Discussion
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?
Note: The figure shown is representative.
Answer: A
She earned ₹ 6,100 per shift on average.
The mean number of patients per shift, weighted by the number of shifts, is
\[ \begin{aligned} \bar{X} &= \frac{5(20) + 6(40) + 7(30) + 8(10)}{100} \\ &= \frac{100 + 240 + 210 + 80}{100} = 6.3 \end{aligned} \]
The earning is linear in X, so the average earning is \(1000(\bar{X} - 0.2) = 1000(6.1) = 6100\) rupees. 6,300 is the mean number of patients times 1000, forgetting to subtract the 0.2 per shift. Because the earning rule is linear, averaging X first and averaging the earnings shift by shift give the same 6,100.
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