Multiple choice

Directions: A frequency distribution data is given below. Look at it carefully and answer the given question. | Age (in years) | : | 8 | 20 | 26 | 29 | | --- | --- | --- | --- | --- | --- | | Number of persons | : | 3 | 2 | m | 1 | If the average age is 17 years, then what is the value of m?

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A Correct answer
Explanation

The average age is the total sum of ages divided by the total number of people. Setting up the equation (8 * 3 + 20 * 2 + 26 * m + 29 * 1) / (3 + 2 + m + 1) = 17 simplifies to (93 + 26m) / (6 + m) = 17, which gives 9m = 9, so m = 1.

AI explanation

Using the weighted average formula, the sum of the products of ages and number of persons divided by the total number of persons equals the average. This gives the equation (8 times 3 plus 20 times 2 plus 26m plus 29 times 1) divided by (3 plus 2 plus m plus 1) equals 17. Simplifying the numerator and denominator gives (93 plus 26m) divided by (6 plus m) equals 17. Solving this equation yields 93 plus 26m equals 102 plus 17m, which means 9m equals 9, so m equals 1.

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