3 Dwayne is a car salesman. The numbers of cars, \(x\), sold by Dwayne each month during the year 2008 are summarised by
$$n = 12 , \quad \Sigma x = 126 , \quad \Sigma x ^ { 2 } = 1582 .$$
- Calculate the mean and standard deviation of the monthly numbers of cars sold.
- Dwayne earns \(\pounds 500\) each month plus \(\pounds 100\) commission for each car sold. Show that the mean of Dwayne's monthly earnings is \(\pounds 1550\). Find the standard deviation of Dwayne's monthly earnings.
- Marlene is a car saleswoman and is paid in the same way as Dwayne. During 2008 her monthly earnings have mean \(\pounds 1625\) and standard deviation \(\pounds 280\). Briefly compare the monthly numbers of cars sold by Marlene and Dwayne during 2008.