40 FREQUENCY TABLES AND THEIR GRAPHSTable 4.5
Workers Illustrating Relative Frequency and Cumulative FrequencyHemoglobin Level (g/cm3) Frequency Relative Frequency (%) Cumulative Frequency (70)Frequency Table of Hemoglobin Levels for 122 Low-Altitude Mine11 .O-11.9 6 4.9 4.9
12.0-12.9 21 17.2 22.1
13.0-13.9 29 23.8 45.9
14.0- 1 4.9 43 35.2 81.1
1 5 .O- 1 5.9 19 15.6 96.1
16.0-16.9 3 2.5 99.2
17.0-17.9 1 0.8 100.0
Sum 122 100.0frequency tables,” Note that the term frequency table in many computer programs
refers to a type of table discussed in Chapter 11.4.1.4 Relative Frequency TablesIf the numbers in the frequency table are expressed as proportions of the total number
in the set, the table is often somewhat easier to interpret. These proportions are
computed by dividing the frequencies in each class interval by the total sample size.
Often, these proportions are converted to percentages by multiplying by 100. The
table may then be called a table of relative frequencies, or it may still be called a
frequency distribution or frequency table. Relative frequency tables are especially
helpful in comparing two or more sets of data when the sample sizes in the two data
sets are unequal.
Table 4.5 gives a frequency table showing the hemoglobin level for 122 low-altitude
miners. Class intervals for Table 4.5 are of length 1 .O g/cm3, as in Table 4.4. Relative
frequencies reported in percents have been calculated for the results for low-altitude
miners. For example, 4.9% has been calculated by dividing 6 by 122, the total sample
size, and then multiplying by 100 to obtain percents.
The last column in Table 4.5 gives cumulative frequency in percent; this is the
percentage of the low-altitude miners who had hemoglobin levels below the upper
limit of each class interval. The figures are obtained by adding the percentages in
the relative frequency column. For example, the first two relative frequencies in the
table for low-altitude miners are 4.9 and 17.2; these add to 22.1, the percentage found
opposite the second class interval under cumulative frequency. This says that 22.1%
of the mine workers had hemoglobin levels measuring < 12.95 g/cm3.
4.2 GRAPHSThe purpose of a graph: is the same as that of a table; to show the essentials of a
set of data visually so that they may be understood quickly and easily. In gathering
data into any type of table, some of the details are lost in achieving the objective of