Page 256 - ICSE Math 8

Construction of a Grouped Frequency Distribution

Step 1: Find the maximum and minimum values of the variates occurring in the data.
Step 2: Decide upon the number of classes to be formed, preferably from 5 to 15 classes.
Step 3: Find the range and the class interval.
Range = Maximum value – Minimum value Class interval = Range
Number of classes
Ensure that the first class interval contains the minimum value and the last class interval contains the
maximum value.
Step 4: Taking one observation from the data at a time, put a tally mark against the class to which the
observation belongs.
Step 5: Count the tally marks and find the frequency of each class.
Step 6: Give a suitable and meaningful title to the frequency distribution table.
Example 2: Study the following frequency distribution Frequency Distribution of Daily
table and answer the questions given below: Income of 600 Workers
(a) What is the size of the class Class interval Frequency
intervals? (Daily income in rupees) (Number of workers)
(b) What is the upper class limit of 100–125 45
the seventh class interval? 125–150 25
(c) Which class has the highest 150–175 55
frequency? 175–200 50
(d) What is the class mark of the 200–225 125
fourth interval? 225–250 140
Solution: (a) Size of each class interval is 25. 250–275 55
(b) Upper class limit of the seventh 275–300 35
class interval (250–275) is 275. 300–325 50
20
(c) Class 225–250 has the highest 325–350 600
Total
frequency, i.e., 140.
175 200+ 375
(d) Class marks of the fourth class interval (175–200) = = = 187.5
2 2
Example 3: Construct a grouped frequency distribution Frequency Distribution of Marks
table from the following marks obtained by the of 20 Students
students of class VIII in an examination. Make Marks of Tally
exclusive class intervals of width 5. students marks Frequency
35, 40, 45, 72, 76, 45, 52, 60, 42, 70,45, 68, 55,
64, 61, 54, 51, 35, 46, 48 35–40 | | 2
40–45 | | 2
Solution: Minimum marks = 35,
Maximum marks = 76 45–50 5

Range = 76 – 35 = 41, 50–55 | | | 3
Width of class intervals = 5 55–60 | 1
Since the minimum marks are 35, the first class 60–65 | | | 3
interval starts with 35. Also the class intervals 65–70 | 1
are exclusive.
70–75 | | 2
75–80 | 1

Total 20

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