Question

How do I construct a sample data set for which n=7, x=9(x bar), and s=0?

Answer 1

To create a sample data set with n=7, a mean of 9, and a standard deviation of 0, all seven data points must be identical to the mean, resulting in the data set {9, 9, 9, 9, 9, 9, 9}.

Step-by-step explanation:

To construct a sample data set with n=7, where \(\overline{x}=9\) (x bar is the sample mean), and s=0 (s is the sample standard deviation), follow these steps:

1. Understand that if the standard deviation s is zero, all data points in the sample must be identical.
2. Since the sample mean \(\overline{x}\) is given as 9, all seven data points in the sample must also be 9 to achieve a standard deviation of 0.
3. Thus, the sample data set will simply be {9, 9, 9, 9, 9, 9, 9}.

Remember that the sample mean is calculated as the sum of all data values divided by the number of values (n), and the sample standard deviation measures the amount of variation or dispersion of a set of values. A standard deviation of zero indicates that all values are identical to the mean.

Answer 2

When the standard deviation = 0, there is no deviation at all. So the numbers are all the same. And there are seven of them. And the average is nine.
So the sample data set would just be seven 9s.