SSC CGL 2025 Tier-II · Paper-I, 19 January 2026 · Mathematical Abilities · Question 23 of 150

We transcribed this text from the pictures of a candidate's response sheet for this paper; the answer is the key SSC marked with a green tick on that sheet. Solution last reviewed 11 September 2026.

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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.

(a)Mode = 7, Number of students scoring above average = 4
(b)Mode = 7, Number of students scoring above average = 3
(c)Mode = 8, Number of students scoring above average = 4
(d)Mode = 8, Number of students scoring above average = 3

Answer

Why

Correct — A. Sort the marks, then read off the mode and work out the mean.

Sorted: 5, 6, 7, 7, 7, 8, 8, 9, 10
7 appears three times, 8 twice, the rest once → mode = 7

Sum: 5 + 6 + 7 + 7 + 7 + 8 + 8 + 9 + 10 = 67
Mean: 67 ÷ 9 = 7.44

Marks above 7.44: 8, 8, 9, 10 → 4 students
Mode 7 and 4 students → option (a)

Why the others are wrong

(b)
Mode = 7, Number of students scoring above average = 3 — 3 counts the distinct marks above 7.44 (8, 9 and 10). Two students scored 8, so the number of students above average is 4.
(c)
Mode = 8, Number of students scoring above average = 4 — Mode = 8 is wrong: 8 appears twice, while 7 appears three times. The count of 4 students is right, but the mode is not.
(d)
Mode = 8, Number of students scoring above average = 3 — Both parts are wrong. The mode is 7, which appears three times to 8's two, and 4 students (8, 8, 9, 10) beat the mean of 7.44.

Concept

The mode is the value that occurs most often. The mean is the sum divided by the count.

Comparing with the mean needs its exact value: 67⁄9 = 7.44, so every mark of 8 or more is above it and every mark of 7 or less is below.

Count students, not values. A mark scored by two students puts two students above the average.

The mean, 7.44, is not a whole number, so no student sits exactly on the average and the count of those above it is clean.

Key facts

Mode = the most frequent value. A data set can have more than one mode.
Mean = sum ÷ number of observations: here 67 ÷ 9 = 7.44.
The median of these nine marks is the 5th sorted value, 7.

Study next

Median of an ungrouped list with an odd or an even countEffect on the mean of adding or removing one observationMean, median and mode from a frequency table

Common traps

Counting the distinct marks above the mean (8, 9, 10) instead of the students.
Dropping a value from the stem's list: it prints '8,7' without a space, and all nine marks must be counted.

Here the mode and an above-average count are asked together, and each option pairs one answer to each part.

Comparing values with an average also decides 19 Jan 2026, 11:00 AM, Maths Q.29, which names the families spending above it, and 10 Sep 2024, 12:30, Quant Q.22, which counts the years above average on a bar graph of bike production.

Related PYQs

No directly related past PYQ was found.

Topic: Statistics and probability — all 6 SSC CGL questions on it, every solved shift.