For the lengths of a batch of bolts, the median is 14 mm and the mode is 12 mm. Each length is halved and then 3 mm is added. What are the new median and mode?

Median 10 mm, mode 9 mmCorrect answerYour answerMedian 7 mm, mode 6 mmCorrect answerYour answerMedian 8.5 mm, mode 7.5 mmCorrect answerYour answerMedian 10 mm, mode 12 mmCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Halving and adding 3 is applied to every value, so the order is kept and every average follows the same rule.
New median = $14 \div 2 + 3 = 10$ mm.
New mode = $12 \div 2 + 3 = 9$ mm.

Worth noting

Adding 3 before halving gives 8.5 and 7.5. The mode moves exactly like the median; it does not stay at 12.

Concept: Scaling and shifting move the median and mode together
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsWhen values change

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

For the lengths of a batch of bolts, the median is 14 mm and the mode is 12 mm. Each length is halved and then 3 mm is added. What are the new median and mode?

Explanation