ZIMSEC O-Level Statistics Question Paper

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This is the ZIMSEC O-Level Statistics question paper. Use it for exam practice under timed conditions.

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Question 1
11 Answer the whole of this question on a single sheet of graph paper.
The table shows the masses of 40 babies born in one month at a district hospital.

 Mass $\mathrm{m}(\mathrm{kg})$  |  $\mathrm{m} \leq 2,1$  |  $2,1<\mathrm{m} \leq 2,5$  |  $2,5<\mathrm{m} \leq 3,0$  |  $3,0<\mathrm{m} \leq 3,5$  |  $3,5<\mathrm{m} \leq 4,0$  |  $4,0<\mathrm{m} \leq 4,5$  |  $4,5<\mathrm{m} \leq 5,0$
 Frequency  |  0  |  3  |  7  |  12  |  14  |  3  |  1

Cumulative
frequency
  |  0  |  3  |  $x$  |  $y$  |  36  |  z  |  40

(a) Find the values of $x, y$ and $z$.

[2]
(b) Using a scale of 2 cm to represent 5 units on the vertical axis and 4 cm to represent 1 unit on the horizontal axis, draw the cumulative frequency curve for the given data.

[3]
(c) Use your graph to estimate the median mass.

[2]
(d) If two babies are chosen at random, find the probability that both weighed more than $2,5 \mathrm{~kg}$ but less than or equal to $3,5 \mathrm{~kg}$.

[2]
(e) Calculate the mean mass of the babies for the month.

[3]