First, we find the mean of all possible samples of a given size then the mean of all these means is known as the sampling distribution. (Bennett, Briggs & Triola, 2014, p. 276).
Hence, to find the mean of sampling distribution means of multiple samples are needed.
In this example, I’ll elaborate on the final English scores of five students at the end of the semester.
Student Average final scores
1 93
2 91
3 90
4 75
5 60
Mean 81.8%
By the replacement method, I’ll repeat the sample six times.
Scores
51 76 88 70 59
67 70 92 99 94
86 52 81 60 75
53 75 60 84 72
66 55 93 60 70
Mean 64.4% 65.6% 82.8% 74.6% 74%
Now mean of the sampling distribution is the mean of all above 6 samples is 73.9%.
References:
“8.1 A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size – Introductory Business Statistics | OpenStax.” Openstax, Openstax, 2022, openstax.org/books/introductory-business-statistics/pages/8-1-a-confidence-interval-for-a-population-standard-deviation-known-or-large-sample-size.
Bennett, J., Briggs, W., Triola, F. (2014) Statistical Reasoning for Everyday Life, 4e [DX
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