Standard deviation of the data

Below question appears in “statistics for DataScience” course. For me the question is not clear. Can any one help here?

How many values in the below series fall within one standard deviation of the mean?
180, 313, 101, 255, 202, 198, 109, 183, 181, 113, 171, 165, 318, 145, 131, 145, 226, 113, 268, 108

Hi @kjnambiar,

You can ask questions related to the course on the course dicsussion itself. Regarding the query you have-

In this question, you have to find the number of points that falls in the range within one standard deviation of the mean.

So, you can first calculate the mean and the standard deviation of the given data. It comes out to be 181.25 and 64.65 respectively.

Now, to calculate one standard deviation above means, you add the standard deviation to the mean once. So, when you add 64.65 (standard deviation) with 181.25 (mean), you approximately get 245, and to calculate one standard deviation below means, you subtract the standard deviation from the mean once. So, when you subtract 64.65 (standard deviation) from 181.25 (mean), you approximately get 117. Hence the range that we get is 117-245.

Hence you need to count the numbers which are within this range. You have 11 numbers in this range, so your answer is 11.

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