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Question
Calculate the missing frequency form the following distribution, it being given that the median of the distribution is 24
| Age (in years) | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Number of persons |
5 | 25 | ? | 18 | 7 |
Solution
Let the missing frequency be x.
To find the median let us put data in the table given below:
| Age (in years) | Number of persons (f) | Cumulative frequency (cf) |
| 0-10 | 5 | 5 |
| 10-20 | 25 | 30 |
| 20-30 | x | 30+x |
| 30-40 | 18 | 48+x |
| 40-50 | 7 | 55+x |
The given median is 24,
∴ the median class is 20-30.
∴ / = 20, ℎ = 10, 𝑁 = 55 + 𝑥, 𝑓 = 𝑥 𝑎𝑛𝑑 𝑐𝑓 = 30
𝑀𝑒𝑑𝑖𝑎𝑛 = 𝑙 +`((N/2 -cf)/f) xx h`
⇒ 24= 20 + `(((55+x)/2-30)/x) xx 10`
⇒`24-20 = ((55+x-60)/(2x))xx 10`
`⇒ 4= ((x-5)/(2x)) xx 10`
⟹ 8𝑥 = 10𝑥 − 50
⟹ 2𝑥 = 50
⟹ 𝑥 = 25
Thus, the missing frequency is 25.
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