Question

Find the standard deviation of the data set (36, 18, 12, 10, 9). Round all calculations to the nearest tenth. Please Help!!!!​

Answer 1

The standard deviation of the data set is
`\sigma=10`

Explanation:

The formula for standard deviation is
`\sigma=\sqrt{(1)/(N)\sum_(n=1)^(\infty)(x_i-\mu)^2 }` where you are basically taking the mean of the data set (
`\mu`), find the mean of the squared differences from the observed values and mean (
`(x_i-\mu)^2`), and square root the result:

Mean:

`\mu=(36+18+12+10+9)/(5)=(85)/(5)=17`

Average of squared differences (variance):

`(1)/(N)\sum_(n=1)^(\infty)(x_i-\mu)^2=((36-17)^2+(18-17)^2+(12-17)^2+(10-17)^2+(9-17)^2)/(5)=(500)/(5)=100`

Standard deviation:

`\sigma=√(100)=10`

This means that the standard deviation of the data set is 10, which tells us that the values of the data set, on average, are separated by 10.