Question

Compute median of the following data :

Hint:

Class interval \(= [Mid-value - h/2, Mid-value + h/2]\). Correctly forming the table is 90\% of the work.

Answer 1

Step 1: Understanding the Concept:
To find the median from mid-values, first convert them into class intervals. The interval size \(h\) is the difference between consecutive mid-values.
Step 2: Key Formula or Approach:
Median \(= l + \left( \frac{\frac{N}{2} - cf}{f} \right) \times h\)
Step 3: Detailed Explanation:
Difference between mid-values \(= 125 - 115 = 10\). So \(h = 10\).
Class boundaries for 115: \(115 \pm \frac{10}{2} \implies 110-120\).

\(N = 100, \frac{N}{2} = 50\).
The cumulative frequency just greater than 50 is 63, so the Median Class is 140-150.
\(l = 140, f = 16, cf = 47, h = 10\).
\[ \text{Median} = 140 + \left( \frac{50 - 47}{16} \right) \times 10 \]
\[ \text{Median} = 140 + \frac{3 \times 10}{16} = 140 + \frac{30}{16} = 140 + 1.875 = 141.875 \]
Step 4: Final Answer:
The median of the given data is 141.875.