Mean, median, mode and range
- Mean = total of the values ÷ number of values. Median = the middle value when the data is in order. Mode = the most common value. Range = largest − smallest.
- For 3, 5, 5, 8, 9: mean = 30 ÷ 5 = 6, median = 5, mode = 5 and range = 9 − 3 = 6.
- With an even number of values, the median is halfway between the two middle values: for 4, 7, 9, 12 it is 8.
Averages from frequency tables
- Mean = total of (value × frequency) ÷ total frequency.
- Goals 0, 1, 2 and 3 with frequencies 4, 7, 6 and 3: total goals = 0 + 7 + 12 + 9 = 28, so the mean is 28 ÷ 20 = 1.4.
- The median is the ((n + 1) ÷ 2)th value. For 20 values, it is halfway between the 10th and 11th values, which are both 1 here.
Grouped data
- Use the midpoint of each group to estimate the mean. The modal class is the group with the highest frequency.
- Times 0–10 (frequency 5), 10–20 (frequency 8) and 20–30 (frequency 7) minutes: estimated mean = (5 × 5 + 15 × 8 + 25 × 7) ÷ 20 = 320 ÷ 20 = 16 minutes.
- It is only an estimate, because you don't know the exact values in each group.
Choosing an average
- The median is better than the mean when there are extreme values (outliers). The mode is the only average for non-numerical data, such as favourite colours.
- The range measures spread: a smaller range means the data is more consistent.
Key terms
- Mean
- The total of the values divided by the number of values.
- Median
- The middle value when the data is in order.
- Mode
- The most common value.
- Range
- The largest value minus the smallest value.
- Outlier
- A value that is much bigger or smaller than the rest.
- Frequency
- How many times something happens.
- Modal class
- The group with the highest frequency.
- Midpoint
- The value halfway through a group, used to estimate the mean.