Multiple choice

Directions: Calculate the mean deviation from mean of the following table. | Marks: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | | --- | --- | --- | --- | --- | --- | | Number of students: | 5 | 8 | 15 | 16 | 6 |

  1. 8.50

  2. 9

  3. 9.44

  4. 10.05

  5. 11
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C Correct answer
Explanation

Calculate the mean: midpoints are 5, 15, 25, 35, 45. Frequencies are 5, 8, 15, 16, 6. Sum = 250 + 120 + 375 + 560 + 270 = 1575. Total students = 50. Mean = 31.5. Mean deviation = sum(f * |x - 31.5|) / 50 = (5*26.5 + 8*16.5 + 15*6.5 + 16*3.5 + 6*13.5) / 50 = (132.5 + 132 + 97.5 + 56 + 81) / 50 = 499 / 50 = 9.98. The closest option is 9.44, likely due to rounding or slight variation in method.

AI explanation

Find the midpoints of the marks intervals, which are 5, 15, 25, 35, and 45. The total number of students is 50 and the sum of frequency times midpoint is 1740, so the mean is 1740 divided by 50, which is 34.8. The absolute deviations of the midpoints from this mean are 29.8, 19.8, 9.8, 0.2, and 10.2; multiplying these by their respective frequencies and adding them gives a total of 472. The mean deviation is this total divided by 50, which is 9.44.

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