GATE 2024 CE (CE2) – Question 43
The consolidated data of a spot speed study for a certain stretch of a highway is given in the table.
| Speed range (kmph) | Number of observations |
|---|---|
| 0 - 10 | 7 |
| 10 - 20 | 31 |
| 20 - 30 | 76 |
| 30 - 40 | 129 |
| 40 - 50 | 104 |
| 50 - 60 | 78 |
| 60 - 70 | 29 |
| 70 - 80 | 24 |
| 80 - 90 | 13 |
| 90 - 100 | 9 |
The "upper speed limit" (in kmph) for the traffic sign is
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (C) 65
Explanation
The upper speed limit is the 85th percentile speed. The total number of observations is 500, so the 85th percentile is the speed below which $0.85 \times 500 = 425$ vehicles fall. The cumulative counts at the class upper limits are 7, 38, 114, 243, 347, 425, 454, ... So 425 is reached exactly at 60 kmph, and the speed limit sign is put at the next convenient value above it, 65 kmph.