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GATE DA 2025 Q10: Average earnings per shift from a bar chart

Question

The number of patients per shift (X)(X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹ 1000(X−0.2)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.

Bar chart of number of shifts against patients per shift X: 20 shifts with X = 5, 40 with X = 6, 30 with X = 7 and 10 with X = 8.
Tap the figure to enlarge

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Answer: A (official GATE 2025 final answer key)

Concept used: Mean of a frequency distribution and linearity of the average.

First step: Find the mean number of patients: Xˉ=(5⋅20+6⋅40+7⋅30+8⋅10)/100\bar X = (5 \cdot 20 + 6 \cdot 40 + 7 \cdot 30 + 8 \cdot 10)/100. Average earnings are then 1000(Xˉ−0.2)1000(\bar X - 0.2).

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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