Question

The following table shows the numbers that were rolled with adie during a game.

Answer 1

Part a.

The mean is the average of all numbers. From the given table, we can see that the number 1 ocurrs 42 times, the number 2 ocurrs 60 times and so on. Then, the mean of the given numbers is

$\operatorname{mean}=\frac{1\times42+2\times60+3\times64+4\times89+5\times11+6\times31}{42+60+67+89+11+31}$

which gives

$\begin{gathered} \operatorname{mean}=\frac{960}{300} \\ \operatorname{mean}=3.2 \end{gathered}$

so the mean is 3.2

Part b.

The sample variance formula is given by:

$S^2=\frac{\sum ^{\infty}_{n\mathop=0}f\cdot(x-\operatorname{mean})^2}{n-1}$

where f is the frequency and n-1=299

So, by substituting the given values, we have

$\begin{gathered} S=\frac{628}{299} \\ S\questeq2.1003 \end{gathered}$

then, the variance is 2.1003