Beginner level · Module 3: Statistics for Decisions · Lesson 1 of 3
Centre and Spread
Choose the right summary of the typical value and describe how much values vary.
In this lesson you will
- Choose mean or median based on the distribution
- Describe spread with IQR and standard deviation
Key concepts
mean and medianskewnessinterquartile rangestandard deviation
The lesson
The mean adds all values and divides by the count; the median is the middle value. When a few values are very large — incomes, land sizes — the mean is pulled upwards and the median describes a typical household better.
Spread matters as much as the centre. The interquartile range (IQR) covers the middle 50% of values; the standard deviation measures typical distance from the mean and is sensitive to extremes like the mean is.
Report the measure that matches your message, and say which one you used: 'median monthly income was 64,000 SSP'.
Step by step
- Calculate the mean and median income.
- Remove the largest value and recalculate both.
- Calculate the IQR and standard deviation.
- Choose and justify the summaries to report.
Why one trader changes the 'average' income
Mean versus median for seven household incomes, one of them very high.
| Item | Working | Amount |
|---|---|---|
| Six households | 45 + 52 + 60 + 64 + 70 + 80 | 371 |
| One trader household | recorded value | 600 |
| Total of all seven | 371 + 600 | 971 |
| Mean of all seven | 971 ÷ 7 | 138.7 |
| Mean without the trader | 371 ÷ 6 | 61.8 |
| Median of all seven (4th of 7 sorted values) | 45, 52, 60, 64, 70, 80, 600 | 64 |
Explanation
The mean of 138,700 SSP is higher than six of the seven incomes — it describes almost nobody. One very high value more than doubles it.
The median, 64,000 SSP, stays at the middle household whatever happens to the extreme. For incomes, land sizes and other skewed data, report the median, and say which measure you used.
Check your understanding
Six of the seven households earn less than the mean, while three earn less and three more than the median — the median is the middle value.
Practice activity
Summarise household income and walking time with justified measures of centre and spread.
Expected result: Correct summaries with a clear reason for each choice.
Check your understanding
-
Why is the median often better for income?
Show answer
A few very high incomes pull the mean up, while the median stays typical.
-
What does the IQR cover?
Show answer
The middle 50% of values.
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