JEE Main 2021MathematicsStatisticsMediumMCQ

JEE Main 2021 — Statistics Question with Solution

JEE Main 2021 (27 Jul Shift 2)

Question

Let the mean and variance of the frequency distribution

x: x1=2 x2=6 x3=8 x4=9
f: 4 4 α β

be 6 and 6.8 respectively. If x3 is changed from 8 to 7, then the mean for the new data will be:

Choose an option

Show full solutionCorrect option: C
Correct answer
C173

Step-by-step explanation

Given

x: x1=2 x2=6 x3=8 x4=9 Total
f: 4 4 α β 8+α+β
fx: 8 24 8α 9β 32+8α+9β
fx-x2: 64 0 4α 9β 64+4α+9β

x=∑i=14fixi∑i=14fi

32+8α+9β=8+α+β×6

⇒2α+3β=16       ...1

Also, for the variance, σ2=∑fixi-x2 i=1                       4                       ∑fi i=1    4      

64+4α+9β=8+α+β×6.8

⇒640+40α+90β=544+68α+68β

⇒28α-22β=96

⇒14α-11β=48     ...2

from 1&2

α=5&β=2

so, new mean =32+35+1815=8515=173

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About this question

This is a previous-year question from JEE Main 2021, 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.