How to Calculate the Standard Deviation of a Data Set: Example with 9 Numbers
Learn how to calculate the standard deviation step-by-step using the data set: 10, 28, 13, 29, 30, 22, 23, 25, and 32. Easy statistical guide.
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Step 1: Calculate the mean: (10 + 28 + 13 + 29 + 30 + 22 + 23 + 25 + 32) / 9 = 23.56. Step 2: Find the squared differences from the mean, sum them up, and divide by the number of observations. Step 3: Take the square root: √((182.44 + 19.56 + 112.36 + 29.16 + 41.76 + 0.19 + 0.19 + 2.09 + 71.29) / 9) ≈ 8.10. Therefore, the standard deviation is 8.10.
FAQs & Answers
- What is standard deviation in statistics? Standard deviation measures the amount of variation or dispersion in a set of data values. A low standard deviation means data points are close to the mean; a high standard deviation indicates more spread.
- How do you calculate standard deviation step-by-step? First, calculate the mean of the data set. Then find the squared differences between each data point and the mean. Sum these squared differences, divide by the number of observations, and finally take the square root of that result.
- Why is standard deviation important in data analysis? Standard deviation helps quantify the variability in data, which is essential for understanding data distribution, consistency, and making informed decisions based on data.