Q. 11

# The mean of the f

Answer :

For equal class intervals, we will solve by finding mid points of these classes using direct method. We have got

Σfi = 63 + x + y and Σfixi = 2775 + 25x + 45y

mean is given by  ( given: mean of pocket allowance is 42)

2646 + 42x + 42y = 2775 + 25x + 45y

42x – 25x + 42y – 45y = 2775 – 2646

17x – 3y = 129 …(i)

As given in the question, frequency(Σfi) = 100

And as calculated by us, frequency (Σfi) = 63 + x + y

Equalizing them, we get

63 + x + y = 100

x + y = 37 …(ii)

We will now solve equations (i) and (ii), multiply eq.(ii) by 3 and then add it to eq.(i), we get

(17x – 3y) + [3(x + y)] = 129 + 111

17x – 3y + 3x + 3y = 240

20x = 240

x = 12

Substitute x = 12 in equation (ii),

12 + y = 37

y = 37 – 12

y = 25

Thus, x = 12 and y = 25.

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