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)
Explanation
From the chart, 20 shifts had 5 patients, 40 had 6, 30 had 7 and 10 had 8, a total of 100 shifts. They saw \(5(20) + 6(40) + 7(30) + 8(10) = 630\) patients, so the mean per shift is \(\bar{X} = \frac{630}{100} = 6.3\).
The earning \(1000(X - 0.2)\) is a linear function of \(X\), so its average is the same function of the average: \(1000(6.3 - 0.2) = 6100\), that is, ₹ 6,100. Forgetting the \(-0.2\) gives 6,300, option B.
Answer: A