Survey on the State of Indian Railways

ByKanishk Agarwal (I001)Atharv Johri (I014)Idhanta Kakkar (I015)Kaizad Katgara (I016)

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.

Problem Statement and SurveyTo 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.CriteriaEach area/category is given 5 rating parameters.1-Needs Improvement2-Poor3-Average4-Good5- ExcellentAfter 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 StationSample : A.C Compartment Passengers who have arrived at these 2 stations from their respective locations.Date of Survey: 31/3/15 , 1/4/15, 2/4/15Number of samples : 100

Survey Questions:

1. Availability of Tickets2. Hygiene in the Compartment as well as the Washroom3. Quality of Food4. Cooling System5. Attendant Service6. Punctuality7. Overall Experience

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 SamplingAny 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.

Calculations and Graphs

• Mean• Median • Mode• Standard

Deviation• Covariance• Skewness• Kurtosis

• Histogram• Frequency

Polygon• Ogive

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

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

Availability of Tickets1 2 21 4 41 4 61 4 81 12 4 22 4 42 1 62 3 82 33 3 23 3 43 1 63 3 83 24 3 24 2 44 1 64 3 84 25 2 25 2 45 3 65 2 85 26 2 26 2 46 3 66 4 86 47 3 27 2 47 2 67 3 87 38 4 28 3 48 2 68 3 88 49 4 29 3 49 4 69 3 89 110 3 30 2 50 4 70 2 90 411 3 31 1 51 2 71 1 91 312 3 32 2 52 3 72 3 92 313 1 33 4 53 3 73 2 93 314 4 34 2 54 3 74 3 94 315 2 35 3 55 4 75 5 95 416 3 36 2 56 4 76 3 96 217 2 37 3 57 3 77 1 97 318 3 38 4 58 3 78 2 98 319 2 39 4 59 3 79 3 99 320 3 40 4 60 3 80 4 100 3

Calculations

Mean - (f.m)/F = 4.62Median - L+[{(N/2)-c.f}*i]/f

(N/2)=50, L=4, c.f=34, i=2,f=43

=4.744Mode - 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)*100S.D=1.826, M=4.62

= 39.52Skewness - (M-Mode)/S.D

M=4.62, Mode=4.923, S.D=1.826= -0.166

Kurtosis - m4’/m2’^2m4’=27.945, m2’=3.336

= 8.376

Histogram, Frequency Polygon and Ogive

Class Interval —>

Frequency

Class Interval —>

C.F

Bell Curve

Hygiene (Compartment)

1 2 21 3 41 3 61 3 81 12 3 22 4 42 3 62 2 82 23 2 23 4 43 1 63 4 83 34 4 24 2 44 2 64 4 84 35 4 25 2 45 1 65 3 85 16 3 26 2 46 3 66 3 86 37 3 27 2 47 3 67 2 87 38 3 28 2 48 4 68 2 88 39 4 29 4 49 4 69 3 89 310 4 30 4 50 4 70 3 90 111 2 31 4 51 2 71 1 91 312 3 32 2 52 4 72 3 92 213 4 33 3 53 2 73 3 93 314 3 34 3 54 5 74 2 94 215 2 35 2 55 3 75 5 95 316 3 36 2 56 2 76 2 96 417 2 37 3 57 1 77 1 97 218 3 38 2 58 3 78 3 98 319 3 39 3 59 2 79 1 99 220 2 40 3 60 2 80 2 100 3

Calculations

Mean - (f.m)/F = 4.4Median - L+[{(N/2)-c.f}*i]/f

(N/2)=50, L=4, c.f=41, i=2,f=41

=4.439Mode - 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)*100S.D=1.9286, M=4.4

= 43.832Skewness - (M-Mode)/S.D

M=4.4, Mode=4.529, S.D=1.9286= -0.067

Kurtosis - m4’/m2’^2m4’=29.576, m2’=3.32

= 8.908

Histogram, Frequency Polygon and Ogive

Class Interval —>

Frequency

C.F

Class Interval —>

Bell Curve

Hygiene Washroom1 21 41 61 812 22 42 62 823 23 43 63 834 24 44 64 845 25 45 65 856 26 46 66 867 27 47 67 878 28 48 68 889 29 49 69 8910 30 50 70 9011 31 51 71 9112 32 52 72 9213 33 53 73 9314 34 54 74 9415 35 55 75 9516 36 56 76 9617 37 57 77 9718 38 58 78 9819 39 59 79 9920 40 60 80 100

Calculations

Mean - (f.m)/F = 3.14Median - L+[{(N/2)-c.f}*i]/f

(N/2)=50, L=2, c.f=31, i=2, f=37

= 3.027Mode - 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)*100S.D=1.794, M=3.14

= 57.133Skewness - (M-Mode)/S.D

M=3.14, Mode=2.8, S.D=1.794= 0.1895

Kurtosis - m4’/m2’^2m4’=22.94, m2’=3.2204

=7.123

Histogram, Frequency Polygon and Ogive

Class Interval —>

Frequency

C.F

Class Interval —>

Bell Curve

Food Quality1 21 41 61 812 22 42 62 823 23 43 63 834 24 44 64 845 25 45 65 856 26 46 66 867 27 47 67 878 28 48 68 889 29 49 69 8910 30 50 70 9011 31 51 71 9112 32 52 72 9213 33 53 73 9314 34 54 74 9415 35 55 75 9516 36 56 76 9617 37 57 77 9718 38 58 78 9819 39 59 79 9920 40 60 80 100

Calculations

Mean - (f.m)/F = 4.06Median - L+[{(N/2)-c.f}*i]/f

(N/2)=50, L=4, c.f=46, i=2, f=42

= 4.19Mode - 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)*100S.D=1.73, M=4.06

= 42.61Skewness - (M-Mode)/S.D

M=4.06, Mode=4.461, S.D=1.73= -0.232

Kurtosis - m4’/m2’^2m4’=21.11, m2’=2.9964

=7.0451

Histogram, Frequency Polygon and Ogive

Class Interval —>

Frequency

C.F

Class Interval —>

Bell Curve

Cooling System1 21 41 61 812 22 42 62 823 23 43 63 834 24 44 64 845 25 45 65 856 26 46 66 867 27 47 67 878 28 48 68 889 29 49 69 8910 30 50 70 9011 31 51 71 9112 32 52 72 9213 33 53 73 9314 34 54 74 9415 35 55 75 9516 36 56 76 9617 37 57 77 9718 38 58 78 9819 39 59 79 9920 40 60 80 100

Calculations

Mean - (f.m)/F =6.24Median - L+[{(N/2)-c.f}*i]/f

(N/2)=50, L=6, c.f=36, i=2, f=56

= 6.5Mode - 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)*100S.D=1.59, M=6.24

= 25.48Skewness - (M-Mode)/S.D

M=6.24, Mode=6.041, S.D=1.59= 0.125

Kurtosis - m4’/m2’^2m4’=25.188, m2’=2.5424

= 9.907

Histogram, Frequency Polygon and Ogive

Class Interval —>

Frequency

C.F

Class Interval —>

Bell Curve

Attendant Service1 21 41 61 812 22 42 62 823 23 43 63 834 24 44 64 845 25 45 65 856 26 46 66 867 27 47 67 878 28 48 68 889 29 49 69 8910 30 50 70 9011 31 51 71 9112 32 52 72 9213 33 53 73 9314 34 54 74 9415 35 55 75 9516 36 56 76 9617 37 57 77 9718 38 58 78 9819 39 59 79 9920 40 60 80 100

Calculations

Mean - (f.m)/F = 4.44Median - L+[{(N/2)-c.f}*i]/f

(N/2)=50, L=4, c.f=40, i=2, f=40

= 4.5Mode - 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)*100S.D=1.877, M=4.44

= 42.274Skewness - (M-Mode)/S.D

M=4.44, Mode=4.625, S.D=1.877= -0.0985

Kurtosis - m4’/m2’^2m4’=31.816, m2’=3.5264

=9.022

Histogram, Frequency Polygon and Ogive

Class Interval —>

Frequency

C.F

Class Interval —>

Bell Curve

Punctuality1 5 21 4 41 4 61 4 81 42 4 22 3 42 3 62 1 82 23 4 23 4 43 3 63 4 83 24 4 24 4 44 2 64 3 84 45 3 25 4 45 4 65 3 85 36 4 26 3 46 4 66 4 86 27 4 27 4 47 3 67 3 87 38 4 28 3 48 4 68 4 88 49 3 29 4 49 2 69 3 89 310 4 30 3 50 3 70 4 90 411 2 31 4 51 3 71 2 91 312 3 32 3 52 3 72 4 92 313 2 33 4 53 3 73 3 93 414 2 34 3 54 5 74 4 94 315 3 35 3 55 4 75 4 95 416 2 36 1 56 4 76 3 96 317 3 37 3 57 3 77 4 97 218 2 38 4 58 3 78 4 98 319 3 39 3 59 4 79 5 99 320 2 40 4 60 4 80 4 100 3

Calculations

Mean - (f.m)/F = 5.62Median - L+[{(N/2)-c.f}*i]/f

(N/2)=50, L=4, c.f=15, i=2, f=40

= 5.75Mode - 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)*100S.D=1.617, M=5.62

= 28.77Skewness - (M-Mode)/S.D

M=5.62, Mode=7.012, S.D=1.617= -0.8608

Kurtosis - m4’/m2’^2m4’=20.7352, m2’=2.6156

=3.0308

Histogram, Frequency Polygon and Ogive

Class Interval —>

Frequency

C.F

Class Interval —>

Bell Curve

Analysis of Punctuality Data

Overall Experience1 3 21 3 41 3 61 4 81 42 3 22 3 42 3 62 3 82 33 4 23 3 43 2 63 3 83 24 4 24 2 44 2 64 3 84 15 2 25 3 45 3 65 4 85 36 3 26 3 46 3 66 3 86 27 2 27 3 47 3 67 2 87 38 4 28 3 48 3 68 4 88 39 4 29 3 49 3 69 3 89 410 4 30 4 50 3 70 3 90 311 2 31 3 51 4 71 4 91 412 3 32 2 52 3 72 3 92 313 3 33 2 53 3 73 3 93 314 3 34 3 54 4 74 1 94 315 3 35 2 55 4 75 4 95 316 3 36 3 56 3 76 2 96 317 4 37 3 57 3 77 4 97 418 3 38 4 58 3 78 3 98 419 3 39 3 59 3 79 4 99 320 2 40 3 60 3 80 1 100 3

Calculations

Mean - (f.m)/F = 5.02Median - L+[{(N/2)-c.f}*i]/f

(N/2)=50, L=4, c.f=18, i=2, f=60

= 5.066Mode - 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)*100S.D=1.399, M=5.02

= 38.5Skewness - (M-Mode)/S.D

M=5.02, Mode=5.084, S.D=1.399= -0.0457

Kurtosis - m4’/m2’^2m4’=13.513, m2’=4.599

= 0.6388

Histogram, Frequency Polygon and Ogive

Class Interval —>

Frequency

C.F

Class Interval —>

Bell Curve

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.

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 routesSpecial trains during holidaysAlso 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