JEE Main 2021 — Statistics Question with Solution
From: JEE Main 2021 (Online) 16th March Evening Shift
Question
Consider the statistics of two sets of observations as follows :
If the variance of the combined set of these two observations is , then the value of n is equal to ___________.
| 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 , then the value of n is equal to ___________.
Enter your answer
Show full solutionCorrect answer: 5
Correct answer
5
Step-by-step explanation
For group - 1 :
For group - 2 :
Now, combined variance
17 (n2 + 20n + 100) = 9(n2 + 40n + 200)
8n2 20n 100 = 0
2n2 5n 25 = 0 n = 5
For group - 2 :
Now, combined variance
17 (n2 + 20n + 100) = 9(n2 + 40n + 200)
8n2 20n 100 = 0
2n2 5n 25 = 0 n = 5
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