The table below gives the ages, to the nearest 5 years of 50 people. Age in years 10 15 20 25 30 No of people 8 19 10 7 6 (a) Construct a cumulative frequen...
Question 1 Report
The table below gives the ages, to the nearest 5 years of 50 people.
| Age in years | 10 | 15 | 20 | 25 | 30 |
| No of people | 8 | 19 | 10 | 7 | 6 |
(a) Construct a cumulative frequency table for the distribution.
(b) Draw a cumulative frequency curve (Ogive)
(c) From your Ogive, find the : (i) median age ; (ii) number of people who are at most 15 years of age ; (iii) number of people who are between 20 and 25 years of age.
Answer Details
(a) Cumulative frequency table. Ages are given to the nearest 5 years, so the class boundaries are \(7.5\text{-}12.5,\ 12.5\text{-}17.5,\) etc.
| Age (nearest 5 yr) | Upper boundary | No. of people | Cumulative freq. |
|---|---|---|---|
| 10 | 12.5 | 8 | 8 |
| 15 | 17.5 | 19 | 27 |
| 20 | 22.5 | 10 | 37 |
| 25 | 27.5 | 7 | 44 |
| 30 | 32.5 | 6 | 50 |
(b) Plot cumulative frequency against upper class boundary and join with a smooth curve (ogive).
(c)(i) Median age. At \(\frac{N}{2} = 25\), reading across from the ogive:
\[\text{Median} = 12.5 + \frac{25 - 8}{19}\times 5 \approx 17 \text{ years}\](c)(ii) At most 15 years. Reading up from \(x = 15\): about 18 people.
(c)(iii) Between 20 and 25 years. Reading the ogive at 25 and at 20 and subtracting:
\[\approx 40.5 - 32 \approx 8 \text{ people}\]Download The App On Google Playstore
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