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A test is marked out of 50. The mean mark is 31 and the population standard deviation is 7 marks…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A test is marked out of 50. The mean mark is 31 and the population standard deviation is 7 marks. The teacher turns every mark into a percentage, then adds 4 to every percentage for a question that was badly printed. Find the new mean, the new standard deviation and the new variance.

Need a reminder? The key ideaShow

For $y = a + bx$ : the mean and the median follow the change; the SD, the IQR and the range are multiplied by $|b|$ ; the variance by $b^2$ . Adding a number never changes a spread.

\displaystyle \bar{y} = a + b\bar{x}

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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