Exercise 7 Page 593

Now, if a standard deviation is equal to 0 the data values do not differ from the mean. This means that all data values are the same. Let's consider an example of the number of meals per day we had in the previous week, assuming that each day we ate 5 meals. { 5,5,5,5,5,5,5 } Here the mean of the above data set is 5 and each data value is equal to the mean, so the standard deviation will be 0. Let's take a look at the formula for standard deviation once again. Standard Deviation sqrt((x_1-x)^2+(x_2-x)^2+...+(x_n-x)^2/n) We can see that standard deviation is defined as a square root of the sum of the squared differences between data values and the mean. Since a square root cannot be a negative number, a standard deviation also cannot be negative.