The mean of 8 observations is 12. If one observation of value 20 is replaced by 4, what is the new mean?

10Correct answerYour answer10.5Correct answerYour answer11Correct answerYour answer12Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The eight observations currently total $8 \times 12 = 96$ .
Replacing 20 by 4 reduces the total by 16, giving $96 - 16 = 80$ .
The count has not changed, so the new mean is $80 \div 8 = 10$ .

Worth noting

The total dropped by 16 spread over 8 observations, so the mean dropped by $16 \div 8 = 2$ . That shortcut works whenever the number of observations stays the same.

Concept: Effect of replacing one value on the mean
Typical timeTypical: 65 s
Your timeYours: —

The rule this testsWhen values change

Practise this chapter →

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

The mean of 8 observations is 12. If one observation of value 20 is replaced by 4, what is the new mean?

Explanation