Measures of central tendency · Ages 14–15
Choosing the mean, median or mode
Extreme values: the median. Categories: the mode.
How to do it
Method
Extreme values: the median. Categories: the mode
$20,000 × 4 and $300,000 a month: mean $76,000, median $20,000
Another way
Are they categories?
The favourite colour: only the mode works
In full
Each measure has its strengths. The mean uses every value but is pulled by an extreme one: four people earning $20,000 a month and one earning $300,000 have a mean of $76,000, far above four of the five. The median depends only on position, so an extreme value doesn't move it (still $20,000 here): incomes and flat prices, with their extremes, usually use the median. The mode is the commonest value; it works for data that aren't numbers (the favourite colour) and for questions like 'which size to stock most of', but there may be more than one, or none. One test: are there extreme values? Then not the mean. Another: are the data categories? Then only the mode.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Five flats have floor areas of 37, 190, 36, 42 and 40 m². By how many m² does the mean exceed the median?
Show the answer and working
Answer: 29 m²
Mean 345 ÷ 5 = 69; the median is the middle one, 40; 29 m² apart: the very large 190 pulls the mean up.
Example 2
A courier delivered 22, 18, 193, 14, 21, 20 parcels on six days, one of them during a big sale. With that extreme value taken out, the mean falls by and the median only by .
Fill in each blank
Show the answer and working
Answer: 29, 0.5
Six days: mean 48, median (20 + 21) ÷ 2 = 20.5. Without 193: mean 95 ÷ 5 = 19, median 20. The mean falls by 29, the median only by 0.5: an extreme value drags the mean a long way and barely moves the median, so with an extreme value the median stands for the typical day.
Example 3
A runner ran 29, 22, 31, 26, 24 km on five runs. The mean and median of these data are less than 2 km apart.
True or false?
Show the answer and working
Answer: True
Mean 26.4, median 26: 0.4 km apart. An extreme value pulls the mean away from the median.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A small firm's five staff earn $21,000, $17,000, $162,000, $22,000 and $18,000 a month. Which figure best represents a typical member of staff's pay?
- A. The highest pay, $162,000
- B. The lowest pay, $17,000
- C. The median, $21,000
- D. The mean, $48,000
Choose the right answer
Answer:
2.A shoe shop is deciding which size to order most of next month. Which measure of last month's sizes sold should it look at?
- A. The largest size
- B. The mode
- C. The mean
- D. The median
Choose the right answer
Answer:
3.An ice-cream shop asked 149 customers for their favourite flavour. Which measure can describe the centre of these data?
- A. Only the mode
- B. Only the median
- C. Any of the three
- D. Only the mean
Choose the right answer
Answer:
4.A courier delivered 21, 15, 239, 13, 20, 16 parcels on six days, one of them during a big sale. With that extreme value taken out, the mean falls by and the median only by .
Fill in each blank
Answer:
5.A runner ran 22, 14, 52, 19, 17 km on five runs. The mean and median of these data are less than 2 km apart.
True or false?
Answer:
All the answers
- 1. C. The median, $21,000
- 2. B. The mode
- 3. A. Only the mode
- 4. 37, 2
- 5. False
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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