Question

Find the median of the following frequency table: 

Hint:

To find the median class, locate where \( \frac{N}{2} \) lies in the cumulative frequency table.

Answer 1

Step 1: Calculate cumulative frequency. 

Step 2: Identify median class. 
Total frequency \( N = 400 \). \[ \frac{N}{2} = 200 \] The cumulative frequency just greater than 200 is 216, so the median class is \( 30–35 \). 

Step 3: Use the median formula. 
\[ \text{Median} = l + \left(\frac{\frac{N}{2} - cf_{\text{before}}}{f}\right) \times h \] Here, \( l = 30, \; cf_{\text{before}} = 130, \; f = 86, \; h = 5 \). 

Step 4: Substitute the values. 
\[ \text{Median} = 30 + \left(\frac{200 - 130}{86}\right) \times 5 = 30 + \frac{70}{86} \times 5 \] \[ = 30 + 4.07 = 34.07 \] Step 5: Conclusion. 
Hence, the median of the data is \( \boxed{34.07} \).