Standard Deviation - Statistics

Card 0 of 4

Calculate the standard deviation of the following data set:

$3, 7, 2, 9, 8, \textup{and }10$

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The standard deviation is found by using the following formula:

$s=$\sqrt{\frac{\sum \left| x-\bar{x}$\right $|^2$}{n}}$

We will start by identifying the components of this equation:

$\sum=\textup{sum}$

$x=\textup{variable in the data set}$

$\bar{x}=\textup{mean of the data set}$

$n=\textup{total number of variables in the data set}$

Now, we can use this information to calculate the standard deviation.

First, we need to identify and $\bar{x}$ . There are six variables in the data set; therefore, we can write the following:

Next, we need to calculate the mean:

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

$\bar{x}=\frac{3+7+2+9+8+10}{6}$$

$\bar{x}=\frac{39}{6}$$

$\bar{x}=6.5$

Second, we need to find the square of the absolute of each variable minus the mean: $\left| x-\bar{x}\right $|^2$$

$\textup{For 3}=\left| 3-6.5\right $|^2$=12.25$

$\textup{For 7}=\left| 7-6.5\right $|^2$=0.25$

$\textup{For 2}=\left| 2-6.5\right $|^2$=20.25$

$\textup{For 9}=\left| 9-6.5\right $|^2$=6.25$

$\textup{For 8}=\left| 8-6.5\right $|^2$=2.25$

$\textup{For 10}=\left| 10-6.5\right $|^2$=12.25$

Last, let's substitute these values into the standard deviation formula and solve.

$s=$\sqrt{\frac{\sum \left | x-\bar{x}$\right $|^2$}{n}}$

$s=$\sqrt{\frac{(12.25+0.25+20.25+6.25+2.25+12.25)}{6}$}$

$s=$\sqrt{\frac{53.5}{6}$}$

Solve.

Calculate the standard deviation of the following data set:

$3, 7, 2, 9, 8, \textup{and }10$

Tap to see back →

The standard deviation is found by using the following formula:

$s=$\sqrt{\frac{\sum \left| x-\bar{x}$\right $|^2$}{n}}$

We will start by identifying the components of this equation:

$\sum=\textup{sum}$

$x=\textup{variable in the data set}$

$\bar{x}=\textup{mean of the data set}$

$n=\textup{total number of variables in the data set}$

Now, we can use this information to calculate the standard deviation.

First, we need to identify and $\bar{x}$ . There are six variables in the data set; therefore, we can write the following:

Next, we need to calculate the mean:

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

$\bar{x}=\frac{3+7+2+9+8+10}{6}$$

$\bar{x}=\frac{39}{6}$$

$\bar{x}=6.5$

Second, we need to find the square of the absolute of each variable minus the mean: $\left| x-\bar{x}\right $|^2$$

$\textup{For 3}=\left| 3-6.5\right $|^2$=12.25$

$\textup{For 7}=\left| 7-6.5\right $|^2$=0.25$

$\textup{For 2}=\left| 2-6.5\right $|^2$=20.25$

$\textup{For 9}=\left| 9-6.5\right $|^2$=6.25$

$\textup{For 8}=\left| 8-6.5\right $|^2$=2.25$

$\textup{For 10}=\left| 10-6.5\right $|^2$=12.25$

Last, let's substitute these values into the standard deviation formula and solve.

$s=$\sqrt{\frac{\sum \left | x-\bar{x}$\right $|^2$}{n}}$

$s=$\sqrt{\frac{(12.25+0.25+20.25+6.25+2.25+12.25)}{6}$}$

$s=$\sqrt{\frac{53.5}{6}$}$

Solve.

Calculate the standard deviation of the following data set:

$3, 7, 2, 9, 8, \textup{and }10$

Tap to see back →

The standard deviation is found by using the following formula:

$s=$\sqrt{\frac{\sum \left| x-\bar{x}$\right $|^2$}{n}}$

We will start by identifying the components of this equation:

$\sum=\textup{sum}$

$x=\textup{variable in the data set}$

$\bar{x}=\textup{mean of the data set}$

$n=\textup{total number of variables in the data set}$

Now, we can use this information to calculate the standard deviation.

First, we need to identify and $\bar{x}$ . There are six variables in the data set; therefore, we can write the following:

Next, we need to calculate the mean:

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

$\bar{x}=\frac{3+7+2+9+8+10}{6}$$

$\bar{x}=\frac{39}{6}$$

$\bar{x}=6.5$

Second, we need to find the square of the absolute of each variable minus the mean: $\left| x-\bar{x}\right $|^2$$

$\textup{For 3}=\left| 3-6.5\right $|^2$=12.25$

$\textup{For 7}=\left| 7-6.5\right $|^2$=0.25$

$\textup{For 2}=\left| 2-6.5\right $|^2$=20.25$

$\textup{For 9}=\left| 9-6.5\right $|^2$=6.25$

$\textup{For 8}=\left| 8-6.5\right $|^2$=2.25$

$\textup{For 10}=\left| 10-6.5\right $|^2$=12.25$

Last, let's substitute these values into the standard deviation formula and solve.

$s=$\sqrt{\frac{\sum \left | x-\bar{x}$\right $|^2$}{n}}$

$s=$\sqrt{\frac{(12.25+0.25+20.25+6.25+2.25+12.25)}{6}$}$

$s=$\sqrt{\frac{53.5}{6}$}$

Solve.

Calculate the standard deviation of the following data set:

$3, 7, 2, 9, 8, \textup{and }10$

Tap to see back →

The standard deviation is found by using the following formula:

$s=$\sqrt{\frac{\sum \left| x-\bar{x}$\right $|^2$}{n}}$

We will start by identifying the components of this equation:

$\sum=\textup{sum}$

$x=\textup{variable in the data set}$

$\bar{x}=\textup{mean of the data set}$

$n=\textup{total number of variables in the data set}$

Now, we can use this information to calculate the standard deviation.

First, we need to identify and $\bar{x}$ . There are six variables in the data set; therefore, we can write the following:

Next, we need to calculate the mean:

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

$\bar{x}=\frac{3+7+2+9+8+10}{6}$$

$\bar{x}=\frac{39}{6}$$

$\bar{x}=6.5$

Second, we need to find the square of the absolute of each variable minus the mean: $\left| x-\bar{x}\right $|^2$$

$\textup{For 3}=\left| 3-6.5\right $|^2$=12.25$

$\textup{For 7}=\left| 7-6.5\right $|^2$=0.25$

$\textup{For 2}=\left| 2-6.5\right $|^2$=20.25$

$\textup{For 9}=\left| 9-6.5\right $|^2$=6.25$

$\textup{For 8}=\left| 8-6.5\right $|^2$=2.25$

$\textup{For 10}=\left| 10-6.5\right $|^2$=12.25$

Last, let's substitute these values into the standard deviation formula and solve.

$s=$\sqrt{\frac{\sum \left | x-\bar{x}$\right $|^2$}{n}}$

$s=$\sqrt{\frac{(12.25+0.25+20.25+6.25+2.25+12.25)}{6}$}$

$s=$\sqrt{\frac{53.5}{6}$}$

Solve.