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Q.

Let the six numbers a1,a2,a3,a4,a5,a6 be in A.P and a1+a3=10. If the mean of these six numbers
is 192 and their variance is σ2 , then 8σ2 is equal to

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a

200

b

105

c

210

d

220

answer is C.

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Detailed Solution

detailed_solution_thumbnail

Given a1,a2,a3,a4,a5,a6 are in A.P 
Let T1=a1=a
Common difference =d
Also given a1+a3=10
a+a+2d=102a+2d=10 (1) 
Mean of six numbers is 192
a1+a2+a3+a4+a5+a66=192a+(a+d)+(a+2d)+(a+3d)+(a+4d)+(a+5d)=6×1926a+15d=3×192a+5d=19.(2)
 Eq. (1) \& (2) 3d=9d=3
 Also 2a+2(3)=102a=4a=2
 six numbers are 2, 5, 8, 11, 14, 17
Wkt variance =σ2=xi2nμ2
=22+52+82+112+142+17261922=4+25+64+121+196+28961922=699636141398108312=31512=1054σ2=10548σ2=8×1054=2×105=210

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