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}=(1*42+2*60+3*64+4*89+5*11+6*31)/(42+60+67+89+11+31)]()
which gives
![\begin{gathered} \operatorname{mean}=(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
then, the variance is 2.1003