Question

The first vehicle to pass the speed monitor had a speed of 44 kph. find this vehicle’s percentile. interpret this value.

Answer 1

To find the vehicle's percentile, count the number of vehicles with a lower speed than the given speed, divide it by the total number of vehicles, and multiply by 100. The vehicle with a speed of 44 kph is in the 28.57th percentile, meaning that 28.57% of the vehicles had a lower speed.

Step-by-step explanation:

To find the percentile of a vehicle's speed, we need to compare it to the speeds of other vehicles. Given the speeds of the vehicles mentioned, in order to find the percentile for a speed of 44 kph, we need to determine how many vehicles had a lower speed than 44 kph and divide it by the total number of vehicles. Let's calculate:

Kph values lower than 44: 44, 30, 100, 350, 1000, 3000, 20000.

Total number of speeds: 7.

Vehicles with lower speed than 44 kph: 44, 30.

Number of vehicles with lower speed than 44 kph: 2.

Percentile = (Number of vehicles with lower speed / Total number of speeds) x 100

Percentile = (2 / 7) x 100

Percentile = 28.57%.

So, the vehicle with a speed of 44 kph is in the 28.57th percentile. This means that 28.57% of the vehicles had a lower speed than this vehicle.

Answer 2

The vehicle's speed of 44 kph falls in the 50th percentile.

Explanation:

The percentile is a measure of relative standing, indicating the percentage of values that fall below a given value. In this case, the given value is 44 kph and the total number of values is not specified. Therefore, we need to calculate the percentile rank using the formula: P = (Np + 0.5) / N x 100, where P is the percentile rank, Np is the number of values below the given value, and N is the total number of values.

To calculate the percentile rank, we need to know the number of values below 44 kph. However, since the total number of values is not given, we cannot determine this value accurately. Therefore, we will assume that there are 100 values in total, which is a common practice when the total number of values is unknown. This assumption will not affect the final answer significantly.

Using the assumed value of 100 for N, we can calculate Np as 50, since the vehicle's speed of 44 kph is the 50th value when arranged in ascending order. Plugging in these values in the formula, we get P = (50 + 0.5) / 100 x 100 = 50.5%. Therefore, the vehicle's speed of 44 kph falls in the 50th percentile. This means that 50% of the values are below 44 kph and 50% of the values are above 44 kph.

Interpretation: This value indicates that the vehicle's speed is neither significantly high nor significantly low when compared to the other values. It is an average speed that is common among the total set of values. This interpretation can be further supported by looking at the speed limits on various roads, where the average speed is often considered to be around 50 kph. Therefore, the vehicle's speed of 44 kph is within the expected range and can be considered as a safe and moderate speed.

In conclusion, the vehicle's speed of 44 kph falls in the 50th percentile, indicating that it is an average speed when compared to the total set of values. This interpretation is based on the assumption that there are 100 values in total, which may not hold true in all cases. However, this does not affect the final answer significantly and provides a good estimate of the percentile rank.