Answer:
Part 1) [tex][(250)^{2}+(-400)^{2}+(-250)^{2}+(350)^{2}+(100)^{2}+(-50)]=420,000[/tex]
Part 2) The variance is equal to [tex]Variance=70,000[/tex]
Part 3) [tex]Standard\ Deviation=265[/tex]
Step-by-step explanation:
step 1
Find the mean of the areas
we have
[tex][2,400,1,750,1,900,2,500,2,250,2,100][/tex]
To find the mean sum all the values and divide by the number of values
The number of values is 6
so
[tex][2,400+1,750+1,900+2,500+2,250+2,100]/6=2.150[/tex]
The Mean is [tex]2.150[/tex]
step 2
For each number subtract the Mean
[tex][(2,400-2,150),(1,750-2,150),(1,900-2,150),(2,500-2,150),(2,250-2,150),(2,100-2,150)][/tex]
[tex][(250),(-400),(-250),(350),(100),(-50)][/tex]
step 3
Find the Variance
To calculate the Variance, take each difference, square it, and then average the result
[tex][(250)^{2}+(-400)^{2}+(-250)^{2}+(350)^{2}+(100)^{2}+(-50)]=420,000[/tex]
[tex]Variance=420,000/6=70,000[/tex]
step 4
Find the standard deviation
The Standard Deviation is just the square root of Variance
so
[tex]Standard\ Deviation=\sqrt{70,000} =265[/tex]
