Multiple choice

Directions: The marks of 150 students of a class in a Mathematics test are as follows. | Marks | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | | --- | --- | --- | --- | --- | --- | --- | | Number of students | 22 | 20 | 25 | 23 | 20 | 40 | Find mean.

  1. 15.47

  2. 17.57

  3. 16.47

  4. 14.57
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C Correct answer
Explanation

Midpoints: 2.5, 7.5, 12.5, 17.5, 22.5, 27.5. Products: 22*2.5=55, 20*7.5=150, 25*12.5=312.5, 23*17.5=402.5, 20*22.5=450, 40*27.5=1100. Sum = 2470. Mean = 2470 / 150 = 16.466... = 16.47.

AI explanation

Find the midpoints of the class intervals 0 to 5, 5 to 10, 10 to 15, 15 to 20, 20 to 25 and 25 to 30, which are 2.5, 7.5, 12.5, 17.5, 22.5 and 27.5. Multiply each midpoint by its corresponding frequency to get 55, 150, 312.5, 402.5, 450 and 1100. The sum of these products is 2470, and the total number of students is 150. Using the direct mean formula, divide 2470 by 150 to get the mean of 16.47.

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