44 FREQUENCY TABLES ANDTHEIR GRAPHS

703

Age (years)

Figure 4.3 Age of 302 deaths from scarlet fever: a frequency polygon

seem to be somewhat less than one-half of the area of the entire histogram. From this

we conclude that less than one-half of the low-altitude hemoglobin levels were under

14 g/cm3. In contrast, we see that only a very small percentage of hemoglobin levels

in the high-altitude group was under 14 g/cm3, since the area of the bars to the left of

14 is very small.

4.2.4 The Frequency Polygon

Instead of a histogram a frequency polygon is often made from a frequency distri-

bution. It is made in the same way, except that instead of a bar of the proper height

over each class interval, a dot is put at the same height over the midpoint of the class

interval. The dots are connected by straight lines to form the frequency polygon.

Sometimes the polygon is left open at each end, but usually it is closed by drawing

a straight line from each end dot down to the horizontal axis. The points on the

horizontal axis that are chosen to close the frequency polygon are the midpoints of

the first class interval (on either end of the distribution) that has a zero frequency.

Figure 4.3 gives a frequency polygon corresponding to the histogram of Figure 4.2.

The frequency polygon differs little from the histogram. To compare two frequency

polygons at a glance may be easier than to compare two histograms. On the other

hand, the frequency polygon has the disadvantage that the picture it gives of areas is

somewhat distorted. The area over a certain class interval is no longer exactly equal

to the proportion of the observations within that interval. The difference is slight,

however, unless the number of class intervals is small.