Basic Engineering Mathematics, Fifth Edition

Presentation of statistical data 297

Acumulative frequency distributionis a table giving
values of cumulative frequency for the values of upper
class boundaries and is shown in Table 31.6. Columns
1 and 2 show the classes and their frequencies. Column
3 lists the upper class boundary values for the classes
given in column 1. Column 4 gives the cumulative fre-
quency values for all frequencies less than the upper
class boundary values given in column 3. Thus, for
example, for the 7.7 to 7.9 class shown in row 3, the
cumulative frequency value is the sum of all frequen-
cies having values of less than 7.95, i.e. 3+ 5 + 9 =17,
and so on.

Table 31.6

1 2 3 4

Class Frequency Upper class Cumulative

boundary less than frequency

7.1–7.3 3 7.35 3

7.4–7.6 5 7.65 8

7.7–7.9 9 7.95 17

8.0–8.2 14 8.25 31

8.3–8.5 11 8.55 42

8.6–8.8 6 8.85 48

8.9–9.1 2 9.15 50

Theogivefor the cumulative frequency distribu-
tion given in Table 31.6 is shown in Figure 31.11.
The co-ordinates corresponding toeachupper class
boundary/cumulative frequency value are plotted and

7.05

Cumulative frequency 10

40

30

20

50

7.35 7.65 7.95 8.25

Upper class boundary values in kilograms

8.55 8.85 9.15

Figure 31.11

the co-ordinates are joined by straight lines (not the best

curve drawn throughtheco-ordinates as inexperimental

work). The ogive is ‘anchored’ at its start by adding the

co-ordinate (7.05, 0).

Now try the following Practice Exercise

PracticeExercise 124 Presentation of

grouped data (answers on page 353)

1. The mass in kilograms, correct to the nearest
   one-tenth of a kilogram, of 60 bars of metal
   are as shown. Form a frequency distribution
   of about 8 classes for these data.
   39.840.1 40.340.0 40.639.7 40.040.4 39.6 39.3
   39.640.7 40.239.9 40.340.2 40.439.9 39.8 40.0

40.240.1 40.339.7 39.940.5 39.940.5 40.0 39.9

40.140.8 40.040.0 40.140.2 40.140.0 40.2 39.9

39.739.8 40.439.7 39.939.5 40.140.1 39.9 40.2

39.540.6 40.040.1 39.839.7 39.540.2 39.9 40.3

2. Draw a histogram for the frequency distribu-
   tion given in the solution of Problem 1.


3. The information given below refers to the
   value of resistance in ohms of a batch of
   48 resistors of similar value. Form a fre-
   quency distribution for the data, having about
   6 classes, and draw a frequency polygon and
   histogram to represent these data diagram-
   matically.

21.022.422.821.522.621.121.622.3

22.920.521.822.221.021.722.520.7

23.222.921.721.422.122.222.321.3

22.121.822.022.721.721.921.122.6

21.422.422.320.922.821.222.721.6

22.221.621.322.121.522.023.421.2

4. The time taken in hours to the failure of 50
   specimens of a metal subjected to fatigue fail-
   ure tests are as shown. Form a frequency dis-
   tribution, having about 8 classes and unequal
   class intervals, for these data.