To find the standard deviation, follow these steps:

1. Calculate the mean (average) of the data set by adding all the numbers and dividing by the number of data points.
2. Calculate the deviation of each data point from the mean by subtracting the mean from each value.
3. Square each deviation to get positive values.
4. Find the sum of these squared deviations.
5. For a sample, divide this sum by (n - 1), where n is the number of data points; for a population, divide by n. This gives the variance.
6. Take the square root of the variance. This result is the standard deviation.

This process measures how spread out the data points are around the mean, with a higher standard deviation indicating greater variability. For example, with data points 46, 69, 32, 60, 52, 41:

• Mean = 50
• Deviations: -4, 19, -18, 10, 2, -9
• Squared deviations: 16, 361, 324, 100, 4, 81
• Sum of squares = 886
• Variance = 886 / (6 - 1) = 177.2
• Standard deviation = √177.2 ≈ 13.31

This method applies whether the data is a full population or a sample (adjusting the divisor accordingly).