Statistics: summarising and interpreting data
What Statistics tests
Statistics tests how data are collected, organised, summarised and interpreted. Foundation questions include frequency tables, bar charts, pie charts, histograms, averages and spread, scatter graphs and the line of best fit. You need to read scales carefully and describe what the data show, not just calculate.
Core rules
- Mean = sum of all values ÷ number of values. For a frequency table, multiply each value by its frequency, add, then divide by the total frequency.
- Median: put values in order and find the middle. With an even number, average the two middle values.
- Mode: the most frequent value. Range = highest - lowest.
- For grouped data, use class midpoints to estimate the mean; the result is an estimate.
- Correlation describes the direction and strength of a relationship on a scatter graph; correlation does not prove causation.
Worked example
The values 1, 2 and 3 have frequencies 4, 5 and 1. Find the mean and median. Total frequency = 4 + 5 + 1 = 10. Sum = (1 × 4) + (2 × 5) + (3 × 1) = 4 + 10 + 3 = 17. Mean = 17 ÷ 10 = 1.7. For the median, the 5th and 6th values are both 2, so the median is 2. The mode is 2, because it has the highest frequency.
Traps that cost marks
- Dividing by the number of different values instead of the total frequency.
- Reading a histogram as if the height were the frequency when the bars have unequal widths.
- Describing a scatter graph as showing a strong correlation without stating positive or negative.
- Treating a percentage in a pie chart as a raw count.