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GATE 2022 CE (CE1) – Question 8

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam. From the data presented above, which one of the following is CORRECT?

Marks 3–9 have frequencies 3, 9, 11, 7, 14, 2 and 4 respectively. See the attached source image.
  1. mean > mode > median
  2. mode > median > mean
  3. mode > mean > median
  4. median > mode > mean 3 9 11 7 14 2 4 0 2 4 6 8 10 12 14 16 3 4 5 6 7 8 9 Frequency Marks

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Correct answer: (B) mode > median > mean

Explanation

The mode is 7 because its frequency 14 is the largest. The total frequency is 50; cumulative counts through marks 5 and 6 are 23 and 30, so both the 25th and 26th observations are 6: median = 6.

The weighted total is $3(3)+4(9)+5(11)+6(7)+7(14)+8(2)+9(4)=292$, so mean = 5.84. Hence **mode > median > mean**, **B**.