Mean vs Median Statistics Example 3

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

Example 3

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Salaries at a small company: \30k, \32k, \35k, \33k, \31k, \150k. Should the company report the mean or median salary to represent a typical employee's pay? Justify.

Solution

  1. 1
    Step 1: Mean = 30+32+35+33+31+1506=3116โ‰ˆ51.8k\frac{30+32+35+33+31+150}{6} = \frac{311}{6} \approx 51.8\text{k}. Median = 32+332=32.5k\frac{32+33}{2} = 32.5\text{k}.
  2. 2
    Step 2: The \150k salary is an outlier pulling the mean up. The median (\32.5k) better represents a typical employee's pay.

Answer

The median (\$32.5k) should be reported as it is not distorted by the outlier salary.
In skewed distributions, the median provides a more accurate picture of what is typical. This is why median household income is often reported instead of mean income.

About Mean vs Median

Mean and median are both measures of center but respond differently to extreme values (outliers). The mean is pulled toward outliers because it uses every value in its calculation, while the median is resistant to outliers because it depends only on the middle position.

Learn more about Mean vs Median โ†’

More Mean vs Median Examples

Example 1 medium

House prices on a street (in thousands): 200, 210, 190, 205, 195, 800. Calculate the mean and median

Example 2 medium

Test scores: 78, 82, 79, 81, 80. Calculate both the mean and median. What do you notice?

Example 4 medium

A runner's practice times (in minutes) are 24, 25, 24, 26, 25, 24. Would the mean or the median bett

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