First, find the mean of the six numbers by adding them all together, and dividing them by six.

88 + 94 + 80 + 79 + 74 + 83 = 498

498/6 = 83

Next, find the variance by subtracting the mean from each of the given numbers and then squaring the answers.

88 – 83 = 5

5² = 25

94 – 83 = 11

11² = 121

80 – 83 = –3

–3² = 9

79 – 83 = –4

–4² = 16

74 – 83 = –9

–9² = 81

83 – 83 = 0

0² = 0

Find the average of the squared answers by adding up all of the squared answers and dividing by six.

25 + 121 + 9 +16 +81 + 0 = 252

252/6 = 42

42 is the variance.

To find the standard deviation, take the square root of the variance.

The square root of 42 is 6.481.

The following is the formula for standard deviation:

Here is a breakdown of what that formula is telling you to do:

1. Solve for the mean (average) of the five test scores
2. Subtract that mean from each of the five original test scores. Square each of the differences.
3. Find the mean (average) of each of these differences you found in Step 2
4. Take the square root of this final mean from #3. This is the standard deviation

Here are those steps:

1. Find the mean of the test scores:

2. Subtract the mean from each of the test scores, then square the differences:

3. Find the mean of the squared values from Step 2:

4. Take the square root of your answer from Step 3:

The following is the formula for standard deviation:

Here is a breakdown of what that formula is telling you to do:

1. Solve for the mean (average) of the five test scores
2. Subtract that mean from each of the five original test scores. Square each of the differences.
3. Find the mean (average) of each of these differences you found in Step 2
4. Take the square root of this final mean from #3. This is the standard deviation

Here are those steps:

1. Find the mean of her score totals:

2. Subtract the mean from each of the test scores, then square the differences:

3. Find the mean of the squared values from Step 2:

4. Take the square root of your answer from Step 3:

Standard deviation is  where  represents the data point in the set,  is the mean of the data set and  is number of points in the set.

The mean is  the sum of the data set divided by the number of data points in the set. 

Plugging in the values: 

By drawing a bell curve, the middle line is . One standard deviation left and right of the middle line is  each. That means one standard deviation within is . 

Standard deviation is the dispersion of the data set. Since it's asking for within one standard deviation, we need to take the mean and add the standard deviation to find the upper bound of the range. Then, we will need to subtract the standard deviation from the mean to identify the lower bound of the range. 

=

Standard deviation is  where  represents the data point in the set,  is the mean of the data set and  is number of points in the set.

The mean is  the sum of the data set divided by the number of data points in the set. 

Plugging in the values: 

Another way to calculate standard deviation is the square root of variance.

Variance is,

 .  

Taking the square root of this is how standard devation can be calculated. 

If mean is  with standard deviation of , then one standard deviation within has a range of  to .

Remember, we find the range by adding the standard deviation to the mean and subtracting the standard deviation from the mean.

Only  is in the range.

The rest of the numbers are more than one standard deviation. 

Variance is, 

.

To find standard deviation is to take the sqaure root of the variance.

.