Page 193 - Maths Skills - 8

Data Handling 191

Step 4: Now calculate the list of groups.

Groups Frequency
0–4 Here, 0–4 means observations greater than or equal to 0 but less
4–8 than 4, and similarly 4–8 means observations greater than or
8–12 equal to 4 but less than 8 and so on.
12–16

16–20

Step 5: Now tally the results to find the frequencies as shown below:

Groups Tally Frequency

0–4 ||| 3 Fact-o-meter

4–8 |||| || 7 � Data presented in this manner

8–12 |||| |||| || 12 is said to be grouped and the

distribution obtained is called
12–16 |||| || 7 grouped frequency distribution.

� Grouped frequency distribution
16–20 |||| |||| 9 helps us to draw meaningful

Total = 38 inferences.

Now, let us learn more through an example.

Let’s Attempt

Example: Construct a grouped frequency distribution with suitable class interval size of marks obtained by
50 students of a class as given below:
23, 50, 38, 42, 63, 47, 75, 12, 33, 26, 39, 35, 47, 43, 52, 59, 64, 77, 15, 21, 51, 54, 72, 56, 68, 36,
65, 52, 60, 27, 34, 48, 58, 59, 62, 51, 48, 50, 41, 55, 57, 65, 54, 43, 56, 44, 30, 46, 67, 53
After making the frequency distribution table, answer the following questions:

(a) How many students have scored less than 40?
(b) What is the class mark of the class interval with frequency 10?
(c) Which class interval has the highest frequency?
(d) What percentage of students scored more than 61?

Solution: Arranging the marks in ascending order, we get the data as below:
12, 15, 21, 23, 26, 27, 30, 33, 34, 35, 36, 38, 39, 41, 42, 43, 43, Fact-o-meter
44, 46, 47, 47, 48, 48, 50, 50, 51, 51, 52, 52, 53, 54, 54, 55, 56,
56, 57, 58, 59, 59, 60, 62, 63, 64, 65, 65, 67, 68, 72, 75, 77 Here, we have considered

Minimum value = 12, Maximum value = 77 number of groups as 10.
Range = 77 – 12 = 65
65
Class Interval Size = Range/ No. of groups = 10 = 6.5 = 7