1.

Consider the first 10 positive integers. If we multiply each numbers by -1 and then add 1 to each number, the variance of the numbers so obtained is A. 8.25 B. 6.5C. 3.87 D. 2.87

Answer»

Consider 10 positive integer 

Let Assume, 1,2,3,4,5,6,7,8,9,10 

Now, If we multiply by -1 in each number we get, 

-1,-2,-3,-4,-5,-6,-7,-8,-9,-10 

And then we add 1 in each number 

0,-1,-2,-3,-4,-5,-6,-7,-8,-9 

Now,

XiX2i
00
-11
-24
-39
-416
-525
-636
-749
-864
-981
 Σxi = - 45 Σx2i = 285

Standard deviation Variance = \(\Big(\frac{\Sigma x^2_i}{N} - \Big(\frac{\Sigma x_i}{N}\Big)^2\Big)\)  

Variance = \(\Big(\frac{285}{10} - \Big(\frac{-45}{10}\Big)^2\Big)\) 

Variance = (28.5 - 20.25)

Var = 8.25

Hence, variance is 8.25


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