SOLUTION: Dear tutor, I have a hard time calculating the variance of the means. almost spent 3 hrs to figure this out. but still no luck. Any help is appreciated. Thank you. Q.The table

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Question 1008328: Dear tutor, I have a hard time calculating the variance of the means. almost spent 3 hrs to figure this out. but still no luck.
Any help is appreciated. Thank you.
Q.The table shows the means and variances from 5 experimental conditions. Compute the variance of the means.
Mean Variance
4.5 1.33
7.2 0.98
3.4 1.03
9.1 0.78
1.2 0.56
What I did was I added all the variance and divided by (1/25) but I do not get the answer 9.717
ANSWER : 9.717
Thank you in advance!
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
Follow directions. You are told to compute the variance of the means.
So you don't pay any attention to those individual variances.
You look at the 5 means only:  

   4.5	 
   7.2	 
   3.4	 
   9.1	 
   1.2


Add them:

   4.5	 
   7.2	 
   3.4	 
   9.1	 
   1.2
------	 
  25.4

Divide the sum by 5 to get the mean of the means.

   4.5	 
   7.2	 
   3.4	 
   9.1	 
   1.2
-------	 
5)25.40
   5.08


Subtract 5.08 from each of the 5 means

   4.5-5.08=-0.58	 
   7.2-5.08= 2.12	 
   3.4-5.08=-1.68	 
   9.1-5.08= 4.02	 
   1.2-5.08=-3.88
-------	 
5)25.40
   5.08

Square each of those:

   4.5-5.08=-0.58   (-0.58)²= 0.3364 	 
   7.2-5.08= 2.12   ( 2.12)²= 4.4944	 
   3.4-5.08=-1.68   (-1.68)²= 2.8224	 
   9.1-5.08= 4.02   ( 4.02)²=16.1604	 
   1.2-5.08=-3.88   (-3.88)²=15.0544
-------	 
5)25.40
   5.08

Add those up:

   4.5-5.08=-0.58   (-0.58)²= 0.3364 	 
   7.2-5.08= 2.12   ( 2.12)²= 4.4944	 
   3.4-5.08=-1.68   (-1.68)²= 2.8224	 
   9.1-5.08= 4.02   ( 4.02)²=16.1604	 
   1.2-5.08=-3.88   (-3.88)²=15.0544
-------	                     ------- 
5)25.40                      38.8680
   5.08

Divide 38.8680 by 1 less than 5, which is 4:

   4.5-5.08=-0.58   (-0.58)²= 0.3364 	 
   7.2-5.08= 2.12   ( 2.12)²= 4.4944	 
   3.4-5.08=-1.68   (-1.68)²= 2.8224	 
   9.1-5.08= 4.02   ( 4.02)²=16.1604	 
   1.2-5.08=-3.88   (-3.88)²=15.0544
-------	                     ------- 
5)25.40                    4)38.8680
   5.08                       9.7170

That number in red is the variance of the means.

Edwin
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