Basic Statistics

36 FREQUENCY TABLES ANDTHEIR GRAPHS

Table 4.1 Hemoglobin Levels of 90 High-Altitude Mine Workers (g/cm3)

18.5 16.8 23.2 19.4 19.5 20.6 22.0 17.8 16.2

23.3 19.7 21.6 24.2 21.4 20.8 19.7 21.1 23.0

21.7 18.4 22.7 20.9 20.5 16.1 16.9 24.8 12.2

17.4 17.8 19.3 17.3 18.3 17.8 17.1 18.4 19.7

17.8 19.0 19.2 15.5 26.2 19.1 20.9 18.0 21.0

20.2 18.3 19.2 17.2 19.8 19.5 20.0 18.4 15.9

19.9 16.4 18.4 17.8 23.0 19.4 20.3 18.2 13.1

20.3 18.5 24.1 14.3 17.8 19.9 23.5 19.7 19.3

20.6 18.3 20.8 17.6 18.1 19.7 19.1 19.5 23.5

18.5 20.0 22.4 18.8 16.2 15.6 15.5 18.5 19.0

First, methods of summarizing the data in stem and leaf and frequency tables are
illustrated in Section 4.1. Then Section 4.2 presents ways of making histograms
and frequency polygons from the results of the frequency tables. When statistical
programs are used, the explanations will help in the choice of the program and also
in choosing among the options.

4.1 NUMERICAL METHODS OF ORGANIZING DATA

In Table 4.1 we have an example of a moderate-sized set of raw data containing

hemoglobin levels for 90 high-altitude miners in grams per cubic centimeter. Without

some rearrangement of the 90 observations, the values are difficult to interpret. Here

in Section 4.1 we discuss making an ordered array of the data, and then show how to

make a stem and leaf table and a frequency table.

4.1.1 An Ordered Array

The simplest arrangement of the data is an ordered array. An ordered array is an
arrangement of the observations according to size from smallest to largest. It can be
done easily by hand for small sets of data. Most statistical packages include a sort
command that will sort any variable (see Minitab, SAS, SPSS, or Stata). From an
ordered array the maximum and minimum values can be seen. A typical value would
be in the middle of the list. Table 4.2 is still cumbersome, however, and contains so
much detail that we cannot easily distinguish its important properties.

4.1.2 Stem and Leaf Tables

The basic idea in making a stem and leaf table is to present the first digit or digits of

each observation in the first column and the rest of the digits in the second column.

Each line is called a called a stem and the information on the stem is called the leaf.

In Table 4.3 we have three digits, and we call the first two the stem and the last one

the leaf. Note that if we look at Table 4.2 for the first number, 12.2, the first two digits