JEE PYQ: Statistics Question 2
Question 2 - 2021 (16 Mar Shift 2)
Consider the statistics of two sets of observations as follows:
| Size | Mean | Variance | |
|---|---|---|---|
| Observation I | 10 | 2 | 2 |
| Observation II | $n$ | 3 | 1 |
If the variance of the combined set of these two observations is $\frac{17}{9}$, then the value of $n$ is equal to ____.
Show Answer
Answer: 5
Solution
Using combined variance formula: $\frac{17}{9} = \frac{(n+20)(n+10)+10n}{(n+10)^2}$. Solving: $2n^2 - 5n - 25 = 0$, $(2n+5)(n-5) = 0$, so $n = 5$.
BETA
