ANALYSING SPEED PROFILE OF DIFFERENT VEHICLES

A Report On –
EXPERIMENT - 2
(Analysing speed profiles of different vehicle types)
Submitted by-
SHRIKRISHNA KESHARWANI
Roll no.-
22CEM3R23
Subject-
TRANSPORTATION ANALYTICS LABORATORY
Bachelor of Technology
In
TRANSPORTATION ENGINEERING
DEPARTMENT OF CIVIL ENGINEERING
NATIONAL INSTITUTE OF TECHNOLOGY WARANGAL
SEPTEMBER, 2022

Transportation Analytics Laboratory
SHRIKRISHNA KESHARWANI (22CEM3R23) 2
Table of Contents
1. Aim-...................................................................................................................................5
2. Software Used-...................................................................................................................5
3. Theory................................................................................................................................5
3.1 Descriptive Statistics........................................................................................................5
3.1.1. Mean: .......................................................................................................................5
3.1.2. Median: ....................................................................................................................5
3.1.3. Range: ......................................................................................................................5
3.1.4 Class Interval: ...........................................................................................................5
3.1.5 Standard Deviation....................................................................................................5
3.1.6 Variance:...................................................................................................................5
3.1.7 Skewness:..................................................................................................................5
3.1.8 Kurtosis:....................................................................................................................6
3.2 Histogram:........................................................................................................................7
3.3 Frequency distribution Curve: .........................................................................................7
3.4 Ogive curve/ S curve/ Cumulative frequency curve:.......................................................7
3.5 Percentile speeds:.............................................................................................................7
4. Procedure-..........................................................................................................................8
5. Analysis of Data- ...............................................................................................................9
6. GRAPHS- ........................................................................................................................15
7. Results:.............................................................................................................................23
8. Conclusion: ......................................................................................................................23
References................................................................................................................................23

List of Tables-
Table 1 Frequency and Cumulative frequency of Small cars....................................................9
Table 2 Frequency and Cumulative frequency of big cars ......................................................10
Table 3 Frequency and Cumulative frequency of two wheelers..............................................10
Table 4 Frequency and Cumulative frequency of Auto...........................................................11
Table 5 Frequency and Cumulative frequency of HCV ..........................................................11
Table 6 Frequency and Cumulative frequency of LCV...........................................................12
Table 7 Frequency and Cumulative frequency of MAV .........................................................12
Table 8 Descriptive statistics of small cars..............................................................................13
Table 9 Descriptive statistics of big cars .................................................................................13
Table 10 Descriptive statistics of TW......................................................................................13
Table 11 Descriptive statistics of Auto....................................................................................13
Table 12 Descriptive statistics of HCV ...................................................................................14
Table 13 Descriptive statistics of LCV....................................................................................14
Table 14 Descriptive statistics of MAV...................................................................................14

List of Figures-
Figure 1 positively and negatively skewed................................................................................6
Figure 2 Types of Kurtosis ........................................................................................................6
Figure 3 Histogram ....................................................................................................................7
Figure 4 Different percentile speeds..........................................................................................8
Figure 5 Frequency distribution of different vehicle speeds ...................................................15
Figure 6 Percentage Cumulative frequency distribution curve................................................15
Figure 7 Frequency distribution of different Car speeds .........................................................16
Figure 8 Percentage Cumulative frequency distribution curve for cars ..................................16
Figure 9 Frequency distribution of big Car speeds..................................................................17
Figure 10 Percentage Cumulative frequency distribution curve for big cars ..........................17
Figure 11 Frequency distribution of TW speeds......................................................................18
Figure 12 Percentage Cumulative frequency distribution curve for TW.................................18
Figure 13 Frequency distribution of Auto speed .....................................................................19
Figure 14 Percentage Cumulative frequency distribution curve for Auto...............................19
Figure 15 Frequency distribution of HCV speed.....................................................................20
Figure 16 Percentage Cumulative frequency distribution curve for HCV ..............................20
Figure 17 Frequency distribution of LCV speed .....................................................................21
Figure 18 Percentage Cumulative frequency distribution curve for LCV...............................21
Figure 19 Frequency distribution of MAV speed....................................................................22
Figure 20 Percentage Cumulative frequency distribution curve for MAV..............................22

1. Aim-
To plot the frequency and cumulative frequency distribution of the speed data of different
vehicle types
2. Software Used-
MS Excel (2016 version)
3. Theory
3.1 Descriptive Statistics.
3.1.1. Mean:
The mean of a series of data is the value equal to the sum of the values of all the observations
divided by the number of observations.
3.1.2. Median:
In statistics and probability theory, a median is a value separating the higher half from the lower
half of a data sample, a population or a probability distribution.
3.1.3. Range:
The Range is the difference between the lowest and highest values.
3.1.4 Class Interval:
Class Interval =
Where N is total number of data (Count).
3.1.5 Standard Deviation:
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a
set of values. A low standard deviation indicates that the values tend to be close to the mean of
the set, while a high standard deviation indicates that the values are spread out over a wider
range.
3.1.6 Variance:
In statistics, variance is the expectation of the squared deviation of a random variable from its
mean. Informally, it measures how far a set of numbers is spread out from their average value.
3.1.7 Skewness:
Skewness is a measure of the degree of asymmetry of a frequency distribution. In general,
when the distribution stretches to the right more than it does to the left, it can be said that the
distribution is right-skewed, or positively skewed. When a distribution is right skewed, the
mean is to the right of the median, which in turn is to the right of the mode. The opposite is
true for left-skewed distribution.
Range
1+3.222 * log10 (N)

I. Positively skewed (right skewed)
II. Negatively skewed (left skewed)
Figure 1 positively and negatively skewed
3.1.8 Kurtosis:
Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from
the tails of a normal distribution. In other words, kurtosis identifies whether the tails of a given
distribution contain extreme values.
i. Leptokurtic: It is a curve having peak than normal curve. Too much concentration
of the items near the center. (kurtosis value >3)
ii. Platy-kurtic: A curve having a lower peak (flatter) than the normal curve. There is
less concentration of items near the center. (kurtosis value < 3)
iii. Meso-kurtic: It is a curve having a normal peak or normal curve. There is equal
distribution around the center value (mean). (kurtosis value = 3)
Figure 2 Types of Kurtosis

3.2 Histogram:
A histogram is a graphical representation of the distribution of data, which is an estimate of the
probability distribution of a continuous variable, usually in bar graph form. The shape of a
histogram describes how the scores are distributed from low to high. Taller Bars in the
histogram indicate more data points are clustered around that point.
Figure 3 Histogram
3.3 Frequency distribution Curve:
Frequency distribution, in statistics, is a graph or data set organized to show the frequency of
occurrence of each possible outcome of a repeatable event observed many times.
3.4 Ogive curve/ S curve/ Cumulative frequency curve:
It is the representation of the cumulative frequencies for the classes in the frequency
distribution.
3.5 Percentile speeds:
i. 98th percentile speed (Design speed): 98th percentile speed is taken for the highway
pavement design. In 98th percentile speed, 98 percentage of all vehicles are passing
below this speed. Only 2% of remaining vehicles will exceeds this speed.
ii. 85th percentile speed (Upper safe speed limit): In 85th percentile speed, 85% of all
vehicles are passing below this speed. Only 15% of vehicles are exceeding this speed.
This speed is the upper safe speed of road.
iii. 15th percentile speed (Lower safe speed limit): In 15 percentile speed, 15% of all
vehicles are passing below this speed and the remaining vehicles will be higher than
this speed. This should be the minimum maintaining speed of vehicle.
iv. 50th percentile speed: It is the average speed of the traffic stream below which 50
percent traffic are moving.

4. Procedure-
i. Upload the speed data into excel sheet.
ii. Select one particular vehicle speed data and find the descriptive statistics.
iii. Descriptive statistics table for that particular class of vehicle which includes mean,
median, standard deviation, variance, skewness, kurtosis and percentile speeds.
iv. Frequency distribution table for different class of vehicles in ms excel.
v. Plot the histogram in excel by frequency values.
vi. Plot the frequency distribution curve in excel between percentage frequency and speed
of vehicle.
vii. Plot the cum frequency distribution curve between percentage cum frequency and speed
of vehicle in excel.
viii. Then repeat the step iii, iv, v, vi and vii for other types of vehicles.
ix. Compare frequency distribution curve and S-curve for different class of vehicles.
Figure 4 Different percentile speeds

5. Analysis of Data-
Excel commands:
i. To find minimum and maximum speed value.
=MIN (number1, number2 …)
=MAX (number1, number2 …)
ii. To find range and count
=MAX-MIN
=COUNT (number1, number2 …)
iii. To find mean, median, standard deviation
=AVERAGE (number1, number2 …)
=MEDIAN (number1, number2 …)
iv. To find frequency distribution of various class interval speed data
=FREQUENCY (DATA ARRAY, MAXIMUM VALUE ARRAY) (Ctrl + Shift + Enter)
v. To find different percentile speeds
=PERCENTILE (DATA ARRAY, k)
Table 1 Frequency and Cumulative frequency of Small cars
MIN MAX MID FEQ
CUMMULATIVE
FREEQUENCY
%CUM.
FREQ.
0 10 5 0 0 0.0
10 20 15 0 0 0.0
20 30 25 0 0 0.0
30 40 35 11 11 2.9
40 50 45 45 56 14.9
50 60 55 91 147 39.2
60 70 65 112 259 69.1
70 80 75 87 346 92.3
80 90 85 25 371 98.9
90 100 95 4 375 100.0
100 110 105 0 375 100.0
110 120 115 0 375 100.0

Table 2 Frequency and Cumulative frequency of big cars
MIN MAX MID FEQ
CUMMULATIVE
FREEQUENCY
%CUM.
FREQ.
0 10 5 0 0 0.0
10 20 15 0 0 0.0
20 30 25 6 6 2.5
30 40 35 8 14 5.9
40 50 45 39 53 22.5
50 60 55 68 121 51.3
60 70 65 54 175 74.2
70 80 75 43 218 92.4
80 90 85 9 227 96.2
90 100 95 8 235 99.6
100 110 105 1 236 100.0
Table 3 Frequency and Cumulative frequency of two wheelers
MIN MAX MID FEQ
CUMMULATIV
E FREEQUENCY
%CUM.
FREQ.
0 10 5 0 0 0.0
10 20 15 0 0 0.0
20 30 25 0 0 0.0
30 40 35 15 15 9.0
40 50 45 34 49 29.5
50 60 55 52 101 60.8
60 70 65 20 121 72.9
70 80 75 29 150 90.4
80 90 85 9 159 95.8
90 100 95 6 165 99.4
100 110 105 1 166 100.0
110 120 115 0 166 100.0

Table 4 Frequency and Cumulative frequency of Auto
MIN MAX MID FEQ
CUMMULATIVE
FREEQUENCY
%CUM.
FREQ.
0 10 5 0 0 0.0
10 20 15 0 0 0.0
20 30 25 7 7 9.9
30 40 35 23 30 42.3
40 50 45 22 52 73.2
50 60 55 16 68 95.8
60 70 65 3 71 100.0
70 80 75 0 71 100.0
80 90 85 0 71 100.0
90 100 95 0 71 100.0
100 110 105 0 71 100.0
110 120 115 0 71 100.0
Table 5 Frequency and Cumulative frequency of HCV
MIN MAX MID FEQ
CUMMULATIVE
FREEQUENCY %CUM. FREQ.
0 10 5 0 0 0.0
10 20 15 0 0 0.0
20 30 25 20 20 6.5
30 40 35 92 112 36.6
40 50 45 112 224 73.2
50 60 55 58 282 92.2
60 70 65 23 305 99.7
70 80 75 1 306 100.0
80 90 85 0 306 100.0
90 100 95 0 306 100.0
100 110 105 0 306 100.0
110 120 115 0 306 100.0

Table 6 Frequency and Cumulative frequency of LCV
MIN MAX MID FEQ
CUMMULATIVE
FREEQUENCY
%CUM.
FREQ.
0 10 5 0 0 0.0
10 20 15 0 0 0.0
20 30 25 9 9 3.1
30 40 35 72 81 28.1
40 50 45 93 174 60.4
50 60 55 88 262 91.0
60 70 65 20 282 97.9
70 80 75 5 287 99.7
80 90 85 1 288 100.0
90 100 95 0 288 100.0
100 110 105 0 288 100.0
110 120 115 0 288 100.0
Table 7 Frequency and Cumulative frequency of MAV
MIN MAX MID FEQ CUMMULATIVE FREEQUENCY %CUM. FREQ.
0 10 5 0 0 0.0
10 20 15 0 0 0.0
20 30 25 11 11 20.0
30 40 35 30 41 74.5
40 50 45 13 54 98.2
50 60 55 1 55 100.0
60 70 65 0 55 100.0
70 80 75 0 55 100.0
80 90 85 0 55 100.0
90 100 95 0 55 100.0
100 110 105 0 55 100.0
110 120 115 0 55 100.0

Table 8 Descriptive statistics of small cars
MEAN 63.5
STANDARD DEVIATION 12.12922
MINIMUM 33.4
MAXIMUM 98.8
COUNT 375
RANGE 65.4
CLASS INTERVAL 7.033412
Table 9 Descriptive statistics of big cars
MEAN 60.4
MINIMUM 26.1
MAXIMUM 108.2
COUNT 236.0
RANGE 82.1
CLASS INTERVAL 9.5
Table 10 Descriptive statistics of TW
MEAN 59.0
MINIMUM 34.9
MAXIMUM 103.3
COUNT 166.0
RANGE 68.3
CLASS INTERVAL 8.4
Table 11 Descriptive statistics of Auto
MEAN 43.3
MINIMUM 26.7
MAXIMUM 61.4
COUNT 71
RANGE 34.7

Table 12 Descriptive statistics of HCV
MEAN 44.4
MINIMUM 23.4
MAXIMUM 75.7
COUNT 306
RANGE 52.3
Table 13 Descriptive statistics of LCV
MEAN 47.3
MINIMUM 22.1
MAXIMUM 86.4
COUNT 288
RANGE 64.3
Table 14 Descriptive statistics of MAV
MEAN 36.2
MINIMUM 21.6
MAXIMUM 56.9
COUNT 55
RANGE 35.3

6. GRAPHS-
Figure 5 Frequency distribution of different vehicle speeds
Figure 6 Percentage Cumulative frequency distribution curve
0
10
20
30
40
50
60
70
0 20 40 60 80 100 120
FREQUENCY
SPEED (KMPH)
FREQUENCY- SPEED
CS CB TW Auto HV LCV MAV
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 20 40 60 80 100 120
%
CUMMULATIVE
FREQUENCY
SPEED (KMPH)
%CUMMULATIVE FREQUENCY- SPEED
CS CB TW Auto HV LCV MAV

Figure 7 Frequency distribution of different Car speeds
Figure 8 Percentage Cumulative frequency distribution curve for cars
0
10
20
30
40
50
60
70
0 20 40 60 80 100 120
FREQUENCY
SPEED (KMPH)
FREQUENCY-SPEED (for Small Cars)
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 20 40 60 80 100 120
%
CUMMULATIVE
FREQUENCY
SPEED (KMPH)
%CUMMULATIVE FREQ. -SPEED (For Small Cars)

Figure 9 Frequency distribution of big Car speeds
Figure 10 Percentage Cumulative frequency distribution curve for big cars
0
5
10
15
20
25
30
35
40
45
0 20 40 60 80 100 120
FREQUENCY
SPEED (KMPH)
FREQUENCY-SPEED (for big cars)
15
50
85
98
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 20 40 60 80 100 120
%CUMMULATIVE
FREQ.
SPEED (KMPH)
% CUMMULATIVE FREQ._ SPEED (big cars)

Figure 11 Frequency distribution of TW speeds
Figure 12 Percentage Cumulative frequency distribution curve for TW
0
10
20
30
40
50
60
0 20 40 60 80 100 120 140
FREQUENCY
SPEED (KMPH)
FREQUENCY-SPEED (For TW)
15
50
85
98
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140
%CUMMULATIVE
FREQUENCY
SPEED (KMPH)
%CUMMULATIVE FREQUENCY-SPEED (TW)

Figure 13 Frequency distribution of Auto speed
Figure 14 Percentage Cumulative frequency distribution curve for Auto
0
2
4
6
8
10
12
14
16
18
0 20 40 60 80 100 120
FREQUENCY
SPEED (KMPH)
FREQUENCY-SPEED (For Auto)
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 20 40 60 80 100 120
%
CUMMULATIVE
FREQUENCY
SPEED (KMPH)
%CUM. FREQ.-SPEED (For Auto)

Figure 15 Frequency distribution of HCV speed
Figure 16 Percentage Cumulative frequency distribution curve for HCV
0
10
20
30
40
50
60
70
0 20 40 60 80 100 120
FREQUENCY
SPEED (KMPH)
FEQ-SPEED (For HCV)
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 20 40 60 80 100 120
%
CUMMULATIVE
FREQUENCY
SPEED (KMPH)
%CUM. FREQ.-SPEED (For HCV)

Figure 17 Frequency distribution of LCV speed
Figure 18 Percentage Cumulative frequency distribution curve for LCV
0
10
20
30
40
50
60
0 20 40 60 80 100 120
FREQUENCY
SPEED (KMPH)
FEQ-SPEED (For LCV)
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 20 40 60 80 100 120
%
CUMMULATIVE
FREQUENCY
SPEED (KMPH)
%CUM. FREQ.-SPEED (for LCV)

Figure 19 Frequency distribution of MAV speed
Figure 20 Percentage Cumulative frequency distribution curve for MAV
0
2
4
6
8
10
12
14
16
18
20
0 20 40 60 80 100 120
FREQUENCY
SPEED (KMPH)
FREQ-SPEED (for MAV)
15
50
85
98
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 20 40 60 80 100 120
%
CUMMULATIVE
FREEQUENCY
SPEED (KMPH)
%CUM. FREQ.-SPEED (for MAV)

7. Results:
Speed profiles of the different vehicles has been obtained using excel and graphsare plotted to
compare the speed distribution for the different types of vehicles.
8. Conclusion:
i. Speed data generally follows normal distribution.
ii. Frequency distribution resembles a bell-shaped curve and Cumulative frequency
distribution as an S-curve.
iii. Mode value can be calculated from frequency distribution curve i.e., the highest peak
of the curve is the mode value.
iv. Mode value is the speed of vehicle with highest frequency.
v. From Fig 5 we can see that the speed distribution of small cars has more deviation with
more standard deviation.
vi. From fig 6 we observe that 85th
and 98th
percentile speeds are high in case of small cars
and big cars.
vii. Cumulative frequency plots are used to find percentile speeds.
 (15th
percentile speed = lower limit of safe speed;
 50th
percentile speed = median speed;
 85th
percentile speed = upper limit of safe speed;
 98th
percentile speed = design speed)
References
(n.d.). Retrieved from springer: https://link.springer.com/referenceworkentry/10.1007/978-3-
642-04898-2_582
Traffic engineering and transport planning. (2013). In L. Kadiyali. Khanna publishers.

ANALYSING SPEED PROFILE OF DIFFERENT VEHICLES

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