Question

Find the median of the following data : 

Hint:

Always ensure the median value falls within the median class (15 to 20). Since 19 is in that range, the result is plausible.

Answer 1

Step 1: Write the given data.
Class intervals and frequencies are:
0–5 → 2
5–10 → 3
10–15 → 8
15–20 → 15
20–25 → 14
25–30 → 8

Step 2: Find the total frequency.
Total frequency \(N\) is the sum of all frequencies:
\(N = 2 + 3 + 8 + 15 + 14 + 8 = 50\).

Step 3: Compute the cumulative frequency.
Cumulative frequencies are calculated as follows:
0–5 → 2
5–10 → 2 + 3 = 5
10–15 → 5 + 8 = 13
15–20 → 13 + 15 = 28
20–25 → 28 + 14 = 42
25–30 → 42 + 8 = 50

Step 4: Determine the median class.
First calculate \( \frac{N}{2} \):
\(\frac{N}{2} = \frac{50}{2} = 25\).
The cumulative frequency just greater than 25 is 28, which corresponds to the class interval 15–20. Therefore, the median class is 15–20.

Step 5: Write the median formula.
Median \(=\; l + \frac{\left(\frac{N}{2} - cf\right)}{f} \times h\)
Where:
l = lower limit of median class = 15
cf = cumulative frequency before median class = 13
f = frequency of median class = 15
h = class width = 5

Step 6: Substitute the values.
\[ \text{Median} = 15 + \frac{25 - 13}{15} \times 5 \]
\[ = 15 + \frac{12}{15} \times 5 \]
\[ = 15 + 4 \]

Final Answer:
The median of the given data is 19.