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.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question