When Finding standard Deviation do you use numbers in the data set that are zero?

Question

I am doing a data report on a survey done on the number of hours students work per month. Some students do not work so their number was 0. I am finding the standard deviation for the data set and I was unsure whether to regard or disregard the students who's work hours were 0?

Answer 1

Hi Haley!

Interesting question.

The answer is yes, you must include the zeros in the sample.

The standard deviation of a sample is a measure of variability. You can find the formula in your textbook.

Let us suppose that that John, a student, worked in five different months 46,54,42,46, and 32 hours. Doing the math, the sample standard deviation is 8. The addition of the hours is 220 and the arithmetic mean is 44 (220/5).

Now, let us suppose that another student, George, worked during 12 months the following hours: 46,0,54,0,0, 42,0,0,46,0,32. The total amount of hours is the same (220). The arithmetic mean is 18.3 (220/12). The standard deviation is 22.1.

Conclusion:

·      If you do not include in the sample the zero hours worked, you will reach the conclusion that the case of John is equal to the case of George.

·      Although John and George worked the same total hours (220), John worked during 5 months at an average of 44 hours per months. George worked during 12 months at an average of 18.3 hours per month.

·      The standard deviation of John was 8, and 22.1 for George. The higher standard deviation of George indicates that the hours worked per month were more variable.