Interpreting statistical data

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

This topic is about reading information correctly from tables and diagrams and then deciding what the data really shows. Always look at the title, the key, the labels and the scale before you read any value.

To compare two sets of data, use two things: an average (mean or median) to say which set is higher or lower in general, and a measure of spread (range or interquartile range) to say which set is more consistent.

You must also know the limits of data. A conclusion is unreliable if the sample is too small or not representative, if a scale is misleading, or if a link between two things is taken as proof that one causes the other.

Rules to remember

Common mistake

Using the range to say which set scored higher. A larger range only means the values are more spread out (less consistent); use the mean or median to say which set is higher.

Worked example

A table shows the goals a team scored in 25 matches: 0 goals in 6 matches, 1 goal in 9 matches, 2 goals in 7 matches and 3 goals in 3 matches. In what percentage of the matches did the team score at least 2 goals?

  1. "At least 2" means 2 or 3 goals: 7 + 3 = 10 matches.
  2. Check the total: 6 + 9 + 7 + 3 = 25 matches.
  3. Percentage = (10 ÷ 25) × 100 = 40%.

Answer: 40% of the matches

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