JEE Main 2023 · 10 April · morning · Numerical answer · +4 / −0
If the mean of the frequency distribution
is 28, then its variance is __________.
| Class : | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|---|---|---|---|---|---|
| Frequency : | 2 | 3 | x | 5 | 4 |
Answer and solution
Answer 151
Solution
Maths sir · 3 steps
Use the mean of 28 to find x first, then take squared deviations from 28 at each class mark.
- Set up the mean. The class marks are 5, 15, 25, 35 and 45. So Σ f = 14 + x and Σ f m = 10 + 45 + 25x + 175 + 180 = 410 + 25x.
- Find x. The mean is 28, so 410 + 25x = 28(14 + x) = 392 + 28x. This gives 3x = 18, so x = 6 and the total frequency is N = 20.
Class mark m f m - 28 f(m - 28)² 5 2 -23 2 × 529 = 1058 15 3 -13 3 × 169 = 507 25 6 -3 6 × 9 = 54 35 5 7 5 × 49 = 245 45 4 17 4 × 289 = 1156 Total 20 — 3020 σ² = (Σ f (m - x̄)²)/(Σ f) = 3020/20
- So. The variance is 3020/20 = 151.
The idea to keep. When a frequency is missing, the given mean is your equation for it. Once you know it, take deviations from that same mean, because a whole-number mean keeps the squares easy.
Answer from the NTA final answer key. Solution by PrepWiser.