Question

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.

Answer 1

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 $=(15.2+15.8+15+14.6+14.2+16.2)/6=15\dfrac16$