Verified Solution • 2025–26 Session moderate

QJEEM21Ma20e2: JEE Main 2021 Mathematics - Class 11 JEEM21Ma20e2 Solution: The first of the two samples in a group has 100 items with mean …

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation 13.44\sqrt {13.44} , then the standard deviation of the second sample is :

Multiple Choice Options

  • A 8
  • B 6
  • C 4
  • D 5

Step-by-Step Verified Solution

n1 = 100

m = 250

X‾\overline X 1 = 15

X‾\overline X = 15.6

V1(x) = 9

Var(x) = 13.44

σ2=n1σ12+n2σ22n1+n2+n1n2(n1+n2)2(x‾1−x‾2)2{\sigma ^2} = {{{n_1}\sigma _1^2 + {n_2}\sigma _2^2} \over {{n_1} + {n_2}}} + {{{n_1}{n_2}} \over {{{({n_1} + {n_2})}^2}}}{({\overline x _1} - {\overline x _2})^2}

n2 = 150, x‾2{\overline x _2} = 16, V2(x) = σ\sigma 2

13.44=100×9+150×σ22250+100×150(250)2×113.44 = {{100 \times 9 + 150 \times \sigma _2^2} \over {250}} + {{100 \times 150} \over {{{(250)}^2}}} \times 1

⇒\Rightarrow σ22{\sigma _2}^2 = 16 ⇒\Rightarrow σ\sigma 2 = 4

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