Question

Suppose the following data show the prices of 4 cars with similar characteristics that sold at a recent auction (in thousands of dollars): 6.6, 5, 10.7, 7.3. Calculate the standard deviation of the sample of selling prices. (please express your answer using 2 decimal places)

Answer 1

Answer: 2.40

Explanation:

Given: The prices of 4 cars with similar characteristics that sold at a recent auction (in thousands of dollars): 6.6, 5, 10.7, 7.3.

Let x: 6.6, 5, 10.7, 7.3.

n= 4

Mean :
`\overline{x}=(\sum x)/(n)`

`\Rightarrow\ \overline{x}=(6.6+5+10.7+7.3)/(4)\\\\=(29.6)/(4)\\\\=7.4`

Now , standard deviation =
`\sqrt{\frac{\sum(x-\overline{x})^2}{n-1}}`

`=\sqrt{((6.6-7.4)^2+( 5-7.4)^2+( 10.7-7.4)^2+( 7.3-7.4)^2)/(4-1)}\\\\=\sqrt{(0.64+5.76+10.89+0.01)/(3)}\\\\=\sqrt{(17.3)/(3)}\approx2.40`

Hence, the standard deviation of the sample of selling prices = 2.40