ECZ 2015 · GCE Paper 2 · Question 12 — Statistics

Answer the whole of this question on graph paper. The heights of 56 plants, grown under experimental conditions, are given in the table below. Height in cmx ≤ 1010 < x ≤ 2020 < x ≤ 3030 < x ≤ 4040 < x ≤ 5050 < x ≤ 6060 < x ≤ 70Number of plants124613228

(a) Copy and complete the cumulative frequency table below. Height in cm≤ 10≤ 20≤ 30≤ 40≤ 50≤ 60≤ 70Number of plants1371356[1]

Verified working — step 1

Add each class frequency to the running total.

(b) Using a horizontal scale of 2 cm to represent a height of 10 cm and a vertical scale of 2 cm to represent 10 plants, draw a smooth cumulative frequency curve for these results.[3]

Verified working — step 1

Scale: horizontal 2 cm to 10 cm of height, vertical 2 cm to 10 plants.

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

(c(i)) the median,[2]

Verified working — step 1

The median sits at 562 = 28.

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

Verified working — step 1

Quartiles sit at 564 = 14 and 3 × 564 = 42.

(c(iii)) the 60th percentile.[1]

Verified working — step 1

The 60th percentile sits at 0.6 × 56 = 33.6.

(d) Plants with height 45 cm or more were classified as healthy. How many plants were healthy?[3]

Verified working — step 1

Read the cumulative frequency at height 45 cm: about 20 plants are shorter than 45 cm.

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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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