How to Calculate the Standard Deviation of 9, 16, 23, 30, 37, and 44
Learn how to find the standard deviation of the numbers 9, 16, 23, 30, 37, and 44 with a step-by-step explanation.
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Standard deviation measures the spread of a set of numbers. For the numbers 9, 16, 23, 30, 37, 44, first find the mean: (9+16+23+30+37+44)/6 = 26.5. Calculate each number9;s deviation from the mean, square it, sum the squares, and divide by the count minus one (6-1). Finally, take the square root: √[(17.5² + 10.5² + 3.5² + 3.5² + 10.5² + 17.5²)/5] = 12.25.
FAQs & Answers
- What is standard deviation and why is it important? Standard deviation is a measure of how spread out numbers are in a dataset. It helps understand the variability or consistency of data values.
- How do you calculate standard deviation step by step? First, find the mean of the numbers, then calculate each number’s deviation from the mean, square these deviations, sum them, divide by the number of data points minus one, and finally take the square root.
- What is the difference between population and sample standard deviation? Population standard deviation divides the sum of squared deviations by the total number of data points, while sample standard deviation divides by one less than the number of data points to correct bias.