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 |
Answer & explanation
Correct answer: option 2
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.