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Mathematics · Statistics · NCERT Examples

Example 1

A complete, independently verified solution for NCERT Example 1.

Mathematics · Chapter 13 · NCERT Examples

Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

NCERT Example

Example 1

The marks obtained by 30 Class X students in a 100-mark Mathematics paper are given below. Find the mean marks.

Marks obtained by 30 students

Marks obtained

Number of students

10

1

20

1

36

3

40

4

50

3

56

2

60

4

70

4

72

1

80

1

88

2

92

3

95

1

Solution

Board-exam working:

Multiply every observation by its corresponding frequency.

Direct-method calculation

Marks (xᵢ)

Frequency (fᵢ)

fᵢxᵢ

10

1

10

20

1

20

36

3

108

40

4

160

50

3

150

56

2

112

60

4

240

70

4

280

72

1

72

80

1

80

88

2

176

92

3

276

95

1

95

fi=30,fixi=1779\sum f_i=30,\qquad \sum f_ix_i=1779
xˉ=fixifi=177930=59.3\bar{x}=\frac{\sum f_ix_i}{\sum f_i}=\frac{1779}{30}=59.3

Final answer

xˉ=59.3 marks\boxed{\bar{x}=59.3\text{ marks}}