Standard Deviation of a Dataset

Standard deviation of a dataset

Standard deviation describes how spread out the data values are around the mean. A small standard deviation means the values are close together; a larger one means they are more spread out.

Method

1. Find the mean of the dataset.
2. Subtract the mean from each value to find each deviation.
3. Square each deviation so negative and positive differences both count.
4. Add the squared deviations.
5. Divide by the correct count used in the exercise.
6. Take the square root of the result to get the standard deviation.

How to work carefully

• Keep your arithmetic organized in a table if there are several values.
• Do not round too early; use exact values as long as possible.
• If the answer is a radical or decimal, simplify it as far as the exercise allows.

Check your answer

• The standard deviation should never be negative.
• If all data values are the same, the standard deviation should be 0.
• A quick reasonableness check: more spread in the data should give a larger standard deviation.