Basic Statistics

GRAPHS 45

Figure 4.4 Histogram with small class intervals.

Frequency polygons can be made using options in computer programs. If the
midpoint of the top of the bar is entered into the computer package as a variable, a
line plot option can be used to correct successive points.

4.2.5 Histograms with Small Class Intervals

If we imagine an immense set of data measured on a continuous scale, we may imagine
what would happen if we picked a very small class interval and proceeded to make
a frequency distribution and draw a histogram adjusting the vertical scale so that the
area of all the bars totals 100%. With the bars of the histogram very narrow, the tops
of the bars would get very close to a smooth curve, as shown in Figure 4.4. If the
large set of data that we are imagining is the population being studied, the smooth
curve will be called the frequency distribution or distribution curve of the population.
A small or moderate-sized sample is not large enough to have its histogram well
approximated by a smooth curve, so that the frequency distribution of such a sample
is better represented by a histogram.

4.2.6 Distribution Curves

Distribution curves may differ widely in shape from one population to another. A few
possibilities are shown in Figure 4.5. Such distribution curves have several properties
in common: (1) The area under each of them is equal to loo%, or 1. (2) We may look
at areas between the curves and the horizontal axis and interpret them as proportions
of the individuals in the population. For example, if (a) is the frequency distribution
for heights of a population, and if we judge that 20% of the area is above the portion
of the horizontal axis to the left of 66 in., we decide that about 20% of the heights
of the population are < 66 in. Similarly, if the area from 66 to 70 in. is 60% of the
entire area, then 60% of the heights are between 66 and 70 in.
The distribution curves depicted in Figure 4.5 are often described verbally. For
example, (a) is called a symmetric distribution, where the right side is a mirror image
of the left side; (b) has what is called a long tail to the right, sometimes called skewed