A shoe shop sold seven pairs one day, in sizes 41, 39, 43, 40, 44, 39, 42. What is the mode of the sizes?

39. The mode is the value that comes most often: 39 comes twice, every other value once.

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 median B. The largest size C. The mean D. The mode Choose the right answer

D. The mode. The mode is the value that comes most often: exactly the best-selling size.

74.5 kg. Weight by the team sizes: (19 × 69 + 11 × 84) ÷ (19 + 11) = 2235 ÷ 30 = 74.5 kg.

Data and probability · Ages 14–15

From “Mean, median and mode” to “Weighted mean word problems”, step by step, each skill with its methods, worked examples and answers.

Mean, median and modeSort first for the median; the mode comes most often
Method3, 8, 5, 8, 6: mean 6, median 6, mode 8
Another way: An assumed meanDifferences −2, 3, 0, 3, 1 average 1, so 5 + 1 = 6
Finding an unknown from an averageSum = mean × how many
Method7, 9, x, 12 with mean 10: x = 40 − 28 = 12
Another way: An equation(7 + 9 + x + 12) ÷ 4 = 10, x = 12
Averages of grouped dataClass marks for the mean; the most frequent class is the modal class
Method(14.5 × 2 + 24.5 × 5 + 34.5 × 3) ÷ 10 = 25.5
Another way: Number the classesClass numbers average 1.1: 14.5 + 1.1 × 10 = 25.5
Choosing the mean, median or modeExtreme values: the median. Categories: the mode
Method$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
How changing the data changes the averagesAdd k to all: add k. Multiply all by k: multiply by k
MethodMean 30, each plus 5 then doubled: (30 + 5) × 2 = 70
Another way: Work it out againWrite the new data, then find the mean
Weighted meanΣ(value × weight) ÷ Σweights
Method(80 × 2 + 90 × 3) ÷ (2 + 3) = 86
Another way: As repeated valuesThe mean of 80, 80, 90, 90, 90 = 86
Weighted mean word problemsWeight a combined mean by the group sizes
Method(20 × 60 + 30 × 70) ÷ 50 = 66
Another way: The gap in proportion60 + (70 − 60) × 3050 = 66

From different skills in this topic. Have a go first, then open each one for the answer and the working.

Example 1Mean, median and mode →
A shoe shop sold seven pairs one day, in sizes 41, 39, 43, 40, 44, 39, 42. What is the mode of the sizes?
Show the answer and working
Answer: 39
The mode is the value that comes most often: 39 comes twice, every other value once.
Example 2Choosing the mean, median or mode →
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 median
- B. The largest size
- C. The mean
- D. The mode
Choose the right answer
Show the answer and working
Answer: D. The mode
The mode is the value that comes most often: exactly the best-selling size.
Example 3Weighted mean word problems →
Team A's 19 people have a mean weight of 69 kg and team B's 11 people 84 kg. What is the mean weight of the two teams together, in kg?
Show the answer and working
Answer: 74.5 kg
Weight by the team sizes: (19 × 69 + 11 × 84) ÷ (19 + 11) = 2235 ÷ 30 = 74.5 kg.

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