Mathematics · Statistics · NCERT Examples

Example 1

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Mathematics · Chapter 13 · NCERT Examples

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NCERT Example

Example 1

mean · ungrouped frequency distribution · direct method

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

\sum f_i=30,\qquad \sum f_ix_i=1779

\bar{x}=\frac{\sum f_ix_i}{\sum f_i}=\frac{1779}{30}=59.3

Final answer

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