with an example for each case.
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