Averages, spread and scatter graphs

Maths · Statistics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

An average gives one typical value for a set of data. The three averages are the mean, the median (middle value when the data is in order) and the mode (most common value). A measure of spread shows how consistent the data is: the range uses the two end values, and the interquartile range uses the middle half, so it is not affected by extreme values.

To compare two sets of data, for example with box plots, make two statements: compare an average, then compare a spread. A smaller spread means more consistent values.

A scatter graph shows whether two variables are linked. This link is called correlation. A line of best fit lets you estimate one value from the other.

Rules to remember

Common mistake

In a grouped table, dividing by the number of classes instead of the total frequency, or using the class end values instead of the midpoints. Always divide the sum of midpoint × frequency by the total frequency.

Worked example

A table shows lengths x cm: 0 < x ≤ 4, frequency 5; 4 < x ≤ 8, frequency 12; 8 < x ≤ 12, frequency 3. Estimate the mean length.

  1. Midpoints are 2, 6 and 10.
  2. Midpoint × frequency: 2 × 5 = 10, 6 × 12 = 72, 10 × 3 = 30. Sum = 10 + 72 + 30 = 112.
  3. Total frequency = 5 + 12 + 3 = 20.
  4. Estimated mean = 112 ÷ 20 = 5.6 cm.

Answer: 5.6 cm

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