Question

The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of the data: 

No. of Mangoes	No. of Trees (f)
50 – 100	33
100 – 150	30
150 – 200	90
200 – 250	80
250 – 300	17

Hint:

To find the median of grouped data, locate the median class where cumulative frequency ≥ \(N/2\), then apply \[ \text{Median} = L + \frac{(N/2 - c.f.)}{f} \times h \]

Answer 1

Step 1: Find the cumulative frequency (c.f.). 

Class Interval	Frequency (f)	Cumulative Frequency (c.f.)
50 - 100	33	33
100 - 150	30	63
150 - 200	90	153
200 - 250	80	233
250 - 300	17	250

Step 2: Find total frequency. 
N = 250 

Step 3: Find median class. 
N/2 = 250 / 2 = 125 
The c.f. just greater than 125 is 153. Hence, the median class is 150 - 200. 

Step 4: Apply the median formula. 
Median = L + ((N/2 - c.f.) / f) × h 

Where: 
L = 150, N = 250, c.f. = 63, f = 90, h = 50 

Substitute the values: 
Median = 150 + ((125 - 63) / 90) × 50 
= 150 + (62 / 90 × 50) 
= 150 + 34.44 = 184.44 

Step 5: Conclusion. 
The median number of mangoes produced per tree is approximately 184.4. 

Final Answer: Median = 184.4