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Maths / Statistics / Mean of Ungrouped Data

a

QUESTION
 

Illustration:   The marks obtained by 30 students of Class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students.

Marks obtained large (x_{i})10203640505660707280889295
Numbers of student large (f_{i})1134324411231
OPTIONS
A. 

61

B. 

59

C. 

59.3

D. 

None of these

Right Option : C
EXPLANATION
Explain TypeExplanation Content
Text

Illustration:   The marks obtained by 30 students of Class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students.

Marks obtained large (x_{i})10203640505660707280889295
Numbers of student large (f_{i})1134324411231

Solution; Recall that to find the mean marks, we require the product of each large (x_{i}) with the corresponding frequency large f_{i}. So, let us put them in a column as shown.

Marks obtained large (x_{i})Number of students large (f_{i})large f_{i}x_{i}

10

20

36

40

50

56

60

70

72

80

88

92

95

1

1

3

4

3

2

4

4

1

1

2

3

1

10

20

108

160

150

112

240

280

72

80

176

276

95

Totallarge sum f_{i}=30large sum f_{i}x_{i}=1779

Now,                  large bar{x}=frac{sum f_{i}x_{i}}{sum f_{i}}=frac{1779}{30}=59.3

Therefore, the mean marks obtained is 59.3.

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(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)
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