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.
| Number of patients per shift (X) | 5 | 6 | 7 | 8 |
|---|---|---|---|---|
| Number of shifts | 20 | 40 | 30 | 10 |
Answer: A
The average earning is ₹ 6,100.
First find the mean number of patients per shift from the 100 shifts:
\[ \begin{aligned} \bar{X} &= \frac{5(20) + 6(40) + 7(30) + 8(10)}{100} \\ &= \frac{100 + 240 + 210 + 80}{100} = 6.3 \end{aligned} \]
The earning is a linear function of X, so its average is the same function of the average:
\[ 1000(6.3 - 0.2) = 6100 \]
₹ 6,300 forgets to subtract 0.2, ₹ 6,000 uses the most common value 6 instead of the mean, and ₹ 6,500 does not match any consistent reading of the chart.
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