Question

standard deviation of four number 9,11,13,15​

Answer 1

Answer:

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Answer 2

The standard deviation of the four numbers is 2.52.

Procedure:

Given:

Numbers: 9, 11, 13, 15

Number of values = n = 4

To Find:

Standard Deviation, s

Formulas used:

$\bar{x}=\frac{\sum(x)}{n}$

Here, $\bar x$ is the mean of the data set

         $x$ is a data member of the given set

         $n$ is the number of data members

$s=\sqrt{ \frac{\sum(x-\bar x)^{2} }{n-1}$

Here, $s$ is the standard deviation

         $\bar x$ is the mean of the data set

         $x$ is a data member of the given set

         $n$ is the number of data members

Step by Step Explanation:

1. The mean of the data set is given by
   $\bar x = \frac{9+11+13+15}{4} = \frac{48}{4} = 12$
2. Now, the standard deviation can be calculated as
   $s=\sqrt{\frac{(9-12)^2+(11-12)^2+(13-12)^2+(15-12)^2}{4-1} }$
   Here, we have substituted the real values in the formula.
3. After simplifying the above, we get
   $s=\sqrt{\frac{3^2+1^2+1^2+3^2}{3} }$
4. On further simplification, we get
   $s = \sqrt{\frac{9+1+1+9}{3} } =\sqrt{\frac{20}{3} }$
5. We use a calculator to solve this and get
   $s=2.5189\approx2.52$

Hence, the standard deviation of the four numbers is 2.52.