Multiple choice

Find the values of 'x' and 'y' in the following data. Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Frequency 13 17 x 15 y 20 The mean of the data is 31.5 and the number of observations is 80.

  1. x = 7, y = 8

  2. x = 3, y = 12

  3. x = 4, y = 11

  4. x = 5, y = 10
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D Correct answer
Explanation

The sum of frequencies is 13 + 17 + x + 15 + y + 20 = 80, so x + y = 15. Using the mean formula with class midpoints (5, 15, 25, 35, 45, 55), the equation 31.5 * 80 = 65 + 255 + 25x + 525 + 45y + 1100 leads to 25x + 45y = 570, or 5x + 9y = 114. Solving the system yields x = 5 and y = 10.

AI explanation

The sum of frequencies gives 13 + 17 + x + 15 + y + 20 = 80, so x + y = 15. Using the assumed mean method, the mean is calculated as 31.5 = (130 + 255 + 25x + 525 + 45y + 1100) / 80, which simplifies to 25x + 45y = 510. Solving the system of equations x + y = 15 and 25x + 45y = 510 results in x = 5 and y = 10.

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