Question

How do I solve this question

Answer 1

Part 1)
`[(250)^(2)+(-400)^(2)+(-250)^(2)+(350)^(2)+(100)^(2)+(-50)]=420,000`

Part 2) The variance is equal to
`Variance=70,000`

Part 3)
`Standard\ Deviation=265`

Explanation:

step 1

Find the mean of the areas

we have

`[2,400,1,750,1,900,2,500,2,250,2,100]`

To find the mean sum all the values and divide by the number of values

The number of values is 6

so

`[2,400+1,750+1,900+2,500+2,250+2,100]/6=2.150`

The Mean is
`2.150`

step 2

For each number subtract the Mean

`[(2,400-2,150),(1,750-2,150),(1,900-2,150),(2,500-2,150),(2,250-2,150),(2,100-2,150)]`

`[(250),(-400),(-250),(350),(100),(-50)]`

step 3

Find the Variance

To calculate the Variance, take each difference, square it, and then average the result

`[(250)^(2)+(-400)^(2)+(-250)^(2)+(350)^(2)+(100)^(2)+(-50)]=420,000`

`Variance=420,000/6=70,000`

step 4

Find the standard deviation

The Standard Deviation is just the square root of Variance

so

`Standard\ Deviation=√(70,000) =265`