Question

The mean of the following data is 42. find the missing frequencies x and y if the total frequency is 100. CLASSES :- 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 FREQUENCY :- 7 10 x13y 10 14 9

Answer 1

7 + 10 + X + 13 + Y + 10 + 14 + 9 = 100
From this we get X + Y = 37 ---------- (i)

In the current scenario, the Mean will be given by the following formula:
[(Midpoint of Ist interval X frequency1) + ...........................+ (Midpoint of 10th interval X frequency10)] ÷ (sum of frequencies)

Therefore we have the following:
(5 x 7) + (15 x 10) + (25 x X) + (35 x 13) + (45 x Y) + (55 x 10) + (65 x 14) + (75 x 9)]/(7 + 10 + X + 13 + Y + 10 + 14 + 9)

Simplifying this we get:
(2775 + 25X + 45Y)/(63 + X + Y) = 42 (because 42 is the given mean)

Further simplifying, we get 17X - 3Y = 129 -------------- (ii)

Let us multiply (i) by 3 : 3X + 3Y = 111 -------------------- (iii)

Adding (i) and (iii), we get 20 X = 240
Therefore X = 12.

Putting the value of X = 20 in X + Y = 37, we get Y = 25

So our answer is X = 12 and Y = 25