To calculate the standard deviation of those numbers:

1. Work out the Mean (the simple average of the numbers)
2. Then for each number: subtract the Mean and square the result.
3. Then work out the mean of those squared differences.
4. Take the square root of that and we are done!

The standard deviation measures the spread of the data about the mean value. For example, the mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. However, the second is clearly more spread out. If a set has a low standard deviation, the values are not spread out too much.

Here’s how you can find population standard deviation by hand:

1. Calculate the mean (average) of each data set.
2. Subtract the deviance of each piece of data by subtracting the mean from each number.
3. Square each deviation.
4. Add all the squared deviations.

There are two standard deviations listed on the calculator. The symbol Sx stands for sample standard deviation and the symbol σ stands for population standard deviation. If we assume this was sample data, then our final answer would be s =2.71.

1. The standard deviation formula may look confusing, but it will make sense after we break it down.
2. Step 1: Find the mean.
3. Step 2: For each data point, find the square of its distance to the mean.
4. Step 3: Sum the values from Step 2.
5. Step 4: Divide by the number of data points.
6. Step 5: Take the square root.

Grading Tests. A class of students took a math test.

How to Calculate Standard Deviation. 1. Look at your data set . This is a crucial step in any type of statistical calculation, even if it is a simple figure like the mean or median. 2. Gather all of your data. You will need every number in your sample to calculate the mean. 3. Add the numbers in your

Standard deviation is a statistical value used to determine how spread out the data in a sample are, and how close individual data points are to the mean — or average — value of the sample. A standard deviation of a data set equal to zero indicates that all values in the set are the same.

Standard deviation is a mathematical tool to help us assess how far the values are spread above and below the mean. A high standard deviation shows that the data is widely spread (less reliable) and a low standard deviation shows that the data are clustered closely around the mean (more reliable).