Time taken ( seconds) | Frequency |
3 | |
8 | |
17 | |
12 | |
7 | |
3 | |
Total | 50 |
Time taken ( seconds) | Frequency |
3 | |
3 + 8 = 11 | |
11 + 17 = 28 | |
28 + 12 = 40 | |
40 + 7 = 47 | |
47 + 3 = 50 | |
Total | 50 |
A company is investigating the length of telephone alls customers make to its help centre.
The company randomly selects 100 phone calls from a particular day and the results are displayed in the cumulative frequency graph below.
Estimate the median, the lower quartile and the upper quartile.
There are 100 pieces of data, so .
So the median is the 50 ^{th} value, the lower quartile the 25 ^{th} value and the upper quartile the 75 ^{th} value.
Draw horizontal lines from these on the cumulative frequency axis until they hit the curve, then draw vertical lines down to the time of calls axis and take readings.
Median = 6.2 minutes (6 m 12 s)
Lower quartile = 4.2 minutes (4 m 12 s)
Upper quartile = 8.2 minutes (8 m 12 s)
There is no need to convert to minutes and seconds unless the question asks you to.
However, writing 6 m 2 s or 6 m 20 s would be incorrect.
The company is thinking of putting an upper limit of 12 minutes on calls to its help centre.
Estimate the number of these 100 calls would have been beyond this limit?
Draw a vertical line up from 12 minutes on the time of calls axis until it hits the curve.
Then draw a horizontal line across to the cumulative frequency axis and take a reading, in this case, 90.
This tells us that up to 12 minutes, 90 of the calls had been accounted for.
The question wants the number of calls that were greater than 12 minutes so subtract this from the total of 100.
100 - 90 = 10
10 (out of 100) calls were beyond the 12 minute limit