Question

The cumulative frequency diagram shows the times taken by the members of two different clubs, The Braineys and The Cleverities, to complete an intelligence test.
a) Find the median and the interquartile range for the Cleverities

b) State which club, on average, was slowest at completing the test. Give the reason for your answer.

Answer 1

Answer:

a) median= 25 mins

   interquartile range= 19mins

b) the braineys , because the braineys took 32mins on average and the cleverites took 25 mins on average which is 7 minutes more.

Step-by-step explanation:

a) find the median by going across the middle of the cumulative frequency (in this case, 40) until it hits the line (the cleverites) and move down to see the time in minutes. 25 mins.

to find the interquartile range, first find the lower quartile. So find the half of the median, or the quarter of the cumulative frequency ( 20) and go across until it hits the line and look down from that point to find the time ( 15 mins). Then, find the upper quartile by finding 3/4 or half+quarter of the cumulative frequency (60) and do the same with the line (34mins)

the interquartile is upper quartile - lower quartile  

34-15= 19 mins

interquartile= 19 mins.

b) the average is the same as the median, so find the median for the cleverites and the median for the braineys, which is 25 mins and 32 mins, therefore the braineys took longer, thus was the slowest at completing the test on average.