Question

If there are ten values each equal to 10, then standard deviation of these values is​

Answer 1

Answer:

If there are ten values each equal to 10, then standard deviation of these values is: O 100.

Answer 2

Standard deviation of these values is​ 0 if there are ten values each equal to 10

Given:

• There are ten values each equal to 10

To Find:

• Standard deviation

Solution:

$\overline{x} =\dfrac{\sum x_i}{N}$

$\sigma=\sqrt{\dfrac{\sum(x_i-\overline{x})^2}{N}$

σ = SD (Standard deviation)  , $\overline{x}=\text{mean}$

If all values are same then Standard deviation is 0

Hence  Standard deviation is 0

Step 1:

Calculate $\overline{x}=\text{mean}$

$\overline{x} =\dfrac{10+10+10+10+10+10+10+10+10+10}{10} = 10$

Step 2:

Calculate    $\sum(x_i-\overline{x})^2$

$x_i$          $x_i-\overline{x}$              $(x_i-\overline{x})^2$

10          10 - 10 = 0         0

10          10 - 10 = 0         0

10          10 - 10 = 0         0

10          10 - 10 = 0         0

10          10 - 10 = 0         0

10          10 - 10 = 0         0

10          10 - 10 = 0         0

10          10 - 10 = 0         0

10          10 - 10 = 0         0

10          10 - 10 = 0         0

            Sum                    0

Step 3:

Calculate SD

$\sigma=\sqrt{\dfrac{\sum(x_i-\overline{x})^2}{N}$

$\sigma=\sqrt{\dfrac{0}{10}$

σ =  0

Hence,  Standard deviation of these values is​ 0