    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 =28.5−20.25=8.25 Hence, the correct answer is option (a).  Suggest Corrections  8      Similar questions
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