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Talk:Statistics/Basic: Difference between revisions
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:Are we dealing with a sample or not? The task states that we use the non-sample formula which is OK as it clearly states what to use. --[[User:Paddy3118|Paddy3118]] 21:30, 2 July 2011 (UTC)
::The task currently says:
:::When talking about a set of sampled data, most frequently used is their [[wp:Mean|mean value]] and [[wp:Standard_deviation|standard deviation (stddev)]]. If you have set of data <math>x_i</math> where <math>i = 1, 2, \cdots n</math>, the mean is <math>\bar{x}\equiv {1\over n}\sum_i x_i</math>, while the stddev is <math>\sigma\equiv\sqrt{{1\over n}\sum_i \left(x_i - \bar x \right)^2}</math>.
::To me, this conveys that we are to supposed to use the population stddev on a set of sampled data. And for that matter, the use of random numbers implies that we are talking about samples. --[[User:Rdm|Rdm]] 21:49, 2 July 2011 (UTC)
:: This is quite complicated. To put it simply, <math>1/(N-1)</math> is used when you need to infer the mean and stddev of an unknown distribution from a very small set of samples from it, while <math>1/N</math> is used when you take the available data set as fully representing the distribution or know exactly the mean of the distribution function. I chose to use the <math>1/N</math> formula is because 1) this task is merely for observing numbers, not doing any variance estimate; 2) it's simpler to derive and understand; 3) it does have its clearly defined meaning regarding how much the data vary, and the distribution is known to be uniform (though strictly speaking then the <math>\bar x</math> should not use the average of samples in this case, it should be exactly 0.5). In any event, when sample size goes up into hundreds, the difference between those two formulas become moot. --[[User:Ledrug|Ledrug]] 23:06, 2 July 2011 (UTC)
::: Ok, yes, that is a good point. If we use 0.5 for the mean in this task, that is the right formula. --[[User:Rdm|Rdm]] 23:30, 2 July 2011 (UTC)
== a bit of duplication ==
There's already a task [[Standard_deviation]] (and it discusses n .v. n-1). At a minimum a reference may be in order. --[[User:Dgamey|Dgamey]] 21:35, 2 July 2011 (UTC)
:This task looks like it is about showing a histogram. I certainly think we need to rename. With some rewording we could probaly shoehorn this into "Statistics/Histograms/Standard Deviation" (which is a really nasty name). Keep thinking guys. [[User:Markhobley|Markhobley]] 08:08, 13 July 2011 (UTC)
== Random number spec ==
Do we need to really specify the range as <math>[0,1]</math>? I ask because it's far more common for random number generators to omit the endpoints, giving a range of <math>(0,1)</math> (due to the way LCPRNGs work). It's a subtle difference I admit. –[[User:Dkf|Donal Fellows]] 10:51, 19 October 2011 (UTC)
:Hi Donal, the task goes on to state: ''". It doesn't matter if you chose to use open or closed range."'' --[[User:Paddy3118|Paddy3118]] 12:32, 19 October 2011 (UTC)
== Perl style ==
I was looking at the perl section, and the code there doesn't seem representative of modern perl style. In particular, the c-style for loop syntax is not very perl-ish. I'd like to change the syntax up a little bit:
<lang perl>my $hist_rows = 10;
my @histogram = map { 0 } 1..$hist_rows; # I filled the array to ensure that $#histogram == $hist_rows-1 - this may be unnecesssary
# alternatively, do away with the $hist_rows variable altogether, using map {0} 1..10 and referring to @histogram instead of $hist_rows below
my $sum = 0;
my $sum_squares = 0;
my $n = $ARGV[ 0 ];
for (1..$n) { # no need to name a variable that is never used
my $current = rand( 1 );
$sum += $current;
$sum_squares += $current ** 2;
$histogram[ $current * $hist_rows ] += 1;
}
my $mean = $sum / $n;
print "$n numbers\n", # concatenation replaced with multiple arguments to print
"Mean: $mean\n",
"Stddev: ", sqrt(($sum_squares / $n) - ($mean ** 2)), "\n";
for my $row_counter (0..$#histogram) {
printf( "%.1f - %.1f : ", $row_counter/$hist_rows, (1/$hist_rows) + ($row_counter/$hist_rows));
print "*" x ($histogram[ $row_counter ]*(30/($n/10))); # loop replaced with x operator
print "\n";
}</lang>
(The comments above are notes to the talk page, and I would erase them before posting the above to the article.)
Needless to say, TMTOWTDI, but this seems more like idiomatic perl to me, and, at least to me, it's more readable. [[User:Flies 1|Flies 1]] 22:26, 5 March 2012 (UTC)
:I concur with the style tweaks, and would go so far as to initialize the array with <tt>(0) x 10</tt> instead of using a <tt>map</tt>. I also dislike the original's style of making <tt>for</tt> look like a function call when it's really a keyword, so I'm glad you're fixing that too. --[[User:TimToady|TimToady]] 00:02, 6 March 2012 (UTC)
::I have updated the code - the page now matches closely what I suggested above. Further improvements to style are welcome! [[User:Flies 1|Flies 1]] 22:06, 6 March 2012 (UTC)
== Bugs in Python Example ==
The previous example code had the following bugs
# Line 36 prints the value of i that was used in a list comprehension (line 35) not the original value of i in the outer loop, so the printed value (in Python 2.7) is the max value not the number of values, e.g. 10^7
# Runtime exceeds 2 minutes on a MacBook Pro. Probably not suitable for an example
So I reduced the maximum list allocated to 100,000 random values, and added a new index variable, j, to take care of the recycled variable i displaying the wrong value (and hanging the terminal update because the string was 10 MB long).
--[[User:Hobs|Hobs]] ([[User talk:Hobs|talk]]) 19:35, 8 April 2013 (UTC)
==Formulae made invisible for most browsers by under-tested cosmetic edits at 20:09, 21 June 2016 ==
Under-tested cosmetic edits made to the task page at 20:09, 21 June 2016, including the injection of spaces around expressions in <math> tags, have left the task description formulae completely invisible to all browsers which display the graphic file version of formulae rather than processing the MathML (this is, in fact, the majority of browsers). The MediaWiki processor does not currently expect such spaces, and generates syntactically ill-formed HTML if they are introduced. Other aspects of these cosmetic edits may further compound the problem. [[User:Hout|Hout]] ([[User talk:Hout|talk]]) 10:06, 24 September 2016 (UTC)
:: Visibility of task description formulae now restored [[User:Hout|Hout]] ([[User talk:Hout|talk]]) 18:58, 10 November 2016 (UTC)
== mean statistic ==
Using statistics to prove a point is just mean. --- anonymous
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