2.1.4 Cumulative Frequency Graph and Percentiles
Cumulative relative frequency,orcumulative percentage, gives the percentage of
persons having a measurement less than or equal to the upper boundary of the
class interval. Data from Table 2.2 for the distribution of weights of 57 children
are reproduced and supplemented with a column for cumulative relative fre-
quency in Table 2.6. This last column is easy to form; you do it by successively
accumulating the relative frequencies of each of the various intervals. In the
table the cumulative percentage for the first three intervals is
8 : 8 þ 33 : 3 þ 17 : 5 ¼ 59 : 6and we can say that 59.6% of the children in the data set have a weight of 39.5
lb or less. Or, as another example, 96.4% of children weigh 69.5 lb or less, and
so on.
The cumulative relative frequency can be presented graphically as in Figure
2.6. This type of curve is called acumulative frequency graph. To construct such
a graph, we place a point with a horizontal axis marked at the upper class
boundary and a vertical axis marked at the corresponding cumulative fre-
quency. Each point represents the cumulative relative frequency and the points
are connected with straight lines. At the left end it is connected to the lower
boundary of the first interval. If disjoint intervals such as
10–19
20–29
etc....are used, points are placed at the true boundaries.
The cumulative percentages and their graphical representation, the cumula-
tive frequency graph, have a number of applications. When two cumulative
frequency graphs, representing two di¤erent data sets, are placed on the same
TABLE 2.6
Weight
Interval (lb) Frequency
Relative
Frequency (%)Cumulative
Relative
Frequency (%)10–19 5 8.8 8.8
20–29 19 33.3 42.1
30–39 10 17.5 59.6
40–49 13 22.8 82.4
50–59 4 7.0 89.4
60–69 4 7.0 96.4
70–79 2 3.5 99 : 9 F 100 : 0
Total 57 100.0
TABULAR AND GRAPHICAL METHODS 67