Question

What is the difference between average castor production and average cotton production ?

• A. 5.28
• B. 3.98
• C. 5.67
• D. 4.28

Hint:

To make calculations faster:
\[ \text{Difference in Average} = \frac{\text{Total Difference}}{7} = \frac{1770 - 1740}{7} = \frac{30}{7} \approx 4.28\text{ Kgs} \]
This simplifies the arithmetic significantly!

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
To find the difference between two averages, we can either compute the two averages separately and subtract them, or find the difference between the total sums first and divide by the total number of years.
Key Formula or Approach:
- Total years, \(N = 7\) (from 2011 to 2017).
- Difference in Average = \(\frac{\text{Total Castor} - \text{Total Cotton}}{7}\).

Step 2: Detailed Explanation:
Let us calculate the total production for both crops over the entire 7-year period (2011 to 2017):
- Total Castor Production:
\[ \text{Total Castor} = 1450\text{ (from 2011-2016)} + 320\text{ (for 2017)} = 1770\text{ Kgs} \]
- Total Cotton Production:
\[ \text{Total Cotton} = 1500\text{ (from 2011-2016)} + 240\text{ (for 2017)} = 1740\text{ Kgs} \]
- Calculating the Averages:
\[ \text{Average Castor} = \frac{1770}{7} \approx 252.857\text{ Kgs} \]
\[ \text{Average Cotton} = \frac{1740}{7} \approx 248.571\text{ Kgs} \]
- Difference in Average:
\[ \text{Difference} = 252.857 - 248.571 = 4.286\text{ Kgs} \approx 4.28\text{ Kgs} \]

Step 3: Final Answer:
The difference between the averages is approximately 4.28 (Option D).