The formula:

<https://i.imgur.com/qLwVFtQ.png>

On 06/03/2022 21:27, Manu Raju wrote:
> The formula:
>
> <https://i.imgur.com/qLwVFtQ.png>
>
>

OK, according to this:

https://www.calculator.net/standard-deviation-calculator.html

There are two slightly different ways of getting the SD. One divides by
N, the other by N-1.

(I had no idea myself, I just copied the method in the OP of the other
thread.)

This suggests that there could be another parameter to the SD function
to select which formula is used.

On Sunday, 6 March 2022 at 21:49:58 UTC, Bart wrote:
> On 06/03/2022 21:27, Manu Raju wrote:
> > The formula:
> >
> > <https://i.imgur.com/qLwVFtQ.png>
> >
> >
>
> OK, according to this:
>
> https://www.calculator.net/standard-deviation-calculator.html
>
> There are two slightly different ways of getting the SD. One divides by
> N, the other by N-1.
>
> (I had no idea myself, I just copied the method in the OP of the other
> thread.)
>
> This suggests that there could be another parameter to the SD function
> to select which formula is used.
>
Yes, to be strictly accurate you should pass in a flag to say whether it is
sample or population deviation. Or have two functions to avoid passing a
confusing boolean.

On 06/03/2022 21:49, Bart wrote:
> On 06/03/2022 21:27, Manu Raju wrote:
>> The formula:
>>
>> <https://i.imgur.com/qLwVFtQ.png>
>>
>>
>
> OK, according to this:
>
> https://www.calculator.net/standard-deviation-calculator.html
>
> There are two slightly different ways of getting the SD. One divides
> by N, the other by N-1.
>
> (I had no idea myself, I just copied the method in the OP of the other
> thread.)
>
> This suggests that there could be another parameter to the SD function
> to select which formula is used.

The full article is at this link:

<https://en.wikipedia.org/wiki/Standard_deviation>

(N - 1) is when you want to apply Bessel's correction factor:
<https://en.wikipedia.org/wiki/Bessel%27s_correction>

I just used a quick method to write a C program because I got bored of
watching Russia Invasion on TV.

On 3/6/2022 10:54 PM, Malcolm McLean wrote:
> On Sunday, 6 March 2022 at 21:49:58 UTC, Bart wrote:
>> On 06/03/2022 21:27, Manu Raju wrote:
>>> The formula:
>>>
>>> <https://i.imgur.com/qLwVFtQ.png>
>>>
>>>
>>
>> OK, according to this:
>>
>> https://www.calculator.net/standard-deviation-calculator.html
>>
>> There are two slightly different ways of getting the SD. One divides by
>> N, the other by N-1.
>>
>> (I had no idea myself, I just copied the method in the OP of the other
>> thread.)
>>
>> This suggests that there could be another parameter to the SD function
>> to select which formula is used.
>>
> Yes, to be strictly accurate you should pass in a flag to say whether it is
> sample or population deviation. Or have two functions to avoid passing a
> confusing boolean.

Well, if all you have is a sequence of samples, then the correct
function to use is what is called the "Sample Standard Deviation" in the
article posted by Bart - i.e. the one that divides by (N-1).

In order to use what is called the "Population standard deviation" (the
one that divides by N) you need to know the exact expected value, which
you can't calculate from a sample, so you can use that formula only if
you pass in the expected value as an extra parameter, which would be
your "flag".

Manu Raju <MR@invalid.invalid> writes:

> The formula:
>
> <https://i.imgur.com/qLwVFtQ.png>

This entire thread so far is weird. The OP --- as far as I can see ---
did not even write a sentence, but somehow everyone seems to have
understood exactly what was being said or discussed or ask and a whole
conversation seems to have taken place.

Not to mention how off-topic it is.

No complaints, no hard feelings. Just weird.

Perhaps sometimes the USENET is used as private chat.

On Sat, 12 Mar 2022 11:45:07 -0300, Meredith Montgomery wrote:

> Manu Raju <MR@invalid.invalid> writes:
>
>> The formula:
>>
>> <https://i.imgur.com/qLwVFtQ.png>
>
> This entire thread so far is weird. The OP --- as far as I can see ---
> did not even write a sentence, but somehow everyone seems to have
> understood exactly what was being said or discussed or ask and a whole
> conversation seems to have taken place.
>
> Not to mention how off-topic it is.
>
> No complaints, no hard feelings. Just weird.
>
> Perhaps sometimes the USENET is used as private chat.

First off, I suspect that Manu Raju started /this/ thread
to relate directly to the wider conversation started by
Malcolm McLean in the "C vis C++ standard deviation function"
thread.

As for the topic, standard deviation is one of those concepts that
- is often taught in high-school and university math programs,
- crops up a lot in scientific and financial computing, and
- is easily implemented in C

Knowing the calibre of the audience in comp.lang.c, I would expect
this sort of discussion around a three-word topic like this :-)

--
Lew Pitcher
"In Skills, We Trust"

Lew Pitcher:

> Knowing the calibre of the audience in comp.lang.c, I
> would expect this sort of discussion around a three-word
> topic like this :-)

I can make a single shot from a small arm: a more
interesting way to calculate standard deviation is via a
numerically stable single-pass algorithm:

https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm

--
() ascii ribbon campaign - against html e-mail
/\ http://preview.tinyurl.com/qcy6mjc [archived]

On 3/6/2022 4:27 PM, Manu Raju wrote:
> The formula:
>
> <https://i.imgur.com/qLwVFtQ.png>

Last year I wrote a short routine to calc the moments of a randomly
generated set of ints. It makes one pass thru the data to calc the
mean, then another pass to determine the other stats.

$ progname N

=======================================================================
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <time.h>

// this program computes the mean, median, mode, variance, std
deviation, skewness and kurtosis
// of a randomly generated set of int numbers

// used the population skewness and Kurtosis formulas from:
//
https://www.calculatorsoup.com/calculators/statistics/descriptivestatistics.php

int randNbr(int low, int high) {
return (low + rand() / (RAND_MAX / (high - low + 1) + 1));
}

int compareint (const void * a, const void * b)
{ if (*(int*)a > *(int*)b) return 1;
else if (*(int*)a < *(int*)b) return -1;
else return 0;
}

int main(int argc, char *argv[])
{ int i=0, lastmode=0;
int N = atoi(argv[1]);
int nums[N];
double sumN=0, median = 0.0;
double sqrdiffmean = 0.0, cubediffmean = 0.0, quaddiffmean = 0.0;
char mode[1000], tmp[12];
srand(time(NULL));
printf("%d Randoms:\nNo commas : ", N);
i=0; while(i<N){nums[i] = randNbr(1,N*2);printf("%d
",nums[i]);sumN+=nums[i];i++;}
i=0; printf("\nWith commas: "); while(i<N){printf("%d,",nums[i++]);}
qsort(nums,N,sizeof(int),compareint);
printf("\nSorted : "); for(i=0;i<N;i++){printf("%d,",nums[i]);}
double mean = sumN/(double)N;
int ucnt = 1, umaxcnt=1;
for(i=0;i<N;i++)
{

sqrdiffmean += pow(nums[i]-mean,2); // for variance
cubediffmean += pow(nums[i]-mean,3); // for skewness
quaddiffmean += pow(nums[i]-mean,4); // for Kurtosis


if(ucnt == umaxcnt && lastmode != nums[i])
{
sprintf(tmp,"%d ",nums[i]);
strcat(mode,tmp);
}

if(nums[i]-nums[i+1]!=0) {ucnt=1;} else {ucnt++;}

if(ucnt>umaxcnt)
{
umaxcnt=ucnt;
memset(mode,'\0',sizeof(mode));
sprintf(tmp,"%d ",nums[i]);
strcat(mode,tmp);
lastmode=nums[i];
}
}

if(N%2==0) {median = (nums[(N/2)-1] + nums[(N/2)]) / 2.0;}
else {median = nums[(N-1)/2];}
printf("\n\nN = %d\n", N);
printf("Sum N = %.0f\n", sumN);
printf("Mean = %.1f\n", mean);
printf("Median = %.1f\n", median);
if(umaxcnt > 1) {printf("Mode(s) = %s (%d occurrences)\n", mode,umaxcnt);}
else {printf("Mode(s) = na (no repeating values)\n");}
printf("Variance = %.2f\n", sqrdiffmean/N);
printf("Std Dev = %.2f\n", sqrt(sqrdiffmean/N));
printf("Skewness P = %.4f\n", cubediffmean / (N *
pow(sqrt(sqrdiffmean/N),3)));
printf("Kurtosis P = %.4f\n", quaddiffmean / (N *
pow(sqrt(sqrdiffmean/N),4)));
return(0);
} =======================================================================