EasyMathematicsHigh School (11–12)Statistics and ProbabilityNumerical

A school has two classes taking the same test…

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

A school has two classes taking the same test. Class A has $45$ students with a mean mark of $62$ . Class B has $35$ students with a mean mark of $70$ . The head teacher wants the mean mark of all the students. A colleague suggests simply averaging the two class means. Find the mean of all $80$ students, and say by how much the colleague's answer is wrong.

Need a reminder? The key ideaShow

$\bar{x} = \dfrac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1 + n_2}$ and $\sigma^2 = \dfrac{n_1\left(\sigma_1^2 + d_1^2\right) + n_2\left(\sigma_2^2 + d_2^2\right)}{n_1 + n_2}$ , where $d_i = \bar{x}_i - \bar{x}$ . To correct a reading, change $\sum x$ and $\sum x^2$ .

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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