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E:\Working\Focus_Learning\Math_Genius-8\Open_Files\05_Chapter_4\Chapter_4
\ 06-Jan-2025 Bharat Arora Proof-6 Reader’s Sign _______________________ Date __________

Marks Obtained Tally marks Number of students
6 || 2

8 | 1

9 || 2
10 ||| 3

11 || 2
12 ||| 3

13 || 2
14 ||| 3

15 |||| 5

17 | 1
18 ||| 3

19 || 2
20 | 1

Total 30
The number of times an observation occurs in the data is called its frequency.

Here, 1 student obtained 20 marks while 5 students obtained
15 marks. We say 1 is the frequency of the observation 20 and Think and Answer
5 is the frequency of the observation 15 and so on. 1. Can you say how many

The difference between the lowest and the highest observations have frequency 3?
observation is called the range of the data. 2. How many students have
obtained more than 10 marks?
In the above table, we can easily observe that the lowest 3. How many marks does the
marks = 6 and the highest marks = 20 maximum number of students
obtain?
\ Difference = 20 – 6 = 14 (Refer above table)

Thus, 14 is called the range of the data (or observation).
The way of organising data in the above table is known as a frequency distribution table or simply
a frequency table. In an ungrouped frequency distribution table, observations are usually
arranged from the lowest to the highest along with their respective frequencies.

Sometimes, we have to deal with ‘large’ data. For example, consider the marks obtained by 60
students in Class VIII in a semester exam (out of 70):

52 28 23 44 64 22 59 46 28 58 31 56
35 14 65 41 18 43 39 7 27 22 48 33
17 11 36 43 51 27 34 22 41 27 13 20

42 47 43 12 44 5 14 24 8 35 45 24
37 17 51 44 21 39 12 41 50 61 38 69

91 Data Handling