The marks obtained by 9 students in a test are: 5, 8, 7, 9, 6, 7, 8, 7, 10.Determine: (i) Mode of the marks, (ii) Number of stude…

Question

The marks obtained by 9 students in a test are: 5, 8, 7, 9, 6, 7, 8, 7, 10.Determine: (i) Mode of the marks, (ii) Number of students scoring above average.

1. A. Mode = 7, Number of students scoring above average = 3
2. B. Mode = 8, Number of students scoring above average = 4
3. C. Mode = 8, Number of students scoring above average = 3
4. D. Mode = 7, Number of students scoring above average = 4 (Correct answer)

Correct Answer

Option D — Mode = 7, Number of students scoring above average = 4

Detailed Solution & Explanation

The correct answer is Mode = 7, Number of students scoring above average = 4.

Key Points

• The marks are 5, 8, 7, 9, 6, 7, 8, 7, 10.
• Mode: 7 occurs three times, more than any other value, so the mode is 7.
• Mean: the total is 5 + 8 + 7 + 9 + 6 + 7 + 8 + 7 + 10 = 67, over 9 students, giving 7.44.
• Marks above 7.44 are 8, 9, 8 and 10 — 4 students.

Additional Information

• The three 7s sit below the mean of 7.44, so they do not count as "above average" — that is the trap separating the options, since answering 3 would require treating 7 as above average.
• Mean, median and mode need not coincide: here the median is also 7 (the fifth of nine ordered values), but the mean is higher because 9 and 10 pull it up.
• A distribution with mean greater than median and mode is positively skewed, as this one is.
• Always compute the mean to at least two decimals before comparing — rounding 7.44 to 7 would change the count.