Verified Solution • 2025–26 Session moderate

QJEEM21Ma310e: JEE Main 2021 Mathematics - Class 11 JEEM21Ma310e Solution: The mean and standard deviation of 20 observations were…

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. if α\alpha and β\sqrt \beta are the mean and standard deviation respectively for correct data, then ( α\alpha , β\beta ) is :

Multiple Choice Options

  • A (11, 26)
  • B (10.5, 25)
  • C (11, 25)
  • D (10.5, 26)

Step-by-Step Verified Solution

Given :

Mean (x‾)=∑xi20=10(\overline x ) = {{\sum {{x_i}} } \over {20}} = 10

or Σ\Sigma xi = 200 (incorrect)

or 200 −- 25 + 35 = 210 = Σ\Sigma xi (Correct)

Now correct x‾=21020=10.5\overline x = {{210} \over {20}} = 10.5

again given S.D = 2.5 ( σ\sigma )

σ2=∑xi220−(10)2=(2.5)2{\sigma ^2} = {{\sum {{x_i}^2} } \over {20}} - {(10)^2} = {(2.5)^2}

or ∑xi2=2125\sum {{x_i}^2} = 2125 (incorrect)

or ∑xi2=2125−252+352\sum {{x_i}^2} = 2125 - {25^2} + {35^2}

= 2725 (correct)

∴\therefore correct σ2=272520−(10.5)2{\sigma ^2} = {{2725} \over {20}} - {(10.5)^2}

σ2{{\sigma } ^2} = 26

or σ\sigma = 26

∴\therefore α\alpha = 10.5, β\beta = 26

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