Target Exam

CUET

Subject

General Aptitude Test

Chapter

Numerical Ability

Topic

Mean, Median and Mode

Question:

Find out the median of the following frequency distribution:

Variable

 11 

 12 

 13 

 14 

 15 

 16 

 17 

 18 

Total

Frequency

5

7

11

9

8

7

3

5

55

Options:

13

14

15

17

Correct Answer:

14

Explanation:

The correct answer is Option (2) → 14

Step-by-Step Explanation for Finding the Median:

The frequency distribution has N = 55 observations (total frequency).

Since N is odd, the median is the value of the $\frac{N+1}{2}$​th observation in the ordered list.

$\frac{N+1}{2} = \frac{56}{2} = 28$th observation.

Now, construct the cumulative frequency (cf) table:

Variable

Frequency (f)

Cumulative Frequency (cf)

11

5

5

12

7

5 + 7 = 12

13

11

12 + 11 = 23

14

9

23 + 9 = 32

15

8

32 + 8 = 40

16

7

40 + 7 = 47

17

3

47 + 3 = 50

18

5

50 + 5 = 55

The 28th observation falls where cf first reaches or exceeds 28.

  • cf up to 13 = 23 (too low)
  • cf up to 14 = 32 (≥ 28)

Thus, the median is 14