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Question

Consider the first 10 positive integers. If we multiply each number by -1 and then add 1 to each number, the variance of the numbers so obtained is


A

8.25

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B

6.5

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C

3.87

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D

2.87

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Solution

The correct option is A

8.25


The first 10 positive integers are 1,2,3,4,5,6,7,8,9,10

Multiplying each number by -1, we get

-1, -2, -3, -4, -5, -6, -7, -8, -9, -10

Adding 1 to each of these numbers, we get

0, -1, -2, -3, -4, -5, -6, -7, -8, -9,

Now,

xi=0+(1)+(2)+(3)+(4)+(5)+(6)+(7)+(8)+(9)=45

x2i=0+1+4+9+16+25+36+49+64+81=225

Variance of the obtained numbers.

=x2i10(xi10)2

=28510(4510)2

=28.520.25=8.25

Hence, the correct answer is option (a).


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