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LABORATORY MANUAL OF ANTHROPOMETRY 



some little chance of error, since the separate individual measures may be 

 anywhere between the limits of each group, yet the error is inconsiderable. 

 A second method of obtaining the arithmetic mean is by assuming a 

 mean, which may be any mid-value in the list, and calculating the correc- 

 tions. It is as follows : 



The first two columns are as before. An average is assumed, in this 

 case we take the group with 15 instances, with the value of 255, the 

 mid-value between 250 and 260, the two extremes of the group taken. 

 We then prepare the third column, by marking the group taken as 0, and 

 successively designating those that are lower as 1, 2, 3, and so on; 

 while the larger groups are also successively, counting from the 0, +1, 

 +2, +3, and so on. The fourth column is made up of the product of the 

 items of the third and the second, the product of the number of instances 

 into the class value of each group. These are summed up in two sums, 

 the + and the , the algebraic sum of the two is obtained, and alge- 

 braically added to the assumed average. This gives the actual average. 



Here, assuming the average to fall at 255, we get, by multiplying 

 column four by column three, the sum of 22 and the sum of +184. 

 The algebraic sum of the two is +162, which should be multiplied by 10, 

 the class interval, and then divided by 100, the total number of indi- 

 viduals used. This gives us, first, 1620, and then 16.20, which, having 

 a + sign, must be added to the assumed average, 255, to get the true 

 average, 271.2, the same as by the other method. If the reader should 

 start with the same two first columns, and assume any other average, as, 

 for example, 275 or 285, the final result would be the same. 



This method is not any simpler to understand than the other, but has 

 the distinct advantage of using lower numbers. 



IV. Deviation 



The arithmetical mean, or average, represents the value of each of the 

 separate items if they were all evened up, with those which were more 



