Variability Math Example 3

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

Example 3

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

Solution

  1. 1
    Range A: 52−48=452 - 48 = 4
  2. 2
    Range B: 90−10=8090 - 10 = 80
  3. 3
    Set B has much greater variability (range = 80 vs 4)

Answer

Set B has greater variability (range = 80 vs. 4).
Even without computing standard deviation, the range provides a quick comparison of spread. Set B's values span the full range from 10 to 90, while Set A's values are concentrated in a 4-unit window around 50.

About Variability

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

Learn more about Variability →

More Variability Examples

Example 1 easy

Three measures of spread exist for the data [formula]: range, IQR, and standard deviation. Calculate

Example 2 medium

Two data sets have the same mean of 50 but different standard deviations: Set A has [formula], Set B

Example 4 hard

A factory produces bolts. Machine A produces bolts with diameter mean 10 mm, SD = 0.1 mm. Machine B

← All Variability Examples Variability Concept