Page 254 - ICSE Math 8

(ii) Inclusive (or Discontinuous) class intervals: When the class intervals are so arranged that the upper
limit of one class is not the lower limit of the next class, it is called inclusive or discontinuous class
interval. For example, 0–4, 5–9, 10–14, etc.

In this method, both the lower as well as the upper limit are included in the class.

Converting inclusive class Interval into exclusive class Interval
The data tabulated in the inclusive class interval method needs to be re-adjusted to exclusive class interval
method for easy comprehension and continuous class interval.
If a–b is a class of inclusive class interval, then in the corresponding exclusive class interval it becomes
Ê hˆ Ê hˆ
-
Á a - 2 ˜ Á b + ˜ ¯ 2 , where h = (Lower limit of a class) – (Upper limit of previous class)
¯ Ë
Ë
Let’s re-consider Table 2. Here the intervals are inclusive class-intervals.

Marks Number of students The difference between the lower limit of class 21–40 and the
(Class intervals) (Frequency) upper limit of class 1–20 is

1–20 4 h = 21 – 20 = 1
h
1
21–40 7 fi 2 = 2 = 05 .
41–60 13 Marks Number of students
61–80 4 (Class intervals) (Frequency)

81–100 7 0.5–20.5 4
Total 35 20.5–40.5 7
40.5–60.5 13
So, to convert inclusive class intervals into exclusive class 60.5–80.5 4
intervals, we subtract 0.5 from the lower limit of each class and
add 0.5 to the upper limit of each class. Hence, the exclusive 80.5–100.5 7
class intervals are: 0.5 – 20.5, 20.5 – 40.5, 40.5 – 60.5, 60.5 – Total 35
80.5, 80.5 – 100.5

Further,
Class size (or width of class interval) = Difference between two successive lower class limits or two successive
upper class limits
Upperlimit +Lower limit
Class marks (or mid-value of the class interval) =
2
Construction of a discrete frequency distribution

Step 1: Collect raw data.
Step 2: Arrange the raw data in a table of three columns:
(i) Variate (ii) Tally marks (iii) Frequency
Step 3: Place all the values of the variates in the first column in ascending order.
Step 4: Place tally marks against observations in the second column till all the observations in the given raw
data are exhausted.
Step 5: Count the tally marks for each value of variates and place it in the third column.
Step 6: Give a suitable and meaningful title to the frequency table.

242