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प्रश्न
The median of the distribution given below is 14.4 . Find the values of x and y , if the total frequency is 20.
| Class interval : | 0-6 | 6-12 | 12-18 | 18-24 | 24-30 |
| Frequency : | 4 | x | 5 | y | 1 |
उत्तर
The given series is in inclusive form. Converting it to exclusive form and preparing the cumulative frequency table, we have
| Class interval | Frequency (fi) | Cumulative Frequency (c.f.) |
| 0–6 | 4 | 4 |
| 6–12 | x | 4 + x |
| 12–18 | 5 | 9 + x |
| 18–24 | y | 9 + x + y |
| 24–30 | 1 | 10 + x + y |
| 10 + x + y = 20 |
Median = 14.4
It lies in the interval 12–18, so the median class is 12–18.
Now, we have
\[l = 12, h = 6, f = 5, F = 4 + x, N = 20\]
We know that
Median `= l + {(N/2 - F)/f} xx h `
\[14 . 4 = 12 + \frac{6 \times \left( 10 - 4 - x \right)}{5}\]
\[ \Rightarrow 12 = 36 - 6x\]
\[ \Rightarrow 6x = 24\]
\[ \Rightarrow x = 4\]
Now,
10 + x + y = 20
\[\Rightarrow x + y = 10\]
\[ \Rightarrow y = 10 - 4 = 6\]
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