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Question

The marks obtained by 110 students in an examination are given below:
Marks: 30 – 35 35 – 40 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65
Frequency: 14 16 28 23 18 8 3

Find the mean marks of the students.

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Solution


Let the assumed mean, A be 47.5.

Here, h = 5

Marks Mid-Values(xi) Frequency (fi) di=xi-47.5 ui=xi-47.55 fiui
30–35 32.5 14 −15 −3 −42
35–40 37.5 16 −10 −2 −32
40–45 42.5 28 −5 −1 −28
45–50 47.5 23 0 0 0
50–55 52.5 18 5 1 18
55–60 57.5 8 10 2 16
60–65 62.5 3 15 3 9
fi=110 fiui=-59

We know

Mean =A+h×fiuifi
∴ Mean marks of the students

=47.5+5×-59110=47.5-2.68=44.82

Hence, the mean marks of the students is 44.82.

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