HardMathematicsHigh School (11–12)Statistics and ProbabilityNumerical

A teacher marks five short tests out of 10…

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

A teacher marks five short tests out of $10$ . She remembers that the mean of the five marks was $4.4$ and the variance was $8.24$ . She also remembers that three of the marks were $1$ , $2$ and $6$ , but the other two marks were written on a sheet that she lost. Every mark is a whole number. The teacher wants to rebuild the full list before she reports the results to the head of department. She decides to use the total of the marks and the total of the squares of the marks. These two totals follow from the mean and the variance, and they are enough to find the two missing marks. Find the sum of the two missing marks, the sum of their squares, and the two marks.

Need a reminder? The key ideaShow

$\sigma^2 = \dfrac{\sum f x^2}{N} - \bar{x}^2$ and $\sigma = \sqrt{\sigma^2}$ . For a sample, divide the sum of squared deviations by $n - 1$ to get $s^2$ .

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.

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