Memorandum To: Jen Keidel From: Christina Ochs (Seat 28) Date: 1/19/12 Re: Spot Speed Memo 1. Introduction The purpose of this experiment was to determine if current speed limit postings are satisfactory for keeping drivers at the set rate. This was determined by calculating the average speed of vehicles driving along a road for a certain amount of time. Other values were calculated to help determine the conclusion including, but not limited to, standard deviation, relative frequency, cumulative frequency, mode, pace, and median. The data can be found in the Results and Description in Section 2. The analysis of this data can be found in Section 3, Discussion. A summary of the whole experiment and conclusions made can be found in section 4. 2. Results and Description The results of the experiment were formulated and are presented in the second attachment in Table 1. Table 1 shows the values determined after the experiment was performed. The mode and 10 mph pace were determined using the relative frequency graph located in the second attachment. The relative frequency graph shows the mode is 28-32 mph because that is the speed interval at which the peak of the frequency curve occurs. The pace could be found by locating the 10 mph interval on the relative frequency curve in which the most cars traveled. 1 of 6
The 50th percentile speed, 15th percentile speed, and 85th percentile speeds were found by looking at the cumulative frequency graph, located in the second attachment. These speeds were determined by finding the percentile on the ordinate axis of the cumulative frequency graph and determining what x-value corresponds with the percent (y-value) on the cumulative frequency curve. The percent of vehicles in pace could be found while looking at the graphs of relative frequency and cumulative frequency simultaneously. The average speed was calculated using equation 1. The estimated standard deviation was determined using equation 2 and the calculated standard deviation was found using equation 3. All these equations and the sample calculations for each can be found in the first attachment. The values for the variables included in the equations are located in Table 2 in the first attachment. Table 2 gives the experimental data. The difference between the lower limit and upper limit of a speed group is 4 mph. The data collected was for a 2 mph interval, but for accurate results on the relative frequency graph, the data was combined to 4 mph intervals. The reason for this is because the relative frequency curve needs to look like a bell curve. With data on 2 mph intervals, the graph was altered to have 2 relative maximums. Therefore, the data needed to be combined to give the relative frequency graph a bell-shaped curve. The number of vehicles in the group was found by looking at the field sheet, displayed as Figure 1 in the second attachment. Figure 2, located in the second attachment, shows the relative frequency and cumulative frequency graphs for the data collected in this experiment. The relative frequency graph is used to determine the mode (28-32 mph) and 10 mph pace (25-35 mph). The median, 85th percentile speed, 15th percentile speed, and % of vehicles in pace, were determined and 2 of 6
labeled on the cumulative frequency graph. The median speed is 31 mph; the 85th percentile speed is 36.5 mph; the 15th percentile speed is 23.5 mph; the percent of vehicles in pace is 55%. 3. Discussion The experiment revealed that the mode for the speed of drivers on Woody Hayes Drive is between 28 mph and 32 mph. The median speed was approximately 31 mph. The 15th percentile speed was 23.5 mph and the 85th percentile speed was 36.5 mph. All these values can be found in Table 1. These values play a key role in deciding whether the current speed limit postings are satisfactory for keeping drivers at the set rate. The mode shows the speed that most cars in the speed trap were travelling. Since the speed limit on Woody Hayes Drive is 25 mph and the mode was between 28 mph and 32 mph, it can be concluded that the majority of cars travel between 3 mph and 7 mph over the posted speed limit. The pace and percent of vehicles in pace show that 55% of vehicles travelling on Woody Hayes Drive travel between the posted speed limit (25 mph) and 10 mph over the speed limit. With the median speed being 31 mph, it can be proven that the majority of cars on Woody Hayes Drive travel faster than the posted speed limit. Table 1 reveals that the pace for this experiment was 25 mph to 35 mph, with 55% of the vehicles in the speed trap travelling within that pace. With this, it can be said that the data exhibits central tendency because over half of the vehicles observed clustered between 25 mph and 35 mph. Since only 55% of the vehicles observed were in the 10 mph pace, dispersion, the scattering of values of a variable around the mean or median of a distribution (www.dictionary.com, 10/24/11) was also exhibited. The speeds of the vehicles observed 3 of 6
ranged from 16 mph to 52 mph. Although over half the data was between 25 mph and 35 mph, there was a wide range of speeds observed, resulting in dispersion. Standard deviation is the measure of dispersion of a set of data from its mean (www.investopedia.com, 10/09/11). Since the standard deviation was approximately 6, this shows there is a relatively wide range of dispersion in this set of data. If the data would have been from the Indy 500, there would be less dispersion because the cars racing would have been travelling at a closer speed to one another, rather than a wide range of speeds. However, if the data was collected on High Street on a Saturday evening in the spring, the dispersion would most likely be greater than the dispersion in this experiment. This is because High Street is a main road so many vehicles would be driving through the speed trap and there would be more traffic than observed on Woody Hayes Drive. The dispersion in the data collected for this experiment was caused by the wide variety of vehicles observed and the accuracy problems associated with this experiment. Some of these accuracy problems included human error, location of a bus stop, and a large crowd of students on the sidewalk. Human error was caused by the reaction times of the flagger and timer. The times of vehicles passing through the speed zone was not 100% accurate due to the inability of humans to react immediately. There would be a delay from when the car entered the speed zone and the timer actually started the stopwatch. During that delay, the flagger had to raise his/her arm, the timer had to interpret that signal, and press the 'start' button on the timer/stopwatch. The same goes for the time delay once the vehicle reaches the end of the speed trap. 4 of 6
The location of a bus stop nearby also skewed the data collected. Approximately 300 feet past the end of the speed trap, there was a bus stop. This means, some of the buses travelling through the speed trap could have begun slowing down while in the speed trap, skewing the data. The final accuracy problem associated with this experiment was the surroundings. Drivers don't expect to see a large group of people spread along the side of the road and students watching vehicles closely and throwing their arms in the air when a vehicle reaches a certain point. This scenario could have distracted drivers and caused them to drive more cautiously through the speed trap, also resulting in skewed data. 4. Summary and Conclusions The purpose of this experiment was to determine if current speed limit postings are satisfactory for keeping drivers at the set rate. Values such as average speed, mode, standard deviation, and pace were determined to reach a conclusion. The average speed was found to be 30.5 mph. The mode was between 28 mph and 32 mph. This means the majority of the vehicles passing through the speed trap were travelling somewhere between 28 mph and 32 mph. Based on the data collected, the current speed limit postings are not satisfactory for keeping drivers at the set rate because the current speed limit on Woody Hayes Drive is 25 mph. In order to gain more accurate results and prevent error, better equipment could have been purchased and used. If given $200 to improve the experiment, it would have been beneficial to attempt to avoid human error. Using an automated timer that could accurately read the position of the vehicles in the speed trap would drastically improve the experimental data. It would be valuable to invest in such a device so that human error would be eliminated and the 5 of 6
speed of the vehicles could be determined without fault. Another device that would have been propitious would have been a radar gun. A radar gun can use the waves bouncing off the vehicle to flawlessly determine the speed of the car and produce accurate data. These devices would also reduce the distractions on the side of the road, resulting in the drivers driving at a regular pace and receiving accurate data. Also, changing the location of the experiment could have resulted in more accurate data. A location without a bus stop nearby would have been ideal. The bus stop at the end of the speed trap skewed the data. If there hadn't been a bus stop, drivers would have been more likely to drive a constant speed, resulting in more accurate data. Attachment: Sample Calculations, 2. Attachment: Figures and Tables, 3. 6 of 6
Sample Calculations Average Speed: (1) = number of vehicles in group i = middle speed of group i N= total number of vehicles observed in experiment Estimated Standard Deviation: (2) = 85th percentile speed = 15th percentile speed Calculated Standard Deviation: (3) = number of vehicles in group i = middle speed of group i = average speed N= total number of vehicles observed in experiment 1 of 2
Sample Calculation for Average Speed = 30.5 mph Sample Calculations for Estimated Standard Deviation Sample Calculations for Calculated Standard Deviation = 6.18 mph Sample Calculation for Relative Frequency Sample Calculation for Cumulative Frequency 2 of 2
Figures and Tables Mode 50th Percentile Speed Table 1: Experimental Data of Vehicles on Woody Hayes Drive 10 mph Pace (x to y mph) Vehicles in Pace (%) 15th Percentile Speed 85th Percentile Speed Average Speed Estimated Standard Deviation Calculated Standard Deviation 28-32 31 25-35 55 23.5 36.5 30.5 6.5 6.18 Speed Group Table 2: Statistics of Vehicle Speeds on Woody Hayes Drive Lower Limit Upper Limit Middle Speed, S # of Vehicles in Group, n Relative Frequency (%) Cumulative Frequency (%) ns 16 20 18 3 2.8037 2.8037 54 20 24 22 14 13.0841 15.8879 308 24 28 26 20 18.6916 34.5794 520 28 32 30 29 27.1028 61.6822 870 32 36 34 20 18.6916 80.3738 680 36 40 38 16 14.9533 95.3271 608 40 44 42 3 2.8037 98.1308 126 44 48 46 1 0.9346 99.0654 46 48 52 50 1 0.9346 100.0000 50 1 of 3
Figure 1: Vehicle Speeds collected throughout experiment 2 of 3
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