Page 318 - Start Up Mathematics_8 (Non CCE)

Table 1 This way of presentation of data is known as frequency
distribution. The marks obtained are called variates and the
No. of students
Marks Tally marks number of students scoring them is called the frequency of the
(Frequency)
8 | | 2 variate.
19 | | 2 Now, if you notice, you can answer the following questions
22 | 1 through the method of tabulation that you just learnt.
27 | | | 3 (a) What are the minimum marks?
35 | 1 (b) What are the maximum marks?
36 | 1 (c) Which marks was obtained by maximum number of
39 | 1 students?
46 5 The above example can be tabulated in a more refined way.
48 | 1 The data can be further condensed into “class groups”. In this
52 | 1 method, the observations are divided into groups called classes
56 | | | | 4 or class intervals.
60 | | 2
65 | 1
73 | | | 3 Remember
85 | | 2 The total of all frequencies
87 | | | 3 should be equal to the total
98 | | 2 number of observations.
Total 35

Now, let’s re-tabulate the above data. Table 2
The class interval 1–20 means the marks obtained Marks No. of students
between 1 and 20, both inclusive. The number of (Class intervals) Tally marks (Frequency)
observations falling in a particular class is called the
frequency of that class or class frequency. 1–20 | | | | 4
Taking the example of class interval 1–20, 1 is the 21–40 | | 7
lower limit and 20 is the upper limit of the class. The 41–60 | | | 13
size of the class interval is the difference between two 61–80 | | | | 4
successive lower class limits or two successive upper 81–100 | | 7
class limits. Therefore, for class intervals 1–20, 21–40,
etc., the class interval is 21 – 1 or 40 – 20 which is 20. Total 35

Frequency Distribution
Frequency table or frequency distribution is a method of presenting the raw data in an easy, comprehensible
form.
Frequency distribution is of two types:
1. Discrete frequency distribution 2. Continuous or grouped frequency distribution
Table 1 and 2 of the earlier explained example are specimens of discrete and continuous frequency distribution
respectively.
Now the data can be further classified according to the class intervals as:
(i) Exclusive (or Continuous) class intervals: When the class intervals are so arranged that the upper limit
of one class is the lower limit of the next class, it is called exclusive or continuous class interval. For
example, 0–10, 10–20, 20–30, etc.

In this method, the upper limit is not included in the class.

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