Question

can someone PLEASE help me understand this standard deviation stuff? i am extremely confused.

"Experiment: Select a random sample of size 3 without replacement from these numbers: 2, 3, 5, 6, 8; 1) Find a sample with the highest standard deviation, 2) Find a sample with the lowest standard deviation"

Answer 1

when you have a set of numbers, you can find the average of them (i.e. the mean)

you can then find the difference of each number in the set from the mean.
we could (but don't) find the "average difference" to get a feel for how far about the numbers are (on average) from the mean. That idea has problems, so instead they
square the difference, and find the average of these "squared differences"
then they take the square root. we end up with the "standard deviation"

Answer 2

a small standard deviation would come from , for example the 3 numbers,
1,1,1
the average is (1+1+1)/3 = 1 (though we can see the average has to be 1 without calculating it)

now find the standard deviation:
first find the difference between each number and the mean
(1-1), (1-1) and (1-1)
in other words, 0,0,0
square each "difference" and we get 0^2 , 0^2 , 0^2 which is still just 0,0,0
find the average, and we get 0
finally, take the square root: sqr(0)= 0
the standard deviation is 0

Answer 3

a big standard deviation would come from
-3,0,3
average is (-3+0+3)/3 = 0/3 = 0

standard deviation is
1) difference: (-3 -0), 0-0, 3-0, = -3, 0 ,3
2) squared differences: 9,0,9
3) average of squared differences: (9+0+9)/3 = 18/3 = 6
4) standard deviation is sqr(6) or about 2.45

Answer 4

For your problem, pick the 2 smallest numbers and the biggest number (you want to try to get a big "spread" , which is what the std dev measures