Data relating to the lifetimes (to the nearest hour) of a random sample of 200 light bulbs from the production line of a manufacturer were summarised in a group frequency table. The mid-point of each group in the table were represented by x and the corresponding frequency for that group by f.



The data were then coded using y = (x-755.0) / 2.5 and summarised as follows:

(Sigma)fy = -467, (sigma)fy^2 = 9179



A) calculate estimates of the mean and the standard deviation of the lifetimes of this sample of bulbs.



An estimate of the interquartile range for these data was 27.7 hours.



B) explain, giving a reason, whether you would recommend the manufacturer to use the interquartile range or the standard deviation to represent the spread of lifetimes of the bulbs from this production line.