The Indian Railways is an integral part of India’s economy. Each and every one of us is directly or indirectly dependent on it. However our railways is very obsolete in nature. A lot has been said nowadays about the introducing metros and bullet trains. However we must first conduct a ground study on the current situation. We must first identify the areas which need urgent improvement. There is no better way that accessing the Indian Railways than by taking a passenger feedback. We therefore decided to understand the situation and arrive at some conclusions by undertaking a passenger survey.

1. Survey on the State of
Indian Railways
By
Kanishk Agarwal (I001)
Atharv Johri (I014)
Idhanta Kakkar (I015)
Kaizad Katgara (I016)

2. Introduction
▪ IR has about 63,028 route kms. of track
▪ IR employs about 1.55 million people
▪ It carries over 13 million passengers & 1.3 million tonnes of freight everyday
▪ It runs about 14,300 trains daily
▪ IR has about 7,000 railway stations
The Indian Railways is an integral part of India’s economy. Each and every one of us is
directly or indirectly dependent on it. However our railways is very obsolete in nature. A
lot has been said nowadays about the introducing metros and bullet trains. However we
must first conduct a ground study on the current situation. We must first identify the
areas which need urgent improvement. There is no better way that accessing the Indian
Railways than by taking a passenger feedback. We therefore decided to understand the
situation and arrive at some conclusions by undertaking a passenger survey.

3. Problem Statement and Survey
To obtain a feedback of the passengers (A.C Compartment) travelling in out-station train regarding the current
situation of the Indian Railways. Various key areas have been identified and accordingly passenger ratings will
be conducted for each of them. To then analyse the obtained data and come up with various solutions to this
problem.
Criteria
Each area/category is given 5 rating parameters.
1-Needs Improvement
2-Poor
3-Average
4-Good
5- Excellent
After the feedback has been conducted. This individual series is converted to a continuous series.
Where rating 1 covers the range of 0-2,rating 2 covers 2-4, rating 3 covers 4-6, rating 4 covers 6-8 and rating 5
covers 8-10.
Survey:
Location : Bombay Central Station and C.S.T Station
Sample : A.C Compartment Passengers who have arrived at these 2 stations from their respective locations.
Date of Survey: 31/3/15 , 1/4/15, 2/4/15
Number of samples : 100

4. Survey Questions:
1. Availability of Tickets
2. Hygiene in the Compartment as well as the Washroom
3. Quality of Food
4. Cooling System
5. Attendant Service
6. Punctuality
7. Overall Experience

5. Sampling Techniques Used
Sampling
Population Sample Element
• A shortcut method for investigating a whole population
• Data is gathered on a small part of the whole parent population or sampling frame, and used to inform what the whole picture is like
- Probability Sampling:
Each and every element has the same chance of occurring within the particular sample.
• Simple Random Sampling:
Each member of the total population has an equal chance of being selected. In this case, out of all the passengers getting off the train(A.C Compartment), we chose
the sample passengers randomly.
• Stratified Sampling:
Where the population has a number of distinct categories, the frame can be organised by these categories into separate "strata." Each stratum is then sampled as an
independent sub-population, out of which individual elements can be randomly selected. In this case, amongst all the passengers boarding and getting out of the
train, we selectively chose only the ones coming out of the A.C compartment.We didn’t survey the passengers from the non a.c compartment.
• Cluster Sampling:
In this type of sampling the population is homogenous amongst groups but heterogeneous within a group. In this case, the two clusters could be Bombay Central
Station and C.S.T Station. Both these clusters are homogenous in terms of passengers. However each cluster within is heterogeneous with respect to
passengers,officials,vendors etc.
• Area Sampling:
In this case, two areas were samples. Bombay Central station and C.S.T Station. People in these two specific areas were only sampled.
-Non-probability Sampling
Any sampling method where some elements of the population have no chance of selection or don’t have an equal probability.
• Judgemental Sampling:
In this case, we used our judgement to only survey only those passengers that have just gotten off the train and not any random person at the station. These
passengers who have just got off would be in the best position to answer our survey as they have just experienced their train journey.

6. Calculations and Graphs
• Mean
• Median
• Mode
• Standard Deviation
• Covariance
• Skewness
• Kurtosis
• Histogram
• Frequency Polygon
• Ogive

7. Mean: The average of a set of numerical values, as calculated by adding them
together and dividing by the number of terms in the set.
Median: The median is the middle point of a number set, in which half the numbers are
above the median and half are below.
Mode:The "mode" is the value that occurs most often. If no number is repeated, then
there is no mode for the list.
Standard Deviation: A measure of dispersion in a frequency distribution, equal to the
square root of the mean of the squares of the deviations from the arithmetic mean of
the distribution.
Covariance: The mean value of the product of the deviations of two variates from their
respective means.
Skewness: In probability theory and statistics, skewness is a measure of the
asymmetry of the probability distribution of a real-valued random variable about its
mean. The skewness value can be positive or negative.
Definitions

8. Kurtosis: Kurtosis characterises the relative peakedness or flatness of a distribution
compared with the normal distribution. Positive kurtosis indicates a relatively peaked
distribution. Negative kurtosis indicates a relatively flat distribution.
Histogram: a diagram consisting of rectangles whose area is proportional to the
frequency of a variable and whose width is equal to the class interval.
Frequency Polygon: Frequency polygons are a graphical device for understanding
the shapes of distributions. They serve the same purpose as histograms, but are
especially helpful for comparing sets of data.
Ogive: A cumulative frequency graph.
Histogram Frequency Polygon Ogive

9. Availability of Tickets
1 2 21 4 41 4 61 4 81 1
2 4 22 4 42 1 62 3 82 3
3 3 23 3 43 1 63 3 83 2
4 3 24 2 44 1 64 3 84 2
5 2 25 2 45 3 65 2 85 2
6 2 26 2 46 3 66 4 86 4
7 3 27 2 47 2 67 3 87 3
8 4 28 3 48 2 68 3 88 4
9 4 29 3 49 4 69 3 89 1
10 3 30 2 50 4 70 2 90 4
11 3 31 1 51 2 71 1 91 3
12 3 32 2 52 3 72 3 92 3
13 1 33 4 53 3 73 2 93 3
14 4 34 2 54 3 74 3 94 3
15 2 35 3 55 4 75 5 95 4
16 3 36 2 56 4 76 3 96 2
17 2 37 3 57 3 77 1 97 3
18 3 38 4 58 3 78 2 98 3
19 2 39 4 59 3 79 3 99 3

10. Calculations
Mean - (f.m)/F = 4.62
Median - L+[{(N/2)-c.f}*i]/f
(N/2)=50, L=4, c.f=34, i=2,f=43
=4.744
Mode - L+[(f1*i)/(f1+f2)]
f1=|43-25|, f2=|43-22|, L=4, i=2
=4.923
Standard Deviation - √(∑fd^2/N)- (∑fd/N)^2 x i
Σfd=-19, Σfd^2=87
=1.826
Covariance - (S.D/M)*100
S.D=1.826, M=4.62
= 39.52
Skewness - (M-Mode)/S.D
M=4.62, Mode=4.923, S.D=1.826
= -0.166
Kurtosis - m4’/m2’^2
m4’=27.945, m2’=3.336
= 8.376

11. Histogram, Frequency Polygon and Ogive
Class Interval —>
Frequency
Class Interval —>
C.F

12. Bell Curve

13. Hygiene (Compartment)
1 2 21 3 41 3 61 3 81 1
2 3 22 4 42 3 62 2 82 2
3 2 23 4 43 1 63 4 83 3
4 4 24 2 44 2 64 4 84 3
5 4 25 2 45 1 65 3 85 1
6 3 26 2 46 3 66 3 86 3
7 3 27 2 47 3 67 2 87 3
8 3 28 2 48 4 68 2 88 3
9 4 29 4 49 4 69 3 89 3
10 4 30 4 50 4 70 3 90 1
11 2 31 4 51 2 71 1 91 3
12 3 32 2 52 4 72 3 92 2
13 4 33 3 53 2 73 3 93 3
14 3 34 3 54 5 74 2 94 2
15 2 35 2 55 3 75 5 95 3
16 3 36 2 56 2 76 2 96 4
17 2 37 3 57 1 77 1 97 2
18 3 38 2 58 3 78 3 98 3
19 3 39 3 59 2 79 1 99 2

14. Calculations
Mean - (f.m)/F = 4.4
Median - L+[{(N/2)-c.f}*i]/f
(N/2)=50, L=4, c.f=41, i=2,f=41
=4.439
Mode - L+[(f1*i)/(f1+f2)]
f1=|41-32|, f2=|41-16|, L=4, i=2
=4.529
Standard Deviation - √(∑fd^2/N)- (∑fd/N)^2 x i
Σfd=-30, Σfd^2=102
=1.9286
Covariance - (S.D/M)*100
S.D=1.9286, M=4.4
= 43.832
Skewness - (M-Mode)/S.D
M=4.4, Mode=4.529, S.D=1.9286
= -0.067
Kurtosis - m4’/m2’^2
m4’=29.576, m2’=3.32
= 8.908

15. Histogram, Frequency Polygon and Ogive
Class Interval —>
Frequency
C.F
Class Interval —>

16. Bell Curve

17. Hygiene Washroom
1 21 41 61 81
2 22 42 62 82
3 23 43 63 83
4 24 44 64 84
5 25 45 65 85
6 26 46 66 86
7 27 47 67 87
8 28 48 68 88
9 29 49 69 89
10 30 50 70 90
11 31 51 71 91
12 32 52 72 92
13 33 53 73 93
14 34 54 74 94
15 35 55 75 95
16 36 56 76 96
17 37 57 77 97
18 38 58 78 98
19 39 59 79 99

18. Calculations
Mean - (f.m)/F = 3.14
Median - L+[{(N/2)-c.f}*i]/f
(N/2)=50, L=2, c.f=31, i=2, f=37
= 3.027
Mode - L+[(f1*i)/(f1+f2)]
f1=|37-31|, f2=|37-26|, L=2, i=2
= 2.8
Standard Deviation - √(∑fd^2/N)- (∑fd/N)^2 x i
Σfd=-93, Σfd^2=167
= 1.794
Covariance - (S.D/M)*100
S.D=1.794, M=3.14
= 57.133
Skewness - (M-Mode)/S.D
M=3.14, Mode=2.8, S.D=1.794
= 0.1895
Kurtosis - m4’/m2’^2
m4’=22.94, m2’=3.2204
=7.123

19. Histogram, Frequency Polygon and Ogive
Class Interval —>
Frequency
C.F
Class Interval —>

20. Bell Curve

21. Food Quality
1 21 41 61 81
2 22 42 62 82
3 23 43 63 83
4 24 44 64 84
5 25 45 65 85
6 26 46 66 86
7 27 47 67 87
8 28 48 68 88
9 29 49 69 89
10 30 50 70 90
11 31 51 71 91
12 32 52 72 92
13 33 53 73 93
14 34 54 74 94
15 35 55 75 95
16 36 56 76 96
17 37 57 77 97
18 38 58 78 98
19 39 59 79 99

22. Calculations
Mean - (f.m)/F = 4.06
Median - L+[{(N/2)-c.f}*i]/f
(N/2)=50, L=4, c.f=46, i=2, f=42
= 4.19
Mode - L+[(f1*i)/(f1+f2)]
f1=|42-33|, f2=|42-12|, L=4, i=2
= 4.461
Standard Deviation - √(∑fd^2/N)- (∑fd/N)^2 x i
Σfd=-47, Σfd^2=97
= 1.73
Covariance - (S.D/M)*100
S.D=1.73, M=4.06
= 42.61
Skewness - (M-Mode)/S.D
M=4.06, Mode=4.461, S.D=1.73
= -0.232
Kurtosis - m4’/m2’^2
m4’=21.11, m2’=2.9964
=7.0451

23. Histogram, Frequency Polygon and Ogive
Class Interval —>
Frequency
C.F
Class Interval —>

24. Bell Curve

25. Cooling System
1 21 41 61 81
2 22 42 62 82
3 23 43 63 83
4 24 44 64 84
5 25 45 65 85
6 26 46 66 86
7 27 47 67 87
8 28 48 68 88
9 29 49 69 89
10 30 50 70 90
11 31 51 71 91
12 32 52 72 92
13 33 53 73 93
14 34 54 74 94
15 35 55 75 95
16 36 56 76 96
17 37 57 77 97
18 38 58 78 98
19 39 59 79 99

26. Calculations
Mean - (f.m)/F =6.24
Median - L+[{(N/2)-c.f}*i]/f
(N/2)=50, L=6, c.f=36, i=2, f=56
= 6.5
Mode - L+[(f1*i)/(f1+f2)]
f1=|56-28|, f2=|56-8|, L=6, i=2
= 6.041
Standard Deviation - √(∑fd^2/N)- (∑fd/N)^2 x i
Σfd=-62, Σfd^2=102
= 1.59
Covariance - (S.D/M)*100
S.D=1.59, M=6.24
= 25.48
Skewness - (M-Mode)/S.D
M=6.24, Mode=6.041, S.D=1.59
= 0.125
Kurtosis - m4’/m2’^2
m4’=25.188, m2’=2.5424
= 9.907

27. Histogram, Frequency Polygon and Ogive
Class Interval —>
Frequency
C.F
Class Interval —>

28. Bell Curve

29. Attendant Service
1 21 41 61 81
2 22 42 62 82
3 23 43 63 83
4 24 44 64 84
5 25 45 65 85
6 26 46 66 86
7 27 47 67 87
8 28 48 68 88
9 29 49 69 89
10 30 50 70 90
11 31 51 71 91
12 32 52 72 92
13 33 53 73 93
14 34 54 74 94
15 35 55 75 95
16 36 56 76 96
17 37 57 77 97
18 38 58 78 98
19 39 59 79 99

30. Calculations
Mean - (f.m)/F = 4.44
Median - L+[{(N/2)-c.f}*i]/f
(N/2)=50, L=4, c.f=40, i=2, f=40
= 4.5
Mode - L+[(f1*i)/(f1+f2)]
f1=|40-30|, f2=|40-18|, L=4, i=2
= 4.625
Standard Deviation - √(∑fd^2/N)- (∑fd/N)^2 x i
Σfd=-28, Σfd^2=96
= 1.877
Covariance - (S.D/M)*100
S.D=1.877, M=4.44
= 42.274
Skewness - (M-Mode)/S.D
M=4.44, Mode=4.625, S.D=1.877
= -0.0985
Kurtosis - m4’/m2’^2
m4’=31.816, m2’=3.5264
=9.022

31. Histogram, Frequency Polygon and Ogive
Class Interval —>
Frequency
C.F
Class Interval —>

32. Bell Curve

33. Punctuality
1 5 21 4 41 4 61 4 81 4
2 4 22 3 42 3 62 1 82 2
3 4 23 4 43 3 63 4 83 2
4 4 24 4 44 2 64 3 84 4
5 3 25 4 45 4 65 3 85 3
6 4 26 3 46 4 66 4 86 2
7 4 27 4 47 3 67 3 87 3
8 4 28 3 48 4 68 4 88 4
9 3 29 4 49 2 69 3 89 3
10 4 30 3 50 3 70 4 90 4
11 2 31 4 51 3 71 2 91 3
12 3 32 3 52 3 72 4 92 3
13 2 33 4 53 3 73 3 93 4
14 2 34 3 54 5 74 4 94 3
15 3 35 3 55 4 75 4 95 4
16 2 36 1 56 4 76 3 96 3
17 3 37 3 57 3 77 4 97 2
18 2 38 4 58 3 78 4 98 3
19 3 39 3 59 4 79 5 99 3

34. Calculations
Mean - (f.m)/F = 5.62
Median - L+[{(N/2)-c.f}*i]/f
(N/2)=50, L=4, c.f=15, i=2, f=40
= 5.75
Mode - L+[(f1*i)/(f1+f2)]
f1=|42-40|, f2=|42-3|, L=6, i=2
= 7.012
Standard Deviation - √(∑fd^2/N)- (∑fd/N)^2 x i
Σfd=31, Σfd^2=75
= 1.617
Covariance - (S.D/M)*100
S.D=1.617, M=5.62
= 28.77
Skewness - (M-Mode)/S.D
M=5.62, Mode=7.012, S.D=1.617
= -0.8608
Kurtosis - m4’/m2’^2
m4’=20.7352, m2’=2.6156
=3.0308

35. Histogram, Frequency Polygon and Ogive
Class Interval —>
Frequency
C.F
Class Interval —>

36. Bell Curve

37. Analysis of Punctuality Data

38. Overall Experience
1 3 21 3 41 3 61 4 81 4
2 3 22 3 42 3 62 3 82 3
3 4 23 3 43 2 63 3 83 2
4 4 24 2 44 2 64 3 84 1
5 2 25 3 45 3 65 4 85 3
6 3 26 3 46 3 66 3 86 2
7 2 27 3 47 3 67 2 87 3
8 4 28 3 48 3 68 4 88 3
9 4 29 3 49 3 69 3 89 4
10 4 30 4 50 3 70 3 90 3
11 2 31 3 51 4 71 4 91 4
12 3 32 2 52 3 72 3 92 3
13 3 33 2 53 3 73 3 93 3
14 3 34 3 54 4 74 1 94 3
15 3 35 2 55 4 75 4 95 3
16 3 36 3 56 3 76 2 96 3
17 4 37 3 57 3 77 4 97 4
18 3 38 4 58 3 78 3 98 4
19 3 39 3 59 3 79 4 99 3

39. Calculations
Mean - (f.m)/F = 5.02
Median - L+[{(N/2)-c.f}*i]/f
(N/2)=50, L=4, c.f=18, i=2, f=60
= 5.066
Mode - L+[(f1*i)/(f1+f2)]
f1=|60-15|, f2=|60-22|, L=4, i=2
= 5.084
Standard Deviation - √(∑fd^2/N)- (∑fd/N)^2 x i
Σfd=1, Σfd^2=49
= 1.399
Covariance - (S.D/M)*100
S.D=1.399, M=5.02
= 38.5
Skewness - (M-Mode)/S.D
M=5.02, Mode=5.084, S.D=1.399
= -0.0457
Kurtosis - m4’/m2’^2
m4’=13.513, m2’=4.599
= 0.6388

40. Histogram, Frequency Polygon and Ogive
Class Interval —>
Frequency
C.F
Class Interval —>

41. Bell Curve

42. Steps Taken To Improve The Condition
Hygiene: For improving upon the standards of cleanliness in coaches, schemes like
‘Intensive mechanised cleaning’ in maintenance depots, ‘On Board House-Keeping
Services (OBHS)’ for cleaning of coaches on run and cleaning attention to trains
during their stoppage at ‘Clean Train Stations’ etc. have also been launched.
Punctuality:
The following steps are taken by Indian Railways to improve operations and the
punctuality of passenger carrying trains: -
• Intensive, round the clock monitoring of trains at all three levels viz., Divisional,
Zonal Head Quarters and Railway Board.
• Punctuality drives are being conducted from time to time.
• Running of trains at maximum permissible speed subject to observance of safety
limits and speed restrictions.
• Improvements in time tabling to provide a clear path.

43. Availability of Tickets:
If there are a lot of people in a waiting list a extra compartment should be attached for some route
More trains in the affected routes
Special trains during holidays
Also ticket e-ticket agents should be from indian railways to regulate the amount of tickets
Quality of food can be improved by giving contacts to private sector without any biasing and free
from corruption to maintain a standard.
Steps to Improve