Question

The number of patients per shift (X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is  ₹1000(X - 0.2), what is the average amount (in ₹) she has earned per shift in the past 100 shifts? 

 

• A. 6,100
• B. 6,300
• C. 6,000
• D. 6,500

Hint:

When calculating averages involving frequency distributions, first calculate the total earnings, then divide by the total number of shifts to find the average.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
The number of shifts corresponding to different numbers of patients per shift is given in the bar graph. The amount Dr. Gita earns is \( 1000(X - 0.2) \), where \( X \) is the number of patients per shift.

The data from the graph is as follows:
For \( X = 5 \), the number of shifts is 20.
For \( X = 6 \), the number of shifts is 40.
For \( X = 7 \), the number of shifts is 30.
For \( X = 8 \), the number of shifts is 10.

Step 2: Calculating the total earnings.

For \( X = 5 \):
\[ \text{Earnings} = 1000 \times (5 - 0.2) \times 20 = 1000 \times 4.8 \times 20 = 96,000 \]
For \( X = 6 \):
\[ \text{Earnings} = 1000 \times (6 - 0.2) \times 40 = 1000 \times 5.8 \times 40 = 232,000 \]
For \( X = 7 \):
\[ \text{Earnings} = 1000 \times (7 - 0.2) \times 30 = 1000 \times 6.8 \times 30 = 204,000 \]
For \( X = 8 \):
\[ \text{Earnings} = 1000 \times (8 - 0.2) \times 10 = 1000 \times 7.8 \times 10 = 78,000 \]

Step 3: Calculating the total earnings and average earnings.
Total earnings for all 100 shifts:
\[ \text{Total Earnings} = 96,000 + 232,000 + 204,000 + 78,000 = 610,000 \]
Average earnings per shift:
\[ \text{Average Earnings} = \frac{610,000}{100} = 6,100 \]

Thus, the average earnings per shift are ₹6,100, which corresponds to Option (A).