# 1) Using Step–Deviation Method, Calculate the Mean Marks of the Following Distribution. 2) State the Modal Class. - Mathematics

1) Using step–deviation method, calculate the mean marks of the following distribution.

2) State the modal class.

 Class Interval 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 80 - 85 85 – 90 Frequency 5 20 10 10 9 6 12 8

#### Solution

1)

 Classinterval Frequency(f) x d = x – A=x – 67.5 t = d/i  i = 5 f xt 50 – 55 5 52.5 -15 -3 -15 55 – 60 20 57.5 -10 -2 -40 60 – 65 10 62.5 -5 -1 -10 65 – 70 10 67.5 0 0 0 70 – 75 9 72.5 5 1 9 75 – 80 6 77.5 10 2 12 80 – 85 12 82.5 15 3 36 85 – 90 8 87.5 20 4 32 Total 80 24

Assumed mean (A) = 67.5

Class size,  i = 5

Mean = A + i (sum ft)/(sum f)

= 67.5 + 5 xx 24/80

= 67.5 + 1.5`

= 69

Thus, the mean of the given data is 69.

2) Modal class is the class corresponding to the greatest frequency.

So, the modal class is 55 – 60.

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