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

विकल्प

•  6.5  

• 2.87   

•  3.87  

• 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

\[= \frac{\sum_{} x_i^2}{10} - \left( \frac{\sum_{} x_i}{10} \right)^2 \]

\[ = \frac{505}{10} - \left( \frac{65}{10} \right)^2 \]

\[ = 50 . 5 - 42 . 25\]

\[ = 8 . 25\]