THE SPECIFICATION OF CONTINUOUS VARIATION 



of a large population which would fall within any specific range 

 of heights; or to put it another way, which would enable us to 

 calculate the chance of any individual taken at random falling within 

 any specific range of heights. 



In Fig. 14 is shown the frequency distribution of height in 1,164 

 men, the grouping being into classes covering i-inch ranges. The 



60 



55 70 



STATURE IN INCHES 



75 



Fig. 14. — The cross-hatched histogram shows the frequency distribution of stature as 

 observed in 1,164 men. The data are grouped into classes of one inch, centred on the 

 half-inches. The curve is the normal distribution fitted to these data, and from 

 which they are assumed to depart only by sampling error. A normal distribution is 

 specified by two parameters, jx which fixes the position of the centre point of the 

 curve, and a which measures its spread by the distance from the centre to the points 

 of maximum slope. These are estimated as the mean, .y , and the standard deviation, s, 

 respectively. 



distribution is characteristic of continuous variation in natural popu- 

 lations in that the middle heights are the most common and the 

 frequencies fall off towards each extreme. In this particular case the 

 distribution is also symmetrical; but symmetry depends on, among 

 other things, the scale used in making the measurements, and adjust- 

 ment of the scale may be necessary before a symmetrical distribution 

 is obtained. This question of choice of scale is not encountered in 

 mendelian genetics, for we do not need to specify how tall a tall pea 



57 



