JEE Main 2021 — Statistics 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 :
\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 =
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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