Basic Stats - Standard Deviation

[amhou]

Fixes the calculation of standard deviation.

Previously, sample standard deviation had returned a denominator of n, this fix gives a denominator of n-1.

[was]

Please add a new example to the docstring that illustrates that this bug has been fixed.

[benjaminfjones]

fix plus an example to test it

[benjaminfjones]

I've attached a new patch witch includes the fix plus an example to test the affected block of code. I couldn't think of a better way to access the block than to define a toy class that has its own mean() function which returns a Python long. If the mean() function from basic_stats.py has to be called, the type of 'x' at line 289 won't ever be 'int' or 'long' so the code block in question is never reached.

Maybe someone can suggest a better example?

Here is a before / after log to show that the fix works and that the example tests it.

sage: R = SillyPythonList()
sage: list(R)
[2L, 4L]
sage: len(R)
2
sage: mean(R)
3L
sage: variance(R)
1
sage: variance(R, bias=True)
1

sage: R = [2,4]
sage: mean(R)
3
sage: variance(R)
2
sage: variance(R,bias=True)
1

### LOG (after patch)
sage: R=SillyPythonList()
sage: len(R)
2
sage: mean(R)
3L
sage: variance(R)
2
sage: variance(R, bias=True)
1
sage: R = [2,4]
sage: variance(R)
2
sage: variance(R, bias=True)
1

[benjaminfjones]

Replying to benjaminfjones:

... and I made sure the doctest passes for the new example. I'm applying the patch to Sage Version 4.6.1.alpha1.

[spice]

All good (reviewed trac_9028_stats_fix+example.patch; trac_9028_stats.patch is obsolete).