Question

Size of U.S. States The total surface area (in square miles) for each of six selected eastern states is listed here.

28,995 PA
37,534 FL
31,361 NY
27,087 VA
20,966 ME
37,741 GA
The total surface area for each of six selected western states is listed (in square miles).
72,964 AZ
70,763 NV
101,510 CA
62,161 OR
66,625 CO
54,339 UT
Find the standard deviation for each data set. Which set is more variable?

Answer 1

Eastern States Standard deviation = 6440.2
Western States Standard deviation = 16178

The Western States is more variable because it has a higher deviation. Also you can tell that the Western States is more variable because the the data/numbers change more than the Eastern States.

Answer 2

Second set.

Explanation:

I put the formula of standart deviation in the image below.

x is each data of the list

μ is the data average

N is the amount of elements.

So, for the first list we have:

μ=
`(28995+37534+31361+27087+20966+37741)/(6)= (183684)/(6)=30614`

DE=
`\sqrt31361-30614`

=
`\sqrt{(2621161+47886400+558009+12439729+93083904+50794129)/(6) }`

=
`\sqrt{(207383332)/(6) }`

=
`√( 34563888.6667 )`

= 5879.1061.

For the other list of elements:

μ=
`(72964+70763+101510+62161+66625+54339)/(6)= (428362)/(6)=71393.66`

DE=

=
`\sqrt{(2465967.71+397732.03+906993934.99+85242010.67+22740118.19+290861427.71)/(6) }`

=
`\sqrt{(1308701191.3)/(6) }`

=
`√(218116865.21 )`

= 6029.32

Then, the second set is more variable.