Question

Consider the numbers 1,2,34,5,67,8,9,10. If 1 is added to each numbers, the variance of the numbers so obtained is

• A. 6.5
• B. 2.87
• C. 3.87
• D. 8.25

Answer 1

The correct option is D

8.25

The given numbers are 1,2,3,4,5,6,7,8,9,10

If 1 is added to each numbers, then the new numbers obtained are :

2,34,5,6,7,8,9,10,11

Now,

$\sum x_i=2+3+4+5+6+7+8+9+10+11=65$

$\sum x_i^2=4+9+16+25+36+49+64+81+100+121=505$

$\therefore$ Variance of the numbers so obtained.

= $\frac{\sum x_i^2}{10}-{\left(\frac{\sum x_i}{10}\right)}^2$

$=\frac{505}{10}-{\left(\frac{65}{10}\right)}^2$
= 50.5- 42.25 = 8.25

Hence, the correct answer is option (d).