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How to Calculate the Standard Deviation of 38, 51, 46, 79, and 57

Step-by-step guide on calculating the standard deviation of the numbers 38, 51, 46, 79, and 57 for better data analysis.

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Video transcript

To find the standard deviation of the numbers 38, 51, 46, 79, and 57:
1. Calculate the mean: (38 + 51 + 46 + 79 + 57) / 5 = 54.2
2. Subtract the mean and square the result for each number: (38-54.2)^2 + (51-54.2)^2 + (46-54.2)^2 + (79-54.2)^2 + (57-54.2)^2
3. Find the average of those squared differences: 945.2 / 5 = 189.04
4. Take the square root: √189.04 ≈ 13.75

Questions and answers

  1. What is standard deviation and why is it important?

    Standard deviation is a measure of how spread out numbers are in a data set. It is important because it shows the variability or dispersion, helping understand data consistency.

  2. How do you calculate standard deviation step-by-step?

    To calculate standard deviation, find the mean, subtract the mean from each data point and square the result, find the average of these squared differences, then take the square root of that average.

  3. What is the difference between sample and population standard deviation?

    Population standard deviation divides by the total number of data points (N), while sample standard deviation divides by one less than the total number (N-1) to account for sample bias.

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