First we need to find the mean and the standadr deviation. For the mean, we sum the values up and divide by the number of data given. We have 8 data, so:
Now, we need the standard deviation. To find it, we use the formula:
The sum symbol in there mean we need to get each data given, substract the mean we calculated, square them and then sum all. N is the number of data, which is 8. Let look one example:
For data 93, we do:
Now, we do the same for the others:
Now we sum all of them:
This goes into the formula.
Now, we want the number of data that is within 2 standard deviation from the mean. Thus, we want the data that are between:
From the given Data, 93 is out of this range, but all the others (65, 67, 67, 67, 65, 66, 65) are in it. So, the number of data within 2 standard deviations from the mean is 7.