The numbers of rooms for 15 homes recently sold were: 8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9. what is the sample standard deviation?

Hence, the sample standard deviation is:

                         1.1832

The data is given by:

8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9.

The mean of these data points is given by:

Now,

x                x-x'                   (x-x')²

8            8-7.4=0.6              0.36

8            8-7.4=0.6              0.36

8            8-7.4=0.6              0.36    

5            5-7.4= -2.4             5.76

9            9-7.4=1.6                2.56

8            8-7.4=0.6              0.36

7            7-7.4= -0.4             0.16

6            6-7.4= -1.4              1.96

6            6-7.4= -1.4              1.96

7            7-7.4= -0.4             0.16

7            7-7.4= -0.4             0.16

7            7-7.4= -0.4             0.16

7            7-7.4= -0.4             0.16

9            9-7.4=1.6                2.56

9            9-7.4=1.6                2.56

                             ∑(x-x')²=19.69          

Now the variance of the sample population is given by:

where  n is the number of data points.

Here n= 15

Hence, n-1=14

Hence, we get:

We know that the standard deviation is the square root of the variance.

i.e.