The histogram below summarises the times, in minutes, that 200 people spent

shopping in a supermarket

Frequency

density

Time in minutes

11 21 26 31 36 41 51 71

(i) Give a reason to justify the use of a histogram to represent these date.

(ii) Given that 40 people spent between 11 and 21 minutes shopping in the super-

market, estimate the number of people that spent between 18 and 25 minutes

shopping in the supermarket.

(iii) Given that 40 people spent between 11 and 21 minutes shopping in the super-

market, estimate the median time spent shopping in the supermarket by these

200 people.

(iv) The mid-point of each bar is represented by x and the corresponding frequency

by f. Show that

fx = 6390

Given that

fx2 = 238430, for the data shown in the histogram, calculate

estimates of the mean and the standard deviation.

(vi) The manager of the supermarket decides to model these data with a normal distribution. Comment on the manager's decision. Justify your answer