In a set of ten different numbers, the smallest is decreased by 5 and the largest is increased by 5. What happens to the mean, the median and the range?

The mean and the median stay the same; the range rises by 10Correct answerYour answerThe mean rises by 1; the median stays the same; the range rises by 10Correct answerYour answerAll three stay the sameCorrect answerYour answerThe mean and the median stay the same; the range rises by 5Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The total changes by $-5 + 5 = 0$ , so the mean is unchanged.
The smallest is still the smallest and the largest still the largest, so the 5th and 6th values, and the median, do not change.
Range = (largest + 5) − (smallest − 5) = old range + 10.

Worth noting

The range gains from both ends, so it grows by 10, not 5.

Concept: Which measures change when both extremes are pushed outwards
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsRange and spread

Practise this chapter →

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

In a set of ten different numbers, the smallest is decreased by 5 and the largest is increased by 5. What happens to the mean, the median and the range?

Explanation