Download The theoretical mean of the distribution of all possible sample

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Some Stata Output for the single sample of size 25:
Variable |
Obs
Mean
Std. Dev.
Min
Max
---------+----------------------------------------------------chgprice |
25
17.3368
23.54894
-13.8
76.01
And from the population from which it was drawn:
Variable |
Obs
Mean
Std. Dev.
Min
Max
---------+----------------------------------------------------chgprice |
7497
12.27294
28.133
-89.36
525
Results of the simulation: 10,000 samples of size 25 and the overall mean of their
individual means (and their overall standard deviation)
Variable |
Obs
Mean
Std. Dev.
Min
Max
---------+----------------------------------------------------chgprice |
10000
12.2264
5.588577
-4.1552
45.1392
The theoretical mean of the distribution of all possible sample means should be the same as the
population mean µx (12.27294 vs 12.2264)
σ
or 5.6266, we got 5.5886 also very
n
close. We would be closer if we had chosen a larger sample size n. Note the shape, it's very close to
normal.
The theoretical standard deviation for this distribution should be
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