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A test was marked out of 60. The marks have a mean of 45 and a standard deviation of 6…

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

A test was marked out of $60$ . The marks have a mean of $45$ and a standard deviation of $6$ . The teacher first rescales every mark to be out of $100$ , by multiplying it by $\dfrac{5}{3}$ . Later she adds $5$ bonus marks to every rescaled mark. She wants to know how the mean, the standard deviation and the coefficient of variation change at each stage. Find the new mean and the new standard deviation after the rescaling, the coefficient of variation after the rescaling, and the coefficient of variation after the bonus.

Need a reminder? The key ideaShow

$\text{CV} = \dfrac{\sigma}{\bar{x}} \times 100\%$ , and the smaller CV is the more consistent. For $y = a x + b$ : $\bar{y} = a\bar{x} + b$ and $\sigma_y = \lvert a \rvert\,\sigma_x$ .

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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