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The given data set includes 10, 15, 18, 22, 36 and 52. Calculate the Standard Deviation.

Question

The given data set includes 10, 15, 18, 22, 36 and 52. Calculate the Standard Deviation.

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Solution

Sure, here are the steps to calculate the standard deviation:

  1. Calculate the Mean (Average): Add up all the numbers and then divide by the number of numbers. (10+15+18+22+36+52) / 6 = 25.5

  2. Subtract the Mean and square the result (this is called the "squared deviation"). (10-25.5)^2 = 240.25 (15-25.5)^2 = 110.25 (18-25.5)^2 = 56.25 (22-25.5)^2 = 12.25 (36-25.5)^2 = 110.25 (52-25.5)^2 = 705.25

  3. Calculate the average of those squared deviations. (240.25+110.25+56.25+12.25+110.25+705.25) / 6 = 205.75

  4. Take the square root of that and we get the standard deviation. The square root of 205.75 is approximately 14.34.

So, the standard deviation of the given data set is approximately 14.34.

This problem has been solved

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