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A sigma value, commonly known as the standard deviation, measures how much the values in a data set deviate from the mean. This metric is crucial for researchers and statisticians to assess the variability of a sample relative to a control group.

Step 1 – Compute the Mean

First, add all values together and divide by the number of observations. For example, with the data set 10, 12, 8, 9, 6, the sum is 45. Dividing by 5 yields a mean of 9.

Step 2 – Determine Deviations from the Mean

Subtract the mean from each data point:

• 10 – 9 = 1
• 12 – 9 = 3
• 8 – 9 = –1
• 9 – 9 = 0
• 6 – 9 = –3

Step 3 – Square Each Deviation

Square the results from step 2 to eliminate negative values:

• 1² = 1
• 3² = 9
• (–1)² = 1
• 0² = 0
• (–3)² = 9

Step 4 – Sum the Squared Deviations

Adding these squared values gives 20.

Step 5 – Adjust for Sample Size

Subtract one from the number of observations to account for degrees of freedom. With 5 data points, 5 – 1 = 4.

Step 6 – Calculate the Variance

Divide the sum from step 4 by the adjusted sample size: 20 ÷ 4 = 5. This value is the sample variance.

Step 7 – Take the Square Root to Obtain Sigma

The sigma (standard deviation) is the square root of the variance. For this example, √5 ≈ 2.24. This figure tells you the typical distance of each observation from the mean.

By following these steps, you can compute sigma for any data set, providing a reliable measure of dispersion that underpins sound statistical analysis.