Browsing as Guest. Progress, bookmarks and attempts are disabled.
Log in to track your work.
Feb/Mar 2023 p52 q1
2477
Each year the total number of hours, \(x\), of sunshine in Kintoo is recorded during the month of June. The results for the last 60 years are summarised in the table.
\(x\)
30 \(\leq x <\) 60
60 \(\leq x <\) 90
90 \(\leq x <\) 110
110 \(\leq x <\) 140
140 \(\leq x <\) 180
180 \(\leq x <\) 240
Number of years
4
8
14
25
7
2
(a) Draw a cumulative frequency graph to illustrate the data.
(b) Use your graph to estimate the 70th percentile of the data.
Solution
To draw the cumulative frequency graph, we first calculate the cumulative frequencies:
Upper value
60
90
110
140
180
240
cf
4
12
26
51
58
60
Plot these cumulative frequencies against the upper class boundaries on a graph.
For part (b), to find the 70th percentile, calculate:
\(60 \times 0.7 = 42\)
Locate 42 on the cumulative frequency axis and read across to the curve, then down to the \(x\)-axis to estimate the 70th percentile, which is approximately 126.