# summation notation

• Sep 6th 2009, 11:07 PM
comet2000
summation notation
Exercise 2.18
Using the data from Exercise 2.16,

(a) Calculate (ΣY)^2 and ΣY^2
(ΣY)^2 = 14.63^2 = 214.0369
ΣY^2 = (1.73^2 + 1.06^2 + 2.03^2 + 1.40^2 + 0.95^2 + 1.13^2 + 1.41^2 + 1.73^2 + 1.63^2 + 1.56^2) = 22.4483

(b) Given the answers to (a), calculate ΣY^2 - (ΣY)^2/N divide by N-1
22.4483 - 214.0369/10 divide by 10-1 = 20.07011222

(c) Calculate the square root of the answer to (b). (You will come across these calculations again in Chapter 5.)
20.07011222^2 = 402.8094046

Exercise 2.16
With reference to Exercise 2.15, the data for the Eyes Elevated condition are 1.73, 1.06, 2.03, 1.40, 0.95, 1.13, 1.41, 1.73, 1.63, 1.56

Using Y for this variable,

(a) What are Y1 and Y10?
Y1 = 1.73, Y10 = 1.56
(b) Calculate ΣY
ΣY = (1.73 + 1.06 + 2.03 + 1.40 + 0.95 + 1.13 + 1.41 + 1.73 + 1.63 + 1.56) = 14.63

did i do the problem correctly? i have included Exercise 2.16 for Exercise 2.18
• Sep 7th 2009, 07:06 AM
TKHunny
Quote:

Originally Posted by comet2000
(ΣY)^2 - ΣY^2/N/N-1
22.4483 - 214.0369/10/10-1

Perhaps this: [(ΣY)^2 - (ΣY^2)/N]/(N-1)

Your arithemetic looks good, but your formula doesn't. Please check that and try again. It appears to me that you have switched (ΣY)^2 and (ΣY^2)

Perhaps this: [(ΣY^2) - {(ΣY)^2}/N]/(N-1)
• Sep 7th 2009, 01:11 PM
comet2000
Quote:

Originally Posted by TKHunny

Perhaps this: [(ΣY)^2 - (ΣY^2)/N]/(N-1)

Your arithemetic looks good, but your formula doesn't. Please check that and try again. It appears to me that you have switched (ΣY)^2 and (ΣY^2)

Perhaps this: [(ΣY^2) - {(ΣY)^2}/N]/(N-1)

sorry, i wasn't sure how to post up the problem since i am not very good with the coding and stuff.
here you go,
ΣY^2 - (ΣY)^2/N divide by N-1 22.4483 - 214.0369/10 divide by 10-1 = 20.07011222 214.0369/10 is a fraction
• Sep 7th 2009, 05:01 PM
TKHunny
Okay, now your formula is better but your arithmetic worse. Have you practiced being careful and consistent?

22.4483 - 214.0369/10 divide by 10-1

or

(22.4483 - [214.0369/10])/(10-1)

or

(22.4483 - 21.40369)/9

Now what?