Statistical Methods in Medical Research 4ed

2 . 5
2
1 . 5
1
0 . 5
< 35
35–46 > 46
HDL cholesterol (mg dl –1 )
2.3 Summarizing numerical data 29
< 142
> 198
142–198
Triglyceride
(mg dl –1 )
Fig 2.10 A `three-dimensional' bar diagram showing the relative risk of coronary heart disease in
men, according to high-density lipoprotein (HDL) cholesterol and triglyceride (reproduced from
Simons et al., 1991, by permission of the authors and publishers).
to 0 5 cm, still making the vertical scale in the histogram represent the relative
frequency per cm. We could imagine continuing this process indefinitely if there
were no limit to the fineness of the measurement of length or to the number of
observations we could make. In this imaginary situation the histogram would
approach closer and closer to a smooth curve, the frequency curve, which can be
thought of as an idealized form of histogram (Fig. 2.11). The area between the
ordinates erected at any two values of the variable will represent the relative
frequency of observations between these two points. These frequency curves are
useful as models on which statistical theory is based, and should be regarded as
idealized approximations to the histograms which might be obtained in practice
with a large number of observations on a variable which can be measured
extremely accurately.
We now consider various features which may characterize frequency distributions.
Any value of the variable at which the frequency curve reaches a peak is
called a mode. Most frequency distributions encountered in practice have one
peak and are described as unimodal. For example, the distribution in Fig. 2.6 has
a mode at four males, and that in Table 2.3 at 40±49 lesions. Usually, as in these
two examples, the mode occurs somewhere between the two extremes of the
distribution. These extreme portions, where the frequency becomes low, are
called tails. Some unimodal distributions have the mode at one end of the
range. For instance, if the emission of g-particles by some radioactive material