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Two sections of Class IX having 30 students each appeared for the mathematics olympiad. The marks obtained by them are shown below:
46 31 74 68 42 54 14 61 83 48 37 26 8 64 57 93 72 53 59 38 16 88 75 56 46 66 45 61 54 27 27 44 63 58 43 81 64 67 36 49 50 76 38 47 55 77 62 53 40 71 60 58 45 42 34 46 40 59 42 29
Construct a group frequency distribution of the data above using the classes 0-9, 10-19 etc., and hence find the number of students who secured more than 49 marks.

Solution:

Given, the data represents the marks obtained by two sections of Class IX having 30 students each who appeared for the mathematics olympiad.

We have to construct the group frequency distribution of the data above using the classes 0-9, 10-19, etc

Class interval Marks obtained by students Number of students
0 - 9 8 1
10 - 19 14, 16 2
20 - 29 26, 27, 27, 29 4
30 - 39 31, 38, 37, 36, 38, 34 6
40 - 49 46,42,48,46,45,47,44,43,49,40,45,42,46,40,42 16
50 - 59 54,57,53,59,56,54,58,50,55,53,58,59 12
60 - 69 68,61,64,66,61,63,64,67,62,60 10
70 - 79 74,72,75,76,77,71 6
80 - 89 83,88,81 3
90 - 99 93 1

The group frequency distribution of the data above is

Class Tally Marks Frequency
0 - 9 | 1
10 - 19 | | 2
20 - 29 | | | | 4
30 - 39 |||| | 6
40 - 49 |||| |||| |||| | 16
50 - 59 |||| |||| | | 12
60 - 69 |||| |||| 10
70 - 79 |||| | 6
80 - 89 | | | 3
90 - 99 | 1

Total frequency = 1 + 2 + 4 + 6 + 16 + 12 + 10 + 6 + 3 + 1= 60

We have to find the number of students who secured more than 49 marks

From the frequency distribution table,

Number of students who secured more than 49 marks = 12 + 10 + 6 + 3 + 1

= 22 + 10

= 32

Therefore, the number of students who scored more than 49 marks is 32.

✦ Try This: Two sections of Class IV having 30 students each appeared for the mathematics olympiad. The marks obtained by them are shown below:
45 32 75 69 43 55 13 62 84 49 38 27 7 63 58 94 73 55 58 39 17 89 74 54 47 66 46 60 53 25 25 45 65 57 45 83 64 66 35 48 50 76 38 42 55 77 61 53 40 70 60 59 44 43 33 44 41 58 43 8. Construct the group frequency distribution of the data above using the classes 0-9, 10-19 etc., and hence find the number of students who secured more than 89 marks.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

NCERT Exemplar Class 9 Maths Exercise 14.4 Sample Problem 2

Two sections of Class IX having 30 students each appeared for the mathematics olympiad. The marks obtained by them are shown below: 46 31 74 68 42 54 14 61 83 48 37 26 8 64 57 93 72 53 59 38 16 88 75 56 46 66 45 61 54 27 27 44 63 58 43 81 64 67 36 49 50 76 38 47 55 77 62 53 40 71 60 58 45 42 34 46 40 59 42 29. Construct a group frequency distribution of the data above using the classes 0-9, 10-19 etc., and hence find the number of students who secured more than 49 marks.

Summary:

Two sections of Class IX having 30 students each appeared for the mathematics olympiad. The marks obtained by them are shown below: 46 31 74 68 42 54 14 61 83 48 37 26 8 64 57 93 72 53 59 38 16 88 75 56 46 66 45 61 54 27 27 44 63 58 43 81 64 67 36 49 50 76 38 47 55 77 62 53 40 71 60 58 45 42 34 46 40 59 42 29. The group frequency distribution of the data above using the classes 0-9, 10-19 etc.,is shown above and hence the number of students who secured more than 49 marks is 32

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