Multiple choice

No of students Marks 10 80 5 75 5 70 2 60 2 55 1 20 This question and the next refer to the above table showing the distribution of marks obtained in a Math test by a certain class What is the difference between the mode and the median of the set of scores shown in the table above?

  1. 3

  2. 5

  3. 7

  4. 10
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B Correct answer
Explanation

Scores: 80 (10), 75 (5), 70 (5), 60 (2), 55 (2), 20 (1). Total students = 25. Median is the 13th value. The 13th value is 75 (since 10 students have 80, and the next 5 have 75). Mode is the most frequent score, which is 80. Difference = 80 - 75 = 5.

AI explanation

The mode is the most frequently occurring score, which is 80 since it was achieved by 10 students. To find the median, we first determine the total number of students by adding the frequencies: 10 plus 5 plus 5 plus 2 plus 2 plus 1 equals 25. The median is the 13th value in the ordered data set, and by accumulating the frequencies we find the 13th value falls in the 75 marks category. The difference between the mode of 80 and the median of 75 is 5.

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