Range (Statistics) Math Example 2

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Example 2

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Two classes took the same test. Class A scores: {55,70,85,90,95}\{55, 70, 85, 90, 95\}. Class B scores: {72,74,76,78,80}\{72, 74, 76, 78, 80\}. Compare the ranges and explain what the difference tells you.

Solution

  1. 1
    Calculate Range for Class A: RangeA=95−55=40\text{Range}_A = 95 - 55 = 40
  2. 2
    Calculate Range for Class B: RangeB=80−72=8\text{Range}_B = 80 - 72 = 8
  3. 3
    Compare: Class A has range 40, Class B has range 8, so Class A has 40−8=3240 - 8 = 32 more spread
  4. 4
    Interpret: Class A scores are much more spread out, suggesting greater variability in student performance, while Class B is more consistent

Answer

Class A range = 40, Class B range = 8; Class A has significantly more variability.
Comparing ranges between groups reveals differences in consistency. A small range indicates homogeneous performance; a large range suggests diverse performance levels. The range is sensitive to extreme values (outliers).

About Range (Statistics)

The statistical range is the difference between the maximum and minimum values in a data set: range=max⁡−min⁡\text{range} = \max - \min.

Learn more about Range (Statistics) →

More Range (Statistics) Examples

Example 1 easy

Find the range of the data set: [formula].

Example 3 easy

Find the range of the monthly temperatures (°F): [formula].

Example 4 hard

A data set has a range of 24. If the maximum value is [formula] and the minimum value is [formula],

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