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Question

The following table shows the marks scored by 140 students in an examination of a certain paper.
Marks: 0−10 10−20 20−30 30−40 40−50
Number of students: 20 24 40 36 20

Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

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Solution

We may prepare the table as shown:

(i) Direct method
We know that mean,
=3620140=25.857

Hence, the mean is 25.857.

(ii) Short-cut method

Let the assumed mean A = 25.

We know that mean,

Hence, the mean is 25.857.

(iii) Step deviation method

Let the assumed mean A = 25 and h = 10.

We know that mean,

Hence, the mean is 25.857.


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