NUMERICAL METHODS OF ORGANIZING DATA 39Table 4.4
Mine Workers (g/cm3)Frequency Table for Hemoglobin Levels of 90 High-AltitudeClass Interval Midpoint Frequency
12.0-12.9
13.0-13.9
14.0- 14.9
15 .O- 1 5.9
16.0-16.9
17.0-17.9
18.0-18.9
19.0-19.9
20.0-20.9
2 1 .O-2 1.9
22.0-22.9
23.0-23.9
24.0-24.9
25.0-25.9
26.0-26.912.45
13.45
14.45
15.45
16.45
17.45
18.45
19.45
20.45
21.45
22.45
23.45
24.45
25.45
26.451
1
1
4
6
11
15
21
12
5 3 6 3 0 1Sum - 90
choice is helpful. Comparison is simpler if the two frequency distributions have the
same class intervals.
Before constructing a frequency table, we examine the range of the data set in order
to decide on the length and starting points of the class intervals. The range is defined
to be the difference between the largest and the smallest observations, so that for the
data in Table 4.2 the range is 26.2 - 12.2 = 14.0. Next, an approximate number of
intervals is chosen. Usually between 6 and 20 intervals are used; too much is lost in
grouping the data into fewer than 6 intervals, whereas tables of > 20 intervals contain
an unnecessary amount of detail. Intervals of equal length are desirable, except in
special cases. To obtain equal intervals, the range is divided by the number of intervals
to obtain an interval length that is then adjusted for convenience. In the example, the
range of the datais 26.2 - 12.2 = 14.0 g/cm3, and if we wish about 12 equal intervals,
14.0/12 = 1.2g/cm3. We then adjust the 1.2 to 1.0, a more convenient length, for
the class interval.
The beginning point of the first class must still be decided upon. It must be at least
as small as the smallest observation; otherwise, the choice is arbitrary, although 12.0
seems most convenient.
One problem with making frequency tables using computer programs is that some
programs do not provide investigators with the freedom to choose the particular class
intervals they desire. Many programs give only the frequencies of each distinct ob-
servation; these counts can be accumulated later or the user may be able to group
their data as a separate procedure before obtaining the frequencies. To make fre-
quency tables in Minitab, see Evans [2005], and in Stata see the “tabulate one way for