A mother's age is three less than three times her daughter's age. The sum of their ages is 45. What is the daughter's age?
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Answer:
In general, sample statistics will tend to be different. With continuous random variables, this should always be the case (until rounding, which brings us back to "actually that's just theoretically continuous") and with discrete random variables this will often be the case with some statistics and perhaps more often not with others (how often it depends on the distribution pattern, sample size, and the particular statistics you are viewing).
Step-by-step explanation:
You can response your particular query by straight experiment, in simple cases.
For example, consider rolling a particular six-sided die (a well-made one that's very close to fair). You could withdraw two samples of some wanted size (n1 = 20
and n2 = 20 say) and calculate your sample statistics. I suggest you try it!
Actually, not being one to ask you to try something I wouldn't do myself, here are my attempts, first with one die (two samples each of size 20) and then a repeat with a different die:
Result of die A: 1 2 3 4 5 6
Sample 1 (Counts) 2 3 3 2 4 6
Sample 2 6 2 3 4 3 2
Result of die B: 1 2 3 4 5 6
Sample 1 (Counts) 3 7 3 0 3 4
Sample 2 1 4 1 5 4 5
And here are some summary statistics:
Die A Range median mean sd
Sample 1 5 4.5 4.05 1,791
Sample 2 5 3 3.10 1,774
Die B Median Mean Range SD
Sample 1 5 2.5 3.25 1,860
Sample 2 5 4 4.10 1,619
If you do, you will probably get the same maximum and minimum both times (I would expect both 1 and 6 to show in a sample of 20 about 95% of the time), but the means and standard deviations would be different.
The medians could be the same (about a 25% chance of that, with the usual definition of sample median even for n
), but easily not.
There is some chance of obtaining the same mean for two of these (because we are sampling a discrete distribution with only a few results), but there is a low probability of seeing it (around 3.7%);
You can also get the same standard deviation, but the chance is much less ... about 2/3 of a percentage.
At larger or smaller sample sizes, those possibilities change; and they change again if you extract from other distributions other than that of a (roughly) fair die.
That all those statistics I mentioned would be the same would be highly unlikely.
