The table below shows the number of eggs laid by the chickens in a man's farm in a year. No of eggs per year No of chickens 45 - 49 10 50 - 54 36 55 - 59 64...
Question 1 Report
The table below shows the number of eggs laid by the chickens in a man's farm in a year.
| No of eggs per year | No of chickens |
| 45 - 49 | 10 |
| 50 - 54 | 36 |
| 55 - 59 | 64 |
| 60 - 64 | 52 |
| 65 - 69 | 28 |
| 70 - 74 | 10 |
(a) Draw a cumulative frequency curve for 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?
Answer Details
(a) Cumulative frequency table
| Number of eggs per year | Class boundaries | Frequency | Cumulative frequency |
|---|---|---|---|
| 45 - 49 | 44.5 - 49.5 | 10 | 10 |
| 50 - 54 | 49.5 - 54.5 | 36 | 46 |
| 55 - 59 | 54.5 - 59.5 | 64 | 110 |
| 60 - 64 | 59.5 - 64.5 | 52 | 162 |
| 65 - 69 | 64.5 - 69.5 | 28 | 190 |
| 70 - 74 | 69.5 - 74.5 | 10 | 200 |
The total number of chickens is \(N=200\). Plot the upper class boundaries against the cumulative frequencies, beginning with \((44.5,0)\), and join the points with a smooth curve.
(b) Interquartile range
\[Q_1=\frac{N}{4}=\frac{200}{4}=50,\qquad Q_3=\frac{3N}{4}=\frac{3(200)}{4}=150.\]
From the cumulative frequency curve, the corresponding egg numbers are approximately \(Q_1=54\) and \(Q_3=63\).
\[\text{Interquartile range}=Q_3-Q_1=63-54=9\text{ eggs}.\]
(c) Chickens laying at least \(60\) eggs per year:
\[52+28+10=90.\]
\[P(\text{at least }60\text{ eggs})=\frac{90}{200}=\frac{9}{20}=0.45.\]
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