REPORT OF THE ANTIIROPOMETEIC COMMITTEE. 245 



'Mv. Francis Galton vjJio has prepared the Tahles VIII. to X. on the Range 

 in Height, Weight, and Strength, has contributed the following remarks 

 upon them. 



In determining the range I have employed and extended the method 

 by which the so-called ' probable error ' is found. That is to say, the 

 observations in each series were arranged in the order of their respective 

 magnitudes, beginning with the lowest and ending with the highest. A 

 definite fraction was then cut off from either end of the series ; the values 

 at tbe exact points where the divisions took place were ascertained by 

 interpolation, and the diiference between these gave the range of the in- 

 termediate portion. 



The fractions so cut ofE were — (1) a half; this gave simply the median 

 value : (2) a quarter ; this gave the upper and lower ' quartile ' values, 

 and consequently the ' interquartile ' range (which is equal to twice the 

 ' probable error ') : (3) a tenth ; this gave the upper and lower ' decile ' 

 values, and consequently the ' iuterdecile ' range. The following are the 

 definitions of these terms, Median, Quartile, and Decile : — 



The Median, in height, weight, or any other attribute, is the value 

 which is exceeded by one-half of an infinitely large group, and which the 

 other half falls short of. 



The Ujjper Quartile is that which is exceeded by one-fourth part of an 

 infinitely large group, and which the remaining three-fourths fall short 

 of. Conversely for the Loiver Quartile. 



The Upper Decile is that which is exceeded by one-tenth of an in- 

 finitely large group, and which the remaining nine-tenths fall short of. 

 The Lower Decile is the converse of this ; one-tenth falls short of it, and 

 nine-tenths exceed it. 



Each line of the annexed tables is to be read as in the following 

 instance, taken from the fourth line of Table Villa. 



Example: — 869 observations were made of boys of the professional 

 classes, of 13 yeai-s of age, whence it appears that — 



(1) There are as many boys above the height of 59-0 inches as below 

 it. This Median value differs from the Average value by 0-1 inch, 

 which shows a trifling want of symmetry in the distribution of the 

 heights. 



(2) One-fonrth of the boys exceeds the height of 60-9 inches, and 

 another fourth falls short of 57-1 inches; in consequence, the difference 

 of 3-8 inches defines the range in height of the intermediate two-fourths, 

 or middle half, of the boys. 



(3) One-tenth of them exceeds 62-8 inches, while another tenth falls 

 short of S-S-'i inches. The difference between these numbers is 7"4, which 

 defines the range in height of the intermediate eight-tenths, or three- 

 quarters of the boys. 



(4) The highest measurement actually taken in these 869 observa- 

 tions was 71-5 inches (reckoning to the nearest inch), and the lowest was 

 similarly 49-5 inches, showing a diffei'ence of 22 inches. 



Tiic information as to the extreme values that happen to have been 

 observed in these 869 cases, is avowedly of little solid value. Their 

 magnitude depends to a great degree upon the accident of this particular 

 series happening to include, or not to include, one very excejjtional 

 instance of great stature and another of small stature. It is beyond the 

 power of statistical science to determine the extreme values that might 

 possibly be observed. 



