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Finding The SE of the Average
(of Box)
SE for the average says how far the average of the dras is likely to be from the average of the box
Formula = SE/#Draws
Example:
Draws = 25
Average of box with numbers (1,2,3,4,5,6,7)
 Ave box = 28(sum of Numbers)/7 = 4
 SD = 2
 EV = [(#draws) x (ave of box)] = 25 x 4 = 100
 SE = Square Root (#draws) x SD] = 5 x 2 =10
Box Averages
 EV of box = Averages = 4
 SE of box = SE for (Sum of Box)/(#draws) 10/25 = .4
So the Average/EV of the (box) is 4 with a Chance error of .4

Using the Normal Curve to estimate more
Estimate that the average of the draws will be more than 4.2
 #draws =100
 ave = 4
 EV = 4 x 100 = 400
 SD = 2
 SE = square root(100) x 2 (SD) = 20
SE of Box = 20/100 = .2
Ave= 4 give or take .2
convert into SU 4 (Average)  4.2/ 2 (SE) = 1 (SU)
 Solve for above 1 using normal scale =
 Area between 1 = 68%  100% = 32% /2 = 16%

SE with no givin SD
 Wants to know average incomes of 25000 families. 1000s families are sampled
 #draws = 1000
 total income= 62,396,714
 Ave income = 62,396,714/1000 =62,400
 SD = Unknown (SD is Found Using BootStrap Method [section, chp 21])
SD (BootStrap Method) = 53,000
SE can now be Caluclated
 SE for sum = squareroot (#draws) x SD
 SE = 31.6 x 53000 = about 1,700,000
now we need the SE for the Average (62,400)
SE for Ave = SE/#draws = 1,700,000/1000 =1700
Answer = 62,400 + 1,700

Which SE
SE shows the likely size of the amount off. It is a giveortake number
SE for sum = Square Root (#draws) x SD
SE for Averages = SE for Sum/#draws
SE for count = SE for Sum, From box (1,0)
SE for Percent = (SE for count/#draws) x 100.

Sampling Average
Estimates the population average but is off by a little. The little is the SE

