wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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 (b) 6.5 (c) 3.87 (d) 2.87

Open in App
Solution

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

xi2=0+1+4+9+16+25+36+49+64+81=285

∴ Variance of the obtained numbers

=xi210-xi102=28510--45102=28.5-20.25=8.25

Hence, the correct answer is option (a).

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Sum of Consecutive Numbers
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon