standard deviation

[memas]

i have 11 numbers 1,2,3,4,5,6,7,8,9,10,11 and i want to know if there any formula that will show me which group of numbers the upper from the middle or the under of the middle has more posibilities

i search with the standard deviation but still this i want is not clear
any idea?
memas
thank you

[moonman239]

What do you mean by "has more possibilities?"

[jemidiah]

Also, what do you mean by "the upper from the middle" or "the under of the middle"? An example would probably be very helpful.

[memas]

example
if we have two groups of students the group A and the group B
we give the same test to examine them
we give them values for their studies according to a scale of 20

and the numbers for the group A are
17,18,20,14,16,14,18,17,13,17,12,19,13,17,15,19,14,16,17,18,17
group B
20,17,19,15,17,19,16,20,15,17,10,14,9,17,9,20,17,16,20,16,17


in both groups
the major value is the same 17 and the frequency 16,75
the middle is the same 16,75
the mathematical average is the same 16,24


which group has the best result? the A or B and why?
thank you
memas

[jemidiah]

I don't know what you mean by "major value" and "frequency". I sorted the groups for convenience and found the mean (average), median (middle value), and mode (most repeated value) for both:

Group A
12,13,13,14,14,14,15,16,16,17,17,17,17,17,17,18,18,18,19,19,20
median=17
mode=17
mean=341/21 = 16.2381...

Group B
9,9,10,14,15,15,16,16,16,17,17,17,17,17,17,19,19,20,20,20,20
median=17
mode=17
mean=340/21 = 16.1905...

Since Group A has a higher mean than group B (which doesn't agree with what you said but I did double check the result) I would say Group A outperformed Group B.

In general, I would say the group with the higher mean does better, since then if you gave the same test to a random pair of people, one person from each group, and the pair performed according to their results above, the group with the higher mean score would win the head-to-head competition more often than the other group, when you weight a "win" according to how much the scores differ. If the means are equal, in a head-to-head competition the two groups would win equal amounts of the time--they would tie.

For instance, if a person from Group A got a 17 and a person from Group B got a 9, Group A would win by a factor of 8. If a person from Group A instead got a 12 and a person from Group B got a 9, Group A would win by a factor of only 3. If you consider all possible pairs of people and add up the win/lose factor of each, the group with the higher mean will end up with a positive "win" factor.

However, there are other valid ways to figure out which group should "win". For instance, you might value people who scored very well more than people who scored poorly--say the low scorers will be expelled from the school. In that case, the mean isn't the best thing to use.

[memas]

thank you very much
can you tell me if there a professional site for statistics that i can register asking all the questions that
need , i am music composer and i fixed a programe that helps me to compose better and i need help about the formulas of statistics
thank you
memas

[jemidiah]

I don't know of one, sorry. You might try getting a book on basic statistics. Good luck.

[memas]

in this example in the first datagrid the winner was a sum that was lower than the 14,47.....13

in the second datagrid the winner was a sum higher than the mean of the variable 16,74.....22

i want to know if theses datagrids show the reason why in the first datagrid the result 13 was lower than the mean 14
and in the second the result was higher than the mean 17...22

thank you memas






1471sml originale 471big
N Valid 134 268 134
Missing 134 0 134
Mean 10,85 14,47 18,09
Std. Error of Mean ,215 ,271 ,226
Median 11,00 14,00 18,00
Mode 12 12a 17
Std. Deviation 2,488 4,433 2,620
Variance 6,188 19,651 6,864
Skewness -,746 ,051 ,729
Std. Error of Skewness ,209 ,149 ,209
Kurtosis -,166 -,430 ,153
Std. Error of Kurtosis ,416 ,297 ,416
Range 10 22 12
Minimum 4 4 14
Maximum 14 26 26
Sum 1454 3878 2424
Percentiles 25 9,00 11,00 16,00
50 11,00 14,00 18,00
75 13,00 18,00 20,00








small originale big
N Valid 134 268 134
Missing 134 0 134
Mean 12,84 16,74 20,63
Std. Error of Mean ,226 ,291 ,248
Median 13,00 17,00 20,00
Mode 16 16 18
Std. Deviation 2,621 4,772 2,875
Variance 6,870 22,770 8,264
Skewness -,526 ,104 ,667
Std. Error of Skewness ,209 ,149 ,209
Kurtosis -,654 -,549 -,166
Std. Error of Kurtosis ,416 ,297 ,416
Range 11 23 12
Minimum 6 6 17
Maximum 17 29 29
Sum 1721 4486 2765
Percentiles 25 11,00 13,00 18,00
50 13,00 17,00 20,00
75 15,00 20,00 23,00

[jemidiah]

I'm sorry, I have no idea what you're trying to ask. You'll have to be clearer.

[memas]

example we have two football teams and the numbers that the variables have are the numbers that i gave them according to their technique
is it possible to know which group will have the most posibilities to win and why
the group A that his numbers are lower than the mean or the group B that their numbers are higher than the mean
thank you






N Valid 268
Missing 0
Mean 14,47
Std. Error of Mean ,271
Median 14,00
Mode 12a
Std. Deviation 4,433
Variance 19,651
Skewness ,051
Std. Error of Skewness ,149
Kurtosis -,430
Std. Error of Kurtosis ,297
Range 22
Minimum 4
Maximum 26
Sum 3878
Percentiles 25 11,00
50 14,00
75 18,00





N Valid 268
Missing 0
Mean 16,74
Std. Error of Mean ,291
Median 17,00
Mode 16
Std. Deviation 4,772
Variance 22,770
Skewness ,104
Std. Error of Skewness ,149
Kurtosis -,549
Std. Error of Kurtosis ,297
Range 23
Minimum 6
Maximum 29
Sum 4486
Percentiles 25 13,00
50 17,00
75 20,00

[jemidiah]

I'm gonna say that the statistics you've shown are for, say, number of points earned per game for two given teams [using American football, since the scores are near 20]. In that case, you actually can't tell with certainty which team would win more often even assuming over a sufficiently long period of time the two teams would perform exactly according to the statistics given. For instance, one team could have very low scoring games on average and the other could have high scoring games, and you couldn't tell without a much more detailed analysis what might happen when the two play each other.

So, no, it is not "possible to know which group will have the most pos[s]ibilities to win". However, it's probably a decent bet to just say the team with the higher average will outperform the team with the lower average.

The situation changes drastically when a win by a large margin is "worth more" than a win by a small margin, and you just track winning amounts instead of absolute scores. This is the situation I described in post #5.

[memas]

thank you for your help
but i want to ask what are the analysis that we need instead to tell which group is better and why

[jemidiah]

It depends entirely on your application. If the groups are football teams and "better" means winning by a higher margin in a long tournament, all you need is the (true) mean winning margin between all teams.

It would probably be much faster and more useful if you just (clearly) explained your application.... So far most of your questions are so general they have no answer.

[memas]

lets put it this way the groups are football teams and i want to know which group has the most posibilities to win
1...what analysis has to do instead to have the correct answer?
2...how accurate the statistic result could be?
thank you memas

[jemidiah]

I'm sorry, you haven't answered my previous question. In particular, you haven't said what the situation is--are your football teams playing each other in a long (or short?) tournament with (or without?) elimination? There are too many unanswered questions.

You can't just "throw statistics" at a problem and hope an answer comes out from the gods of math. Math is just reasoning with clear assumptions. Unfortunately, you haven't been clear, so math has no answer to your questions.

[memas]

the groups are football teams and i want to know which group has the most posibilities to win
1...what analysis has to do instead to have the correct answer?
2...how accurate the statistic result could be?
thank you memas

[jemidiah]

the groups are football teams and i want to know which group has the most posibilities to win
1...what analysis has to do instead to have the correct answer?
2...how accurate the statistic result could be?
thank you memas

This yet again doesn't clarify my (incredibly necessary) questions. I'm sorry, I'm not going to respond to this thread anymore. Metaphorically, you're asking me to build a rocket without telling me if it has to go to the moon or carry a firework.