Question

Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number, the variance of the numbers so obtained is

(a) 6.5 (b) 2.87 (c) 3.87 (d) 8.25

Answer 1

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

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

2, 3, 4, 5, 6, 7, 8, 9, 10, 11

Now,

$\sum _{}{x}_i=2+3+4+5+6+7+8+9+10+11=65$

$\sum _{}{x}_i^2=4+9+16+25+36+49+64+81+100+121=505$

∴ Variance of the numbers so obtained

$$\begin{gathered} =\frac{\sum _{}{x}_i^2}{10}-{\left(\frac{\sum _{}{x}_i}{10}\right)}^2 \\ =\frac{505}{10}-{\left(\frac{65}{10}\right)}^2 \\ =50.5-42.25 \\ =8.25 \end{gathered}$$

Hence, the correct answer is option (d).