It was necessary to compare these with another series containing a
larger average, say that of 100 heads in 200 throws. I confess the
labour of tossing pennies two hundred at a time was little to our taste.
So from a bag of pennies borrowed from the bank, we weighed out samples
containing two hundred, and for an evening we were busy counting heads
and tails in these. The heads in sixty samples ranged from 80 to 114.
One hundred heads occurred seven times. The extent and frequency of the
errors is shown in the table.
------+-------+------+-------+------+-------
Error.|No. of |Error.|No. of |Error.|No. of
| Times.| | Times.| | Times.
------+-------+------+-------+------+-------
1 | 8 | 6 | 3 | 11 | 1
2 | 5 | 7 | 3 | 14 | 3
3 | 6 | 8 | 3 | 15 | 1
4 | 3 | 9 | 7 | 18 | 2
5 | 6 | 10 | 1 | 20 | 1
--------------------------------------------
We may call the limit of error 21. Twenty-nine results out of sixty, say
one-half, had an error not exceeding 4; and the mean error is 5.6. In
comparing these with the series 10 in 20 we must, working by rule,
divide not by 10 but by 3.16, the square root of 10; for if we multiply
an average by any number[126] the error is also multiplied but only by
the square root of the number.
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