Sec. 2.5 



CALCULATION OF fi AND a FROM TABLES 



29 



example, if some objects have been weighed to the nearest pound it 

 is reasonable to suppose that an interval written as 20-24 actually 

 means 19.5 to 24.5. If the class intervals are so written, the above- 

 stated rules apply. The length of the class interval will be 5 as be- 

 fore, but the midpoint will be computed as 19.5 -f (1/2) (5) = 22.0 

 instead of 22.5, as it would be if computed on the assumption that 

 the interval started at 20. 



If we are summarizing data which can only be integers, a class 

 interval such as 20-24 should include only the numbers 20, 21, 22, 

 23, and 24. It then is reasonable to take z = 22. The length of the 

 class interval should be taken as 5 again so that the numerical dis- 

 tance between midpoints will coincide with the length of the class 

 interval, which seems to be a reasonable requirement. The proper 

 procedure for other methods of measurement can be figured out along 

 the lines just outlined. 



TABLE 2.51 



Illustration of a Method of Calculating h and <r from the Data in a 

 Frequency Distribution Table with Class Intervals of Equal Lengths 



2/-z 317.5 



2/ 



25 



12.7; o- = 



2/-(z-m) 5 



S/ 



= 5.19, approximately. 



Another, and easier, method of computing fx and o- from a frequency 

 distribution table with equal class intervals is illustrated in Table 

 2.52 along with a partial demonstration of the generality of the 

 method. The procedure involves the same assumption made above 

 and produces exactly the same values for fi and o-. However, in this 

 method the class interval is employed as the computational unit, 

 with the result that the sizes of the numbers needed in the process 

 are smaller than those of Table 2.51. This makes the computations 

 simpler. 



