JEE Main 2021MathematicsStatisticsCalculation Of Standard Deviation Variance And Mean Deviation Of Grouped And Ungrouped DatamediumMCQ

JEE Main 2021Statistics Question with Solution

From: JEE Main 2021 (Online) 27th July Evening Shift

Question

Let the mean and variance of the frequency distribution

\matrix{ {x:} & {{x_1} = 2} & {{x_2} = 6} & {{x_3} = 8} & {{x_4} = 9} \cr {f:} & 4 & 4 & \alpha & \beta \cr }

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
C

Step-by-step explanation

Given 32 + 8 + 9 = (8 + + ) 6

2 + 3 = 16 ..... (i)

Also, 4 16 + 4 + 9 = (8 + + ) 6.8

640 + 40 + 90 = 544 + 68 + 68

28 22 = 96

14 11 = 48 ..... (ii)

from (i) & (ii)

= 5 & = 2

So, new mean =

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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.