Respuesta :
the mean is add all of them which is 113 then divide by 7 which is 16.14
the standard deviation is 3.85
the standard deviation is 3.85
Answer:
Mean of given data is 16.15 and standard deviation is 3.56
Step-by-step explanation:
We have been given a data
[tex]20,16,18,14,9,20,16[/tex]
We need to find the mean and standard deviation:
mean=[tex]\frac{\text{sum of observations}}{\text{number of observations }}[/tex]
Here sum of observations are 20+16+18+14+9+20+16=113
Number of observations are 7
Substituting the values in the formula for mean we will get
[tex]mean=\frac{113}{7 }=16.1428=16.15[/tex]
Formula for standard deviation is
[tex]\sigma=\sqrt{\frac{\sum(x-\bar{x})^2}{n}}[/tex]
[tex]\text{where, mean is }\bar{x}[/tex]
x are the values given for the data
n is 7 the number of observations
On substituting the values in the given formula we will get
[tex]\sigma=\sqrt\frac{(20-16.15)^2+(16-16.15)^2+(18-16.15)^2+(14-16.15)^2+(9-16.15)^2+(20-16.15)^2+(16-16.15)^2}{7}[/tex]
After simplification we will get
[tex]\sigma=\sqrt\frac{(3.85)^2+(-0.15)^2+(1.85)^2+(-2.15)^2+(-7.15)^2+(3.85)^2+(-0.15)^2}{7}[/tex]
After further simplification we will get
[tex]\sigma=\sqrt\frac{(14.8225)+(.0225)+(3.4225)+(4.6225)+(51.1225)+(14.8225)+(.0225)}{7}[/tex]
[tex]\Rightarrow \sigma=\sqrt\frac{88.8575}{7}[/tex]
[tex]\Rightarrow \sigma=\sqrt{12.6939}=3.56[/tex]
Therefore mean of given data is 16.15 and standard deviation is 3.56
