Question

# The mean of the following data is 42. Find the missing frequencies x and y if the sum of frequencies is 100. Class interval0−1010−2020−3030−4040−5050−6060−7070−80Frequency710x13y10149

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Solution

## The given data is shown as follows: Class interval Frequency (fi) Class mark (xi) (fixi) 0 - 10 7 5 35 10 - 20 10 15 150 20 - 30 x 25 25x 30 - 40 13 35 455 40 - 50 y 45 45y 50 - 60 10 55 550 60 - 70 14 65 910 70 - 80 9 75 675 Total ∑fi=63+x+y ∑(fi×xi)=2775+25x+45y Sum of the frequencies = 100 ⇒ ∑fi = 100 ⇒ 63 + x + y = 100 ⇒ x + y = 100 - 63 ⇒ x + y = 37 ⇒ y = 37 - x – – – – – – (1) Now, the mean of the given data is given by ¯x = ∑(fi×xi)/∑fi ⇒42= 2775+25x+45y100 ⇒ 4200 = 2775 + 25 x + 45y ⇒4200 - 2775 = 25x + 45y ⇒ 1425 = 25x + 45(37 - x) [from (1)] ⇒ 1425 = 25x + 1665 - 45x ⇒ 20x = 1665 - 1425 ⇒ 20x = 240 ⇒ x = 12 If x = 12, then y = 37 - 12 = 25 Thus, the value of x is 12 and y is 25.

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