The curves show the waiting times, in minutes, of 100 customers at Shop X and 100 customers at Shop

Question

The curves show the waiting times, in minutes, of 100 customers at Shop X and 100 customers at Shop Y. - Find the median and the interquartile range of the waiting times at each shop. - Lina says, “Shop X’s curve is above Shop Y’s curve everywhere, so Shop X’s customers waited longer.” Explain whether you agree. - Find the percentage of customers at each shop who waited more than 20 minutes.

Accepted Answer

(a) X: median $10$ min, IQR $10$ min; Y: median $15$ min, IQR $10$ min (b) Disagree: the higher curve has more customers at or below each time, so Shop X’s customers waited less (median $10$ min against $15$ min). (c) X $10\%$ (accept $8\%$ to $12\%$), Y $25\%$ (accept $23\%$ to $27\%$)

Waiting times at two shops

Waiting times at two shops

Solution:

Solution locked