Data presentation and interpretation

The times, in minutes, that 40 customers spent in a shop are summarised below.

Time, t (min)	0 ≤ t < 10	10 ≤ t < 20	20 ≤ t < 30	30 ≤ t < 60
Frequency	8	14	10	8

(a) Use linear interpolation to estimate the median. (b) A histogram is drawn. Find the frequency density for the class 30 ≤ t < 60. (c) Estimate the mean time.

For 10 days, a café recorded the maximum temperature, x °C, and the number of cold drinks sold, y. The temperatures ranged from 10 °C to 30 °C. The regression line of y on x is y = 12.5 + 3.2x and the product moment correlation coefficient is 0.87. (a) Interpret the value 3.2 in context. (b) Estimate the number of cold drinks sold on a day with a maximum temperature of 25 °C, and comment on the reliability of your estimate. (c) Explain why the line should not be used to estimate sales when x = 40. (d) Test, at the 5% level, whether there is evidence of positive correlation. (One-tailed critical value for n = 10: 0.5494.)