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Question
The following is the frequency distribution with unknown frequencies :
| Class | 60-70 | 70-80 | 80-90 | 90-100 | Total |
| frequency | `"a"/2` | `(3"a")/2` | 2a | a | 50 |
Find the value of a, hence find the frequencies. Draw a histogram and frequency polygon on the same coordinate system.
Solution
Total frequency = 50
∴ `a/2 + (3a)/2 + 2a + a = 50`
⇒ `(a + 3a + 4a + 2a)/2 = 50`
⇒ `(10a)/2 = 50`
⇒ `a = (50 xx 2)/10`
⇒ a = 10
∴ `a/2 = 10/2 = 5`
`(3a)/2 = (3 xx 10)/2 = 15`
2a = 2 × 20 = 40
a = 10
Hence the total would be represented as given below:
| Class | 60-70 | 70-80 | 80-90 | 90-100 | Total |
| frequency | 5 | 15 | 20 | 10 | 50 |
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