JEE Main 2023MathematicsStatisticsEasyNumerical

JEE Main 2023 — Statistics Question with Solution

JEE Main 2023 (08 Apr Shift 1)

Question

Let the mean and variance of 8 numbers x, y, 10, 12, 6,12, 4, 8 be 9 and 9.25 respectively. If  x>y, then 3x-2y is equal to _______

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Show full solutionCorrect answer: 25
Correct answer
25

Step-by-step explanation

Given, the data x, y, 10, 12, 4, 6, 8, 12.

So,

Mean=x+y+10+12+4+6+8+128

⇒9=x+y+528

⇒x+y+52=72

⇒x+y=20

And,

Variance=∑xi2n-∑xin2

⇒9.25=x2+y2+100+144+16+36+64+1448-92

⇒x2+y2=218

⇒x+y2-2xy=218

⇒202-2xy=218

⇒2xy=182

⇒xy=91

Now solving x+y=20 & xy=91 we get,

x=13, y=7⇒3x-2y=25

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About this question

This is a previous-year question from JEE Main 2023, 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.