A test was marked out of 60. The marks have a mean of 45 and a standard deviation of 6…
Contributed by StemPy LabTry 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 . The marks have a mean of and a standard deviation of . The teacher first rescales every mark to be out of , by multiplying it by . Later she adds 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.
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The worked solution
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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.
Step 1. After the rescaling. The mean is and the standard deviation is .
Step 2. The coefficient of variation. . It equals the original , because multiplying by a constant does not change it.
Step 3. After the bonus. The mean is and the standard deviation stays . Then .
Answer: mean , standard deviation , CV after rescaling and after the bonus.
Watch out. Adding the bonus made the data look more consistent, although the marks are just as far apart. This is why the CV is used only for data with a true zero.
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