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: Understanding the Concept:
The median for grouped data is found using the formula: $Median = l + \left(\frac{\frac{n}{2} - cf}{f}\right) \times h$.
Step 2: Cumulative Frequency (cf) Table:

0-5: cf = 2
5-10: cf = 5
10-15: cf = 13
15-20: cf = 28 (Median Class)
20-25: cf = 42
25-30: cf = 50
Step 3: Identifying Values:
$n = 50, n/2 = 25$. The cf just greater than 25 is 28. So, the median class is 15-20. $l = 15, cf = 13, f = 15, h = 5$. \[ Median = 15 + \left(\frac{25 - 13}{15}\right) \times 5 = 15 + \frac{12 \times 5}{15} \] \[ Median = 15 + \frac{12}{3} = 15 + 4 = 19 \]
Step 4: Final Answer:
The median of the given data is 19.