Question

Please show your work to find the mean and standard deviation of the data. Round to the nearest tenth. 20, 16, 18, 14, 9, 20, 16

Answer 1

Answer:

Mean of given data is 16.15 and standard deviation is 3.56

Step-by-step explanation:  

We have been given a data

$20,16,18,14,9,20,16$

We need to find the mean and standard deviation:

mean=$\frac{\text{sum of observations}}{\text{number of observations }}$

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

$mean=\frac{113}{7 }=16.1428=16.15$

Formula for standard deviation is

$\sigma=\sqrt{\frac{\sum(x-\bar{x})^2}{n}}$

$\text{where, mean is }\bar{x}$

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

$\sigma=\sqrt\frac{(20-16.15)^2+(16-16.15)^2+(18-16.15)^2+(14-16.15)^2+(9-16.15)^2+(20-16.15)^2+(16-16.15)^2}{7}$

After simplification we will get

$\sigma=\sqrt\frac{(3.85)^2+(-0.15)^2+(1.85)^2+(-2.15)^2+(-7.15)^2+(3.85)^2+(-0.15)^2}{7}$

After further simplification we will get

$\sigma=\sqrt\frac{(14.8225)+(.0225)+(3.4225)+(4.6225)+(51.1225)+(14.8225)+(.0225)}{7}$

$\Rightarrow \sigma=\sqrt\frac{88.8575}{7}$

$\Rightarrow \sigma=\sqrt{12.6939}=3.56$

Therefore mean of given data is 16.15 and standard deviation is 3.56

Answer 2

The mean is add all of them which is 113 then divide by 7 which is 16.14
the standard deviation is 3.85