JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Statistics

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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

, then the standard deviation of the second sample is :

(A)4✓ Correct
(B)6
(C)5
(D)8

Answer: (A)

Solution

The second sample has

n_{2} = 250 - 100 = 150

items. The combined mean gives

250 (15.6) = 100 (15) + 150 \overset{x}{ˉ}_{2}

, so

\overset{x}{ˉ}_{2} = 16

. The two sample means deviate from the group mean by

d_{1} = 15 - 15.6 = - 0.6

and

d_{2} = 16 - 15.6 = 0.4

. The combined variance satisfies

250 (13.44) = 100 (3^{2} + 0.36) + 150 (σ_{2}^{2} + 0.16)

3360 = 936 + 24 + 150 σ_{2}^{2}

, giving

σ_{2}^{2} = 16

. The standard deviation of the second sample is

4

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option

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