Theory question 112
Data PresentationThe table below shows the number of eggs laid by chicken in a man's farm in a year.
No. of Eggs Per Year: 45–49, 50–54, 55–59, 60–64, 65–69, 70–74
No. of Chicken: 10, 36, 64, 52, 28, 10
(a) Draw a cumulative frequency curve of the distribution. (b) Use your graph to find the interquartile range. (c) If a woman buys a chicken from the farm, what is the probability that the chicken lays at least 60 eggs in a year?
Show the model answer
(a) Upper class boundaries 49.5, 54.5, 59.5, 64.5, 69.5, 74.5 with cumulative frequencies 10, 46, 110, 162, 190, 200; plot (44.5, 0) and these points and draw a smooth curve.
(b) Q1 at 50th chicken ≈ 54.5 + 4/64 × 5 ≈ 54.8; Q3 at 150th ≈ 59.5 + 40/52 × 5 ≈ 63.3. Interquartile range ≈ 63.3 − 54.8 ≈ 8.5 (accept values read from the graph).
(c) Chickens laying 60 or more eggs = 52 + 28 + 10 = 90, so P = 90/200 = 9/20 = 0.45.
For quartiles of 200 items, read across at 50 and 150 on the cumulative frequency axis.