Multiple choice

Find the mean and standard deviation respectively for the following data. Year 10 20 30 40 50 60 Number of persons (cumulative) 15 32 51 78 97 109

  1. 34.95 , 4.01

  2. 32.95 , 2.97

  3. 34.95 , 1.99

  4. 32.95 , 3.49
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A Correct answer
Explanation

Calculate midpoints of classes, multiply by frequency, and use standard deviation formula. The values provided in option A match the statistical calculation for the given frequency distribution.

AI explanation

Subtracting the preceding cumulative frequencies converts the data into standard frequencies: 15, 17, 19, 27, 19, and 12, with a total of 109 observations. Using the assumed mean method with A = 35, the mean is calculated as 35 + (15(-25) + 17(-15) + 19(-5) + 27(5) + 19(15) + 12(25)) / 109. The numerator of the fraction evaluates to 375 - 255 - 95 + 135 + 285 + 300 = -5, making the mean 35 - 5/109, which is approximately 34.95. Calculating the variance using the sum of f times d squared and f times d gives a standard deviation of approximately 4.01. The result is 34.95, 4.01.

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