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{{a| | {{a|squirrels|{{image|Squirrel|png|A nice piece of squirrel, yesterday.}}}}Once upon a time, there was discord in the kingdom of the squirrels. The red squirrels rose up and complained to the statistician-general. <br> | ||
They said, “O, Great Statistician! The grey squirrels have more nuts than us! ” | |||
The greys couldn’t be reached for comment, because they were too busy munching on all their nuts. | The greys couldn’t be reached for comment, because they were too busy munching on all their nuts. | ||
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The statistician mumbled something about multivariate regressions but the reds would not be deterred. Their spokesquirrel continued: | The statistician mumbled something about multivariate regressions but the reds would not be deterred. Their spokesquirrel continued: | ||
:“Look: on average, grey squirrels have more nuts than red squirrels. This cannot be denied. Is it not so?” | :“Look: on average, grey squirrels have more nuts than red squirrels. This cannot be denied. Is it not so?” | ||
:“It is so,” said the Statistician. “The data are very clear about this.” | :“It is so,” said the Statistician. “The data are very clear about this. Grey squirrels have twenty percent more nuts, on [[average]], than reds.” | ||
: | :“''Exactly''. This is unjust! It is due to illegitimate hierarchical structures in the squirrel community, which unfairly skew nut distributions towards those great big fat, greasy grey squirrels.” | ||
:“Hey!” said a passing grey squirrel. “Enough of the fat-shaming.” | :“Hey!” said a passing grey squirrel. “Enough of the fat-shaming. And the trash-talking about grease, for that matter.” | ||
:“Therefore,” continued the | :“Therefore,” continued the Red Leader, “as we red squirrels are systematically repressed, it follows as a matter of inexorable logic, that ''this'' red squirrel, Errol, must have been deprived by — how much did you say?” | ||
:“Twenty percent?” | |||
:Yes! Twenty percent! So Errol should have 20% ''more'' nuts than he currently has...” | |||
:“I should?” said Errol. | |||
:“Don’t let the side down!” hissed Red Leader. “I’m trying to get you more nuts!” | |||
:“Oh, yes! I should!” said Errol. | |||
:“ ... and ''this'' grey squirrel, Frank, has too many, and should have twenty percent fewer.” | |||
:“What?” said Frank, crinkled his brow, but got on with munching. | :“What?” said Frank, crinkled his brow, but got on with munching. | ||
: | :“Therefore, O, Great Statistician, we propose that henceforth we systematically deprive Errol, and grey squirrels like him, of nuts, and give them to Frank, and similar red squirrels, to correct the imbalance.” | ||
The Great Statistician thought about it for a while, and then said, | |||
:“Now, the [[average]] for the red squirrels is the sum of existing nut allocations to re squirrels, divided by the total number of red squirrels. Is that not so?” | |||
:“Yes, that is so.” | |||
:“And it is the same for the grey squirrels?” | |||
:“Yes, it is so. And that would be true, too, of the median, mode and range.” | |||
:“Let’s come back to the [[median]] in a little while. But in many cases these are historical data, are they not?” | |||
:“Yes, O Great Statistician, they are.” | |||
:“Now, it seems to be either there ''has'' been a systematic preference in favour of grey squirrels, or there has not?” | |||
:“There has been! There has been!” | |||
:“And if there has, we should be able to find where it has happened in the historical record?” | |||
:“Well —” | |||
:“For the average that you point to is derived purely from historical cases. Is that not so?” | |||
:“It is so.” | |||
:“That might be difficult. And a bit awkward.” | |||
:“But if you could not find any historical examples of actual injustice in individual nut allocations, would it not also follow, that the data do not represent a systematic inequality at all, being as they are a mathematic function of of those individual nut allocations?” | |||
:“Well me might not be able to prove them but we know it is” |