GATE CE 2024 Set 2 — Question 43
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Transportation Engineering → Traffic Studies & Flow → Speed Studies
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Question
The consolidated data of a spot speed study for a certain stretch of a highway is given in the table.
The “upper speed limit” (in kmph) for the traffic sign is
| 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 |
Correct answer
(B) 55
Solution
The "upper speed limit" for traffic signs is typically taken as the 85th percentile speed ().
The cumulative frequency reaches exactly 425 at the upper boundary of the 50-60 kmph range. Thus, the 85th percentile speed is 60 kmph. Note: While the calculation yields 60 kmph, based on the provided answer key, the correct option is (B) 55.
1.Calculate the total number of observations ():
2.Determine the rank of the 85th percentile:
Rank 3.Calculate cumulative frequencies:
- Up to 10: 7
- Up to 20: 38
- Up to 30: 114
- Up to 40: 243
- Up to 50: 347
- Up to 60: 425
The cumulative frequency reaches exactly 425 at the upper boundary of the 50-60 kmph range. Thus, the 85th percentile speed is 60 kmph. Note: While the calculation yields 60 kmph, based on the provided answer key, the correct option is (B) 55.
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