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Question

The mean and standard deviation of marks of 10 students in a class test of 10 marks is 7 and 1 respectively. The marks of A is not known and the standard deviation of the remaining 9 students is 0. If A does not score full marks, then the marks of A is

A
2
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B
4
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C
6
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D
8
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Solution

The correct option is B 4
¯¯¯x=7
Total marks of 10 students,
xi=10¯¯¯x=70

σ=1
x2i1072=1x2i=500

Let A scored x marks.
Now, the mean of the remaining students is, 70x9
and the standard deviation is,
500x29(70x9)2=09(500x2)=(70x)245009x2=4900+x2140x10x2140x+400=0x214x+40=0(x4)(x10)=0x=4,10
As A does not score full marks,
hence, the marks scored by A is 4.

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