Sample Standard deviation ( measures center )
SD = √[Σ(xi – x̄)² / (n – 1)]
Actually, the sample standard deviation (SD) is a measure of dispersion, not a measure of center. The sample SD is a commonly used statistical measure that quantifies how spread out the data in a sample is. The formula to compute the sample SD is:
SD = √[Σ(xi – x̄)² / (n – 1)]
where xi represents each observation in the sample, x̄ represents the mean of the sample, and n represents the sample size.
The sample SD is used to quantify the amount of dispersion, or variability, that exists in a set of data. A smaller SD indicates that the data is clustered more tightly around the mean, while a larger SD indicates a more spread out distribution.
For example, imagine we have a sample of five people, and we want to calculate the SD of their ages:
– Person 1: 20 years old
– Person 2: 22 years old
– Person 3: 25 years old
– Person 4: 27 years old
– Person 5: 30 years old
The mean age of the sample is (20 + 22 + 25 + 27 + 30) / 5 = 24.8 years.
Using the formula above, we can calculate the sample SD:
SD = √[((20-24.8)² + (22-24.8)² + (25-24.8)² + (27-24.8)² + (30-24.8)²) / 4] = 4.07
This indicates that the ages in the sample are relatively spread out, with an SD of 4 years.
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