ECZ 2014 · O-Level Paper 2 · Question 8 — Statistics

A bag containing 250 potatoes was supplied to a supermarket. Each of the potatoes was weighed to the nearest gram and the results were as shown in the table below. Mass in g50 < x ≤ 100100 < x ≤ 150150 < x ≤ 200200 < x ≤ 250250 < x ≤ 300300 < x ≤ 350Number of potatoes53065105405

(a) Copy and complete the cumulative frequency table below. Mass in g≤50≤100≤150≤200≤250≤300≤350Number of potatoes0535250[1]

Verified working — step 1

Add each class frequency to the running total.

(b) Using a scale of 2 cm to represent 50 grams on the x-axis and 4 cm to represent 50 potatoes on the y-axis, draw a smooth cumulative frequency curve.[3]

Verified working — step 1

Scale: x-axis 2 cm to 50 g, y-axis 4 cm to 50 potatoes.

(c) Showing your method clearly, use your graph to estimate

(c(i)) the median mass,[1]

Verified working — step 1

The median is the 125th value (2502).

(c(ii)) the interquartile range,[2]

Verified working — step 1

Quartiles sit at 2504 = 62.5 and 3 × 2504 = 187.5.

(c(iii)) the 60th percentile.[2]

Verified working — step 1

The 60th percentile sits at 0.60 × 250 = 150.

(d) Potatoes weighing between 180 g and 290 g are graded 'B'. Use your graph to estimate the number of grade 'B' potatoes.[3]

Verified working — step 1

Read the cumulative frequency at 180 g: about 74.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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