Question

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?

Answer 1

From the data set given:
8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9
to get the standard deviation we use the formula for variance given by:
σ²=[Σ(x-μ)²]/(n-1)
σ² is the variance
μ is the mean
The mean of the data will be:
μ=(8+8+8+5+9+8+7+6+6+7+7+7+7+9+9)/15=7.4
The variance will be found as follows:
σ²=[(8-7.4)²×4+(5-7.4)²+3×(9-7.4)²+5×(7-7.4)²+2×(6-7.4)²]/(15-1)
σ²=1.4
thus
σ=√1.4=1.1183

Answer 2

Answer:

Hence, the sample standard deviation is:

                         1.1832

Step-by-step explanation:

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:

$Mean(x')=\dfrac{8+8+8+5+9+8+7+6+6+7+7+7+7+9+9}{15}\\\\i.e.\\\\Mean(x')=\dfrac{111}{15}\\\\i.e.\\\\Mean(x')=7.4$

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:

$Variance=\dfrac{\sum (x-x')^2}{n-1}$

where  n is the number of data points.

Here n= 15

Hence, n-1=14

Hence, we get:

$Variance=\dfrac{19.6}{14}\\\\i.e.\\\\Variance=1.4$

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

i.e.

$Standard\ deviation=\sqrt{1.4}\\\\i.e.\\\\Standard\ deviation=1.1832$