ECZ 2011 · O-Level Paper 2 · Question 10 — Statistics

The table below shows the masses of 100 babies at birth, recorded at a hospital. Mass x kg1.5 < x ≤ 2.02.0 < x ≤ 2.52.5 < x ≤ 3.03.0 < x ≤ 3.53.5 < x ≤ 4.04.0 < x ≤ 4.54.5 < x ≤ 5.0Number of babies312202425142

(a) Copy and complete the cumulative frequency table below. Mass x kg≤1.5≤2.0≤2.5≤3.0≤3.5≤4.0≤4.5≤5.0Frequency0315100[2]

Verified working — step 1

Add each class frequency to the running total.

(b) Using a horizontal scale of 2 cm to represent 0.5 kg for masses from 1.5 kg to 5.0 kg and a vertical scale of 2 cm to represent 10 babies, draw a smooth cumulative frequency curve.[3]

Verified working — step 1

Scale: horizontal 2 cm to 0.5 kg (1.5 to 5.0), vertical 2 cm to 10 babies.

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

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

Verified working — step 1

The median sits at 1002 = 50.

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

Verified working — step 1

Quartiles sit at 1004 = 25 and 3 × 1004 = 75.

(c(iii)) the 40th percentile.[1]

Verified working — step 1

The 40th percentile sits at 0.40 × 100 = 40.

(d) How many babies weighed more than 4.3 kg?[3]

Verified working — step 1

At 4.3 kg the cumulative frequency is 84 + (0.30.5) x 14 = 92.4.

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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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