Center vs Spread Math Example 3

Follow the full solution, then compare it with the other examples linked below.

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?

Solution

  1. 1
    The mean alone is insufficient — the spread is equally important
  2. 2
    If SD is large (e.g., SD = 5 mm), many bolts will be far from 50 mm even though the average is correct
  3. 3
    Additional information needed: standard deviation (or IQR) to assess how consistently bolts hit the target

Answer

Need spread (SD or IQR); a large SD means many bolts deviate from target despite correct mean.
In manufacturing and quality control, both center and spread matter. A process can be centered correctly but still produce defects if variability is too high. Spread measures are essential complements to measures of center.

About Center vs Spread

Center and spread are two complementary ways to describe a data distribution. Center (mean, median, mode) tells you where values cluster; spread (range, interquartile range, standard deviation) tells you how far values are from that center. Together they give a complete picture of any dataset.

Learn more about Center vs Spread →

More Center vs Spread Examples

Example 1 easy

For the data [formula]: calculate the mean (center) and standard deviation (spread), then explain wh

Example 2 medium

Three data sets all have mean = 10: Set A = [formula], Set B = [formula], Set C = [formula]. Calcula

Example 4 hard

For symmetric distributions, which pair (mean ± SD) or (median, IQR) is preferred? For skewed distri

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