JEE Main 2020 — Statistics Question with Solution
From: JEE Main 2020 (Online) 7th January Evening Slot
Question
If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively,
then x.y is equal to _______.
Enter your answer
Show full solutionCorrect answer: 54
Correct answer
54
Step-by-step explanation
Mean = = 10
16 = x + y ....(1)
Variance () = 25
- 100 = 25
125 × 8 = 9 + 49 + 81 + 144 + 169 + 400 + x2 + y2 - 800
x2 + y2 = 148
We know, (x + y)2 = x2 + y2 + 2xy
256 = 148 + 2xy
x.y = 54
16 = x + y ....(1)
Variance () = 25
- 100 = 25
125 × 8 = 9 + 49 + 81 + 144 + 169 + 400 + x2 + y2 - 800
x2 + y2 = 148
We know, (x + y)2 = x2 + y2 + 2xy
256 = 148 + 2xy
x.y = 54
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This is a previous-year question from JEE Main 2020, covering the Statistics chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.