An Apple Orchard Survey of Ontario County 209 



Averages 



The average value which symbolizes the individuals of a population 

 may be determined in different ways, three of which will be discussed 

 briefly. 



Mode. — The value or measure which occurs most frequently is called 

 the mode. The true mode is the highest point of the theoretical frequency 

 curve, but the mode ordinarily used is the maximum observed frequency, 

 called empirical mode. It is this latter value that is used as mode in the 

 present survey. 



Median. — If all the individuals in the population were arranged in 

 order of their increasing values, the value of the individual in the middle 

 of the group would be the median. The importance of this average lies 

 in the fact that half the individuals lie above the median and half below; 

 the chances are even, therefore, that any previously unknown measure 

 may exceed or fall short of the median. 



Mean. — The average m.ost commonly used is the arithmetical mean, 

 ordinarily called simply the mean, without a limiting adjective. This is 

 determined by adding the values of the individuals and dividing the sum 

 by the total population. Such a mean is considered the best rule for de- 

 termining the most probable measure in a group of observed cases, because 

 the algebraic sum of the positive and negative deviations of the obser^^ed 

 values from the mean is zero. It is this mean that has been used in the 

 tables of the present survey. 



In a nonnal distribution in which the individuals arrange themselves 

 symmetrically about the mean, as is shown graphically by the normal 

 curve, these different values (mode, median, and mean) approximate each 

 other very closely, and any of them may be used to describe the popula- 

 tion. In many cases, however, the curve of the distribution is not 

 symmetrical, but is what Professor Pearson calls a skew curve, in which 

 case the mode may deviate widely from the mean. 



Measure of variability 



Standard deviation. — An average in itself will not give an adequate 

 description of the population. The individuals deviate from the mean, 

 some above it and some below it; some lie very close to the mean, others 

 deviate widely from it. It is desirable to measure this variability and the 

 degree of concentration about the mean. Such a measure is found in the 

 standard deviation, which is determined by the method of least squares. 

 If the standard deviation is small, the mean may be taken as representing 

 closely the values of the general run of the population. On the other hand, 

 if the standard deviation is large there is vvide variation from the mean, 



