Question

Form a group of eight students in your class or section. Determine the general weighted average of the members of the group. List them

1.list all the possible samples of size 2 and their corresponding means

2.construct the sampling distribution of the sample means

3.calculate the mean of the sampling distribution of the sample means

Answer 1

Let the weight of students are (in kg)

50 , 52 , 53 , 54 , 56 , 57 , 58 , 60

Average weight = $\dfrac{50+52+53+54+56+57+58+60}{8}=55$

So,  general weighted average of the members of the group = 55 kg

(1) Sample of size 2 = $^8C_2=28 \ samples$

(2)

(3) Mean of sampling distribution of the sample means = mean of the population

Mean of sampling distribution of the sample Mean $\bar X = \dfrac{1}{n}\sum X_i=\dfrac{1540}{28}=55$