Question

I need help with my statistics homework " -compute the range ,sample variance,and sample standard deviation cost."

Answer 1

We need to find the range, sample variance, and sample standard deviation cost.

The range is already given: $247. It can be found by subtracting the least from the greatest value:

`466-219=247`

Now, in order to find the sample variance and the sample standard deviation, we first need to find the mean of the sample:

`\text{ mean }=\text{ }(415+466+400+219)/(4)=(1500)/(4)=375`

Now, we can find the sample variance s² using the formula:

`s²=\frac{\sum_{i\mathop{=}1}^n(x_i-\text{ mean})²}{n-1}`

where n is the number of values (n = 4) and the xi are the values of the sample.

We obtain:

`\begin{gathered} s²=((415-375)²+(466-375)²+(400-375)²+(219-375)²)/(4-1) \\ \\ s²=(40²+91²+25²+(-156)²)/(3) \\ \\ s²=(1600+8281+625+24336)/(3) \\ \\ s²=(34842)/(3) \\ \\ s²=11614 \end{gathered}`

Now, the sample standard deviation s is the square root of the sample variance:

`\begin{gathered} s=√(11614) \\ \\ s\cong107.8 \\ \\ s\cong108 \end{gathered}`

Therefore, rounding to the nearest whole numbers, the answers are:

Answer

range: $247

s² = 11614 dollars²

s ≅ $108