What is the difference between average black tea consumers and coffee consumers ?
Show Hint
Calculating the difference between the totals first and then dividing by 5 saves you from performing two separate divisions, reducing both calculation steps and potential errors.
Step 1: Understanding the Concept:
To find the difference between the average of two groups, we can either calculate the individual averages first and then find their difference, or calculate the difference between their total sums first and then divide by the number of cities (5). Key Formula or Approach:
Using the sum-based approach:
\[ \text{Difference between Averages} = \frac{\text{Total Coffee Consumers} - \text{Total Black Tea Consumers}}{\text{Total Number of Cities (5)}} \]
Step 2: Detailed Explanation:
Let us use the values calculated in previous questions:
- From Question 65: \( \text{Total Coffee Consumers} = 3210 \)
- From Question 67: \( \text{Total Black Tea Consumers} = 2790 \)
Calculate the difference between these total sums:
\[ \text{Difference in Totals} = 3210 - 2790 \]
\[ \text{Difference in Totals} = 420 \]
Now, divide this difference by the total number of cities (5) to find the difference in averages:
\[ \text{Difference in Averages} = \frac{420}{5} = 84 \]
Alternatively, let us verify by calculating individual averages:
- Average Coffee Consumers = \( \frac{3210}{5} = 642 \)
- Average Black Tea Consumers = \( \frac{2790}{5} = 558 \)
- Difference in Averages = \( 642 - 558 = 84 \)
Both methods yield exactly 84. Step 3: Final Answer:
The correct option is (C).
