Present a complete process in computing the mean of the sampling distribution of the sample
means given the General Mathematics 20- item quiz result of 6 students; 12, 16, 18, 20, 10, 15.
Consider a sample size of 5.
Solution:
Given result of 6 students; 12, 16, 18, 20, 10, 15.
Here, a sample size of 5, so n=5
We consider no repetition.
Samples are: (12, 16, 18, 20, 10), (16, 18, 20, 10, 15), (12, 18, 20, 10, 15), (12, 16, 20, 10, 15), (12, 16, 18,10, 15), (12, 16, 18, 20,15).
Their means are:
Mean of (12, 16, 18, 20, 10)"=(12+16+18+20+10)\/5=15.2"
Mean of (16, 18, 20, 10, 15)"=(16+18+20+10+15)\/5=15.8"
Mean of (12, 18, 20, 10, 15)"=(12+15+18+20+10)\/5=15"
Mean of (12, 16, 20, 10, 15) "=(12+16+15+20+10)\/5=14.6"
Mean of (12, 16, 18,10, 15) "=(12+16+18+15+10)\/5=14.2"
Mean of (12, 16, 18, 20,15)"=(12+16+18+20+15)\/5=16.2"
Now, mean of sampling distribution "=(15.2+15.8+15+14.6+14.2+16.2)\/6=15\\dfrac16"
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