32 LABORATORY MANUAL OF ANTHROPOMETRY 



In the above list, which is grouped in fives instead of in tens, as in the 

 table above, the group 270-275 is excepted, as containing the mean. 

 The frequency is indicated in the next column, and in the next is indi- 

 cated the rank of each group, above and below that containing the mean. 

 In the fourth is placed the product of rank of each group with the fre- 

 quency of each, and all, both plus and minus, are added together arith- 

 metically, since the amount of the deviation, and not its direction, is 

 sought in each case. This amount is found to be 126 minus, and 134 plus, 

 or 260 in all. But as we have been considering groups of five units, the 

 actual value of these deviations must be multiplied by 5, or 260 X 5 = 

 1300, and as the items included within the group which contains the 

 mean do not count as deviating, this sum is divided by the total num- 

 ber of items, in this case 100, which gives the Average Deviation, if equally 

 distributed to each item, as 13.00. 



There are, however, several small errors not noted in the above, which 

 may now be removed by a little calculation. If the mean were at exactly 

 the mid-point of the group in which it lies, i.e., 272.50, the calculation 

 would be correct as it stands, but in this case it is a very little less than 

 this, or 271.20, a discrepancy of 1.30, which should be subtracted from each 

 item on the minus side of the line, and added to each on the plus side. The 

 items represented on the two sides naturally balance in part, as may be 

 found by subtracting the one group from the other, in this case 126 

 from 134, leaving 8 to account for; the sum of the deviation of these 8 

 items, each of which differs from the figure used by 1.30 ,or in all 10.40, 

 must be added to the sum obtained before division; that is, 1300 + 10.40 

 = 1310.40. This corrects the items except those within the group 270 — 

 275, which may be supposed to differ from the mean by the same amount, 

 1.30. Hence the sum 1.30 X 12 (the number of items involved) or 15.60 

 must be also added, which will increase the total figure to 1326.00. When 

 this amended sum is divided by the total number of items the corrected 

 figure is 13.26, the correct Average Deviation. 



For calculating the deviation of a series of numbers from a mean most 

 statisticians recommend, instead of the above, the Standard Deviation, 

 in which' the calculations are based upon the squares of the successive 

 deviations, rather than the simple numbers, and the final result is ob- 

 tained by extracting the square root of the results thus obtained. This 

 method yields more satisfactory results, but involves more that is purely 

 mathematical. 



IV — Coefficient of Variation 



The calculation of deviation shows the actual amount by which the 

 single item?, on the aveiage, deviate from the mean; in such studies as 

 are discussed here, the actual number of millimeters. It is plain, however, 

 that in a tablo which treats of short measures, involving, perhaps, 100 

 to 150 mm., an average deviation of 10 mm. shows a larger relative devia- 



