Question

n studying the sampling distribution of the mean, you were asked to list all the different possible samples from a small population and then find the mean of each of them. Consider the following: Personal phone calls received in the last three days by a new employee were 2, 4, and 7. Assume that samples of size 2 are randomly selected with replacement from this population of three values. What different samples could be chosen? What would be their sample means?

Answer 1

The Total outcome with replacement will be given by ,3² = 9, the mean of the samples will be  2 , 4.5 , 3 , 7 , 4

What is Mean ?

Mean predicts the central tendency of a data set , It is determined by the ratio of sum of all the numbers to the total numbers in the data set.

On the basis of given data

The number given is 2,4,7

Size of the sample = 2 with replacement

The Total outcome with replacement will be given by

3² = 9

Possible outcome can be

2,2   2,4   2,7   4,4  4,2  4,7  7,7  7,2  7,4

The sample mean can be calculated as

(a+b)/2

(2+2)/2 = 2

similarly the mean of the samples will be  2 , 4.5 , 3 , 7 , 4

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