3.6 Bar and Pie Charts 39two digits. The way to reconstruct the data from the diagram is as
follows: The interval with the stem 18 only has one value, and the leaf
is a 3. So the value of the data point is 18.3. The fourth interval from
the top has a stem of 21, and there are nine observations in the intervals.
The leaves are 1, 1, 1, 3, 3, 5, 9, 9, and 9. So the nine values are 21.1,
21.1, 21.1, 21.3, 21.3, 21.5, 21.9, 21.9, and 21.9. The data in the other
intervals are reconstructed in exactly the same way.
3.5 BOX PLOTS
In order to appreciate box plots, we need to explain the interquartile
range. The interquartile range is the middle 50% of the data. The lower
end is the 25th percentile of the data, and the upper end is the 75th
percentile. The width of the interquartile range is equal to:
75th Percentile – 25th Percentile.
As we will see later in the text, the interquartile range is a
robust measure of variability. The box plot, or, more formally, the
box - and - whisker plot, is given as follows: The midline of a box - and -
whisker plot is the median or 50th percentile. The body or box portion
of the plot is the interquartile range going from the 25th percentile to
the 75th percentile. The ends of the whiskers are given different defi ni-
tions by several authors. Often, it runs in the lower end from the 1st
percentile to the 25th percentile, and in the upper end from the 75th
percentile to the 99th percentile. Sometimes, the lower end is the 5th
percentile, and the upper end, the 95th percentile. Points beyond the
ends of the whiskers are potential outliers, and are highlighted as indi-
vidual dots.
The following cartoon shows an example of what the box - and -
whisker plot looks like (Fig. 3.2 ).
3.6 BAR AND PIE CHARTS
We shall use a particular data set that we call the Pugh data to exhibit
both bar charts and pie charts. Both types of charts can be applied to
categorical data. Bar charts are preferred when the categories have a
natural ordering. The bars are displayed across as the order of the cat-
egories increases. The pie chart is preferred to give a good idea of the
proportion of the data in each category. By using a pie or circular shape,