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A sample was done, collecting the data below. Calculate the standard deviation, to one decimal place.

A sample was done, collecting the data below. Calculate the standard deviation, to-example-1
User Peiwen
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1 Answer

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The standard deviation of the data: 12, 24, 16, 22, 17 is equal to 4.3 to one decimal place.

We can calculate the standard deviation of data as follows:

First we find the mean by adding up all the values and divide by the number of values.

mean = (12 + 16 + 17 + 22 + 24)/5

mean = 91/5

mean = 18.2

Next we find the squared difference from the mean for each data point by subtracting the mean from each data point and square the result.

(12 - 18.2)² = 38.44

(16 - 18.2)² = 4.84

(17 - 18.2)² = 1.44

(22 - 18.2)² = 14.44

(24 - 18.2)² = 33.64

Then we find the average of these squared differences by adding up all the squared differences and divide by the number of values.

(38.44 + 4.84 + 1.44 + 14.44 + 33.64)/5 = 92.8/5

(38.44 + 4.84 + 1.44 + 14.44 + 33.64)/5 = 18.56

And lastly we take the square root of the result 18.56

√18.56 = 4.3081

Thus, the standard deviation for the data is derived as approximately 4.3 to one decimal place.

User Kimo
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