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 \({\rupee} 1000(X - 0.2)\), what is the average amount (in \rupee) she has earned per shift in the past 100 shifts?
\includegraphics[width=0.5\linewidth]{10.png}

• 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 \(X = 5\): \[ {Earnings} = 1000 \times (5 - 0.2) \times 20 = 1000 \times 4.8 \times 20 = 96,000. \] For \(X = 6\): \[ {Earnings} = 1000 \times (6 - 0.2) \times 40 = 1000 \times 5.8 \times 40 = 232,000. \] For \(X = 7\): \[ {Earnings} = 1000 \times (7 - 0.2) \times 30 = 1000 \times 6.8 \times 30 = 204,000. \] For \(X = 8\): \[ {Earnings} = 1000 \times (8 - 0.2) \times 10 = 1000 \times 7.8 \times 10 = 78,000. \] Step 3: Calculating the total earnings and average earnings.
Total earnings for all 100 shifts:
\[ {Total Earnings} = 96,000 + 232,000 + 204,000 + 78,000 = 610,000. \] The average earnings per shift: \[ {Average Earnings} = \frac{610,000}{100} = 6,100. \] Thus, the average earnings per shift are \rupee6,100, which corresponds to Option (A).