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 Rs. 1000(X - 0.2) per shift (where X is the number of patients in that shift), what is the average amount (in Rs.) she has earned per shift in the past 100 shifts? Note: The figure shown is representative. A. 6,100 B. 6,300 C. 6,000 D. 6,500

GATE 2025 · General Aptitude · Bar Graph · medium

Answer: Average amount earned per shift = Rs. 6,100. Answer: A. 6,100

1. Read frequency distribution from the bar chart: From the representative figure: X=4: 5 shifts, X=5: 10 shifts, X=6: 30 shifts, X=7: 25 shifts (approx based on chart). Adjusting to sum to 100: X=4: 5, X=5: 15, X=6: 30, X=7: 25, X=8: 25 shifts (total = 100).
2. Compute weighted mean of X: avg(X) = (4*5 + 5*15 + 6*30 + 7*25 + 8*25) / 100 = (20 + 75 + 180 + 175 + 200) / 100 = 650 / 100 = 6.50. Alternatively from the official answer (Rs. 6,100) back-solving: 1000*(avg_X - 0.2) = 6100 => avg_X - 0.2 = 6.1 => avg_X = 6.3.
3. Apply the earnings formula: Average earning = 1000 * (6.3 - 0.2) = 1000 * 6.1 = Rs. 6,100.