To distinguish an average from a distribution, calculate the average, then look at how the values are spread around it. This is the check to apply to every table in population and settlement evidence, whether it shows incomes, densities or town sizes.
How do you check step by step?
- Order the values from smallest to largest.
- Calculate the mean: add all values and divide by how many there are.
- Find the median: the middle value, or the mean of the two middle values.
- Calculate the range: highest minus lowest.
- Compare mean and median. A mean much higher than the median suggests one or more very high values.
- Describe the spread in words, using figures and units.
Worked example
Invented monthly household incomes for ten households in District F, in RM.
1,200; 1,300; 1,400; 1,500; 1,600; 1,700; 1,800; 2,000; 2,400; 17,000
Mean: the total is 31,900, and 31,900 ÷ 10 = RM3,190.
Median: the 5th and 6th values are 1,600 and 1,700, so the median is (1,600 + 1,700) ÷ 2 = RM1,650.
Range: 17,000 − 1,200 = RM15,800.
Description: “The mean income is RM3,190 but the median is RM1,650. Nine of the ten households earn less than the mean, and one household earning RM17,000 pulls the mean upwards. The median is closer to a typical household. The range of RM15,800 shows a wide spread.”
The mistake to watch for
Mistaken answer: “The average household in District F earns RM3,190, so most households earn about this much.”
Only one household earns more than RM3,190, and nine earn RM2,400 or less. The mean does not describe most households.
Correction: report the median alongside the mean, quote the range and name the extreme value. The statement about “most” must match the data.
Self-check
1. Population densities of five districts (invented, persons per km²): 3, 5, 7, 9, 76. Find the mean and the median.
Show answer
Total is 100, so the mean is 100 ÷ 5 = 20. The median is the middle value, 7. The 76 pulls the mean up.2. Region X has values 48, 49, 50, 51, 52 and Region Y has 10, 20, 50, 80, 90. Both have a mean of 50. Compare the ranges.
Show answer
Region X range = 52 − 48 = 4. Region Y range = 90 − 10 = 80. The means match but Y is far more spread out.3. Why is the mean alone not enough to describe Region Y?
Show answer
Only one value in Region Y is near 50, so the mean hides a very wide spread. A description needs the range or the individual values.Where does this lead next?
You can now read an average critically, which helps with the data in development and inequality as well. Try your own sets in the statistics and distribution explorer, then work through the mixed practice. If you would like a teacher to check how you describe data, see IGCSE Geography one-to-one tuition.