To get the standard deviation, we need to calculate the variance, which is the average of the squared differences from the mean, so we will start by getting the mean.

Then, subtract the mean from each value...

...and take the mean of these resulting values, which is equal to the variance.

The square root of this value is the standard deviation. The answer is presented as ,

but you may also calculate it and find it equal to about 

Formula for the standard deviation:

1. Find the mean

2. Subtract the mean from each number in the data set

3. Sum up the square of the differences and divide by n

4. Take the square root of the variance

The first step in solving for standrd deviation is to find the mean of the data set.

For this problem:

.

Now we can evaluate the summation:

Now we can rewrite the standard deviation expression:

There are 5 data points, so n = 5

The 68-95-99.7 rule states that nearly all values lie within 3 standard deviations of the mean in a normal distribution. In this case the question asks for 95% so we want to know what 2 standard deviations from the mean is.

We are given the variance, so to find the standard deviation, take the square root.

So two standard devations is 8 inches. 95% of heights should be within 8 inches of the mean.

To begin, we must remember the formula for standard deviation:

where is the standard deviation, N is the number of values in our set,   is the value we're currently evaluating in the summation, and is the mean of our set of numbers. All the summation part of the equation means is that we subtract our mean from each number in the set, square that value, and then add all of those values for each number together. So before we find the values that will be added together, we must first find our mean for the set of numbers:

Now we can determine the value for our summation for each number in the set:

Looking at our equation for standard variation, now all we must do is sum all of the values above, divide by N, and take the square root:

The standard deviation of a set of numbers is how much the numbers deviate from the mean. More formally, the standard deviation is 

where  is a number in the series,  is the mean, and  is the number of data points. So, to calculate the standard deviation, we must first calculate the mean. The mean of this data set is

Now that we know the mean, we can start calculating the standard deviation. We first need to find the sum of each data point minus the average squared.

Calculating that, we get that the variance from the mean is . Plugging that into our equation for standard deviation, with  being ten data points, we get

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: