Respuesta :
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
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:
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:
[tex]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[/tex]
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:
[tex]Variance=\dfrac{\sum (x-x')^2}{n-1}[/tex]
where n is the number of data points.
Here n= 15
Hence, n-1=14
Hence, we get:
[tex]Variance=\dfrac{19.6}{14}\\\\i.e.\\\\Variance=1.4[/tex]
We know that the standard deviation is the square root of the variance.
i.e.
[tex]Standard\ deviation=\sqrt{1.4}\\\\i.e.\\\\Standard\ deviation=1.1832[/tex]
