9709 P53 - Nov 2023 - Q4 - 10 marks
2422
The weights, \(x\) kg, of 120 students in a sports college are recorded. The results are summarised in the following table.
| Weight \(x\) (kg) | \(x\le40\) | \(x\le60\) | \(x\le65\) | \(x\le70\) | \(x\le85\) | \(x\le100\) |
|---|---|---|---|---|---|---|
| Cumulative frequency | 0 | 14 | 38 | 60 | 106 | 120 |
(a) Draw a cumulative frequency graph to represent this information. [2]
(b) It is found that 35% of the students weigh more than \(W\) kg. Use your graph to estimate the value of \(W\). [2]
(c) Calculate estimates for the mean and standard deviation of the weights of the 120 students. [6]
