What is the value of (9x + 2y), if mean of the following distribution is 64?Class 0-20 20-40 40-60 60-80 80-100 Total Frequency 8 20 x 6 y 80
113
The frequencies add up to the total: 8 + 20 + x + 6 + y = 80, so x + y = 46.
The class midpoints are 10, 30, 50, 70 and 90, so the sum of (frequency × midpoint) is 8(10) + 20(30) + x(50) + 6(70) + y(90) = 1,100 + 50x + 90y.
The mean is 64, so 1,100 + 50x + 90y = 64 × 80 = 5,120, giving 50x + 90y = 4,020, i.e. 5x + 9y = 402.
Substituting x = 46 − y: 5(46 − y) + 9y = 402, so 230 + 4y = 402, y = 43 and x = 3.
Therefore 9x + 2y = 9(3) + 2(43) = 27 + 86 = 113.
Hence, the answer is 113.
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