For the lengths of phone calls at a helpline, the mode is 27 seconds and the mean is 30 seconds. Using the empirical relation, what is the median?

27 secondsCorrect answerYour answer28 secondsCorrect answerYour answer28.5 secondsCorrect answerYour answer29 secondsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Mode = 3 Median − 2 Mean, so 3 Median = Mode + 2 Mean.
3 Median = $27 + 60 = 87$ , so Median = 29 seconds.

Worth noting

28 seconds swaps the weights, $(2 \times 27 + 30) \div 3$ . 28.5 seconds is the plain average of mode and mean. For moderately skewed data the median lies between the mode and the mean, one-third of the way from the mean.

Concept: Rearranging the empirical relation to find the median
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsMean, median and mode

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Ten questions from Mean, Median and Mode, at your own pace.

For the lengths of phone calls at a helpline, the mode is 27 seconds and the mean is 30 seconds. Using the empirical relation, what is the median?

Explanation