Mean, median and a fair share
Calculate two measures of centre and explain what each summarises.
Before you begin
- Ordering numbers
- Addition and division
Interpret the mean as redistribution
The mean is the total of all values divided by the number of observations. Imagine redistributing a collection equally: the shared amount is the mean. It need not match any observed value, and it can be a decimal even when every observation is a whole number. Including one unusually large or small value can shift it because every value contributes to the total.
Locate the median after ordering
The median is the middle of an ordered list. With an odd number of observations, select the middle value. With an even number, average the two middle values. Each repeated observation keeps its place in the list. The median describes the middle position rather than an equal share, so explain which interpretation is relevant to the question.
Worked example
Find the mean and median of 3, 4, 4, 5 and 14 minutes.
Show the worked solution
- Add the five values: 3 + 4 + 4 + 5 + 14 = 30.
- Mean = 30 ÷ 5 = 6 minutes.
- The ordered middle observation is the third value, 4 minutes. The value 14 pulls the mean above the median.
Mean 6 minutes; median 4 minutes.
Try it yourself
What is the median of 2, 3, 8 and 11?
Common mistakes
- Divide by the number of observations, including repeats.
- Sort before finding a median.
What can you explain now?
Five test scores have mean 8. Four scores are 6, 7, 8 and 9. Find the fifth score.
Compare with the explanation
10.
A mean of 8 across five values requires a total of 40. The known values sum to 30, so the missing score is 10.
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Common Core mathematics standards ↗