sent the amount of information contained in the sample. The real explanation
forn1 is hard to present at the level of this book; however, it may be seen
this way. What we are trying to do withsis to provide a measure of variability,
a measure of the average gap or average distance between numbers in the
sample, and there aren1 gaps betweennnumbers. Whenn¼2 there is only
one gap or distance beween the two numbers, and whenn¼1, there is no
variability to measure.
Finally, it is occasionally useful to describe the variation by expressing the
standard deviation as a proportion or percentage of the mean. The resulting
measure,
CV¼
s
x100%
is called thecoe‰cient of variation.Itisanindex, a dimensionless quantity
because the standard deviation is expressed in the same units as the mean and
could be used to compare the di¤erence in variation between two types of
measurements. However, its use is rather limited and we will not present it at
this level.
2.2.4 Box Plots
Thebox plotis a graphical representation of a data set that gives a visual
impression of location, spread, and the degree and direction of skewness. It also
allows for the identification of outliers. Box plots are similar to one-way scatter
plots in that they require a single horizontal axis; however, instead of plotting
every observation, they display a summary of the data. A box plot consists of
the following:
- A central box extends from the 25th to the 75th percentiles. This box is
divided into two compartments at the median value of the data set. The
relative sizes of the two halves of the box provide an indication of the
TABLE 2.11
Weight Interval fm m^2 fm fm^2
10–19 5 14.5 210.25 72.5 1,051.25
20–29 19 24.5 600.25 465.5 11,404.75
30–39 10 34.5 1,190.25 345.0 11,902.50
40–49 13 44.5 1,980.25 578.5 25,743.25
50–59 4 54.5 2,970.25 218.0 11,881.00
60–69 4 64.5 4,160.25 258.0 16,641.00
70–79 2 74.5 5,550.25 149.0 11,100.50
Total 57 2,086.5 89,724.25
80 DESCRIPTIVE METHODS FOR CONTINUOUS DATA