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Mean, Median and Mode · Question 9 of 67

Question 9

MediumOriginal question

In a survey of the number of flats in each apartment block of a township, the mode is 52 flats and the median is 48 flats. Assuming the empirical relation holds, what is the mean number of flats per block?

Options for question 9

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. Mode = 3 Median − 2 Mean, so 2 Mean = 3 Median − Mode.

  2. 2 Mean = 3×48−52=923 \times 48 - 52 = 92.

  3. Mean = 922=46\frac{92}{2} = 46.

Worth noting

92 forgets to halve. 54 comes from swapping median and mode, (3×52−48)÷2(3 \times 52 - 48) \div 2. 50 is just the average of the two given numbers.

Concept
Rearranging the empirical relation to find the mean
Typical time
70 s
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