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MathidiaMathematics Academy
Data collection and representation
Lesson 45 of 75
Review

Measures of location and spread

Objective. Calculate and compare statistics in context.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
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Learn: the key idea

Measures of location (mean, median, mode) describe a typical or central value of a data set, while measures of spread (range, interquartile range, variance, standard deviation) describe how dispersed the values are around that centre. The mean is calculated as the sum of all values divided by the number of values, while the median is the middle value when data is ordered, more resistant to extreme outliers than the mean. Standard deviation measures average distance from the mean, calculated as the square root of variance, and a larger standard deviation indicates more spread-out data. For example, data set 2, 4, 4, 6 has mean 4, and comparing this to another set's mean and spread lets you judge which is more consistent.

Worked example

A data set of test scores is 12, 15, 18, 20, 25. Calculate the mean and the range as summary statistics for this data.

1215182025
Bar chart of the values 12, 15, 18, 20, 25
  1. 1Sum the values: 12 + 15 + 18 + 20 + 25 = 90.
  2. 2Divide by the number of values: mean = 90/5 = 18.
  3. 3Find the range: maximum − minimum = 25 − 12.
  4. 4Compute the range: 25 − 12 = 13.

Answer: Mean = 18, range = 13

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Common mistake. Students sometimes report the mean as the best measure of centre even when outliers are present, when actually the median better represents typical values in skewed data since it is not distorted by extreme values.

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