The report helps us to analyse region wise the number of Rape Convicts and safety issues.

1. By Sayanto Tripathy
Gayathri E.A (4666860)
Khizar
2014
Indian rape Convict
Statistic Analysis
[INDIAN RAPE CONVICT STATISTIC REPORT]

2. Table of Contents
1. Introduction................................................................................................................................3
2. Data Segmentation......................................................................................................................4
3. Descriptive Analysis.....................................................................................................................5
North States Description .................................................................................................................6
South States Description .................................................................................................................7
East States Description....................................................................................................................8
West State Description....................................................................................................................8
4. Scatter Diagram...........................................................................................................................9
5. Correlation................................................................................................................................11
6. Box plot statistics.......................................................................................................................12
7. SamplingProbability..................................................................................................................14
8. Confidence Interval....................................................................................................................17
9. Anova Test................................................................................................................................20
10. Conclusion ................................................................................................................................24
11. References................................................................................................................................25
12. Appendix...................................................................................................................................26

3. 1. Introduction
Rape in India is one of the most common and brutal crime against women. Rape case in India
has doubled from 1990 to 2007. While the rape case increased from 16,075 in 2001 to 24,500 in
2011 , the conviction rate decreased from 40.8% to 24% .The annual rape rate in India has
increased from 1.5 to 2.0 per 100,000 people over 2010-2012 periods which is quite low when
compared to other countries like USA, Morocco, Mexico and Bahrain. But still as the day
passes, the question of women security is raised and this needs to be solved. The statistical
study which is conducted by us here in to analyze how Indian States vary in the amount of rape
convicts. As the day passes by, the rape cases in India are becoming more intense and we are
here analyzing geographical regions (North. South, East and West) of how they differ from each
other in rape convict statistics. The study of rape convicts pattern should be prioritized region
wise to understand the lack of security for women and how it can be strengthen. For some
states like Gujarat , Haryana the rape convict number increases gradually whereas for some
states like Meghalaya, Manipur and the north-eastern states the rape convicts number are
pretty low. This unique pattern of low numbers in North-East and high numbers in North &
Central part of India needs to be analyzed statistically and the problem should be analyzed to
implicate the security and women safety culture in those high rape convicted areas. We would
also extend our study to understand how the rape convict numbers for each region differs when
compared to the past years..
Interestingly while studying the Rape-Convict Data region wise, we analyze that all India
average is much lower when compared to other countries described below with some
impressive records shown by Southern States. The complete study of Rape Convicts helps us
to conclude the region which needs much stringent action to control the rape cases and come
out with much stricter action.

4. 2. Data Segmentation

5. Indian being a vast state , we segment the sates geographically into North , South, East and
West and see how each of this areas vary from one another. We include the following states in
our Segmentation as per geographical location:-
North :- Chhattisgarh, Haryana, Himachal Pradesh, Jammu Kashmir, Madhya Pradesh, Punjab,
Uttar Pradesh, Uttarakhand, Chandigarh, Delhi
South: - Andhra Pradesh, Karnataka, Kerala, TamilNadu, Andaman&Nicobar Island,
Lakshadweep, Pondicherry
East: - Assam, Bihar, Jharkhand, Manipur, Meghalaya, Mizoram, Nagaland, Odhisa, Sikkim,
Tripura, West Bengal
West: - Goa, Gujarat, Maharashtra, Rajasthan, Dadra & Nagar, Daman Diu,
Segmentation of data helps us to analyze how each region behave and how they differ from
each other and which region needs utmost attention
3. Descriptive Analysis
From the data that we have with regards to the rape convicts for each state for the period of
2001-2010, we try to calculate the Average and the Standard Deviation of all the states
comprising in India. Over here we look at the graph to understand how the number of rape
convicts number where progressing from each year.
Average rape Convicts per year (2001-2010): - 5021.1087 person
Standard Deviation: - 816.814
Table for Average Rape Convicts Each Year in India
Year Average(Person)
2001 114.73
2002 105.20
2003 143.11
2004 142.17
2005 156.79
2006 189.02
2007 151.79
2008 164.24
2009 156.02
2010 144.84

6. The figure above gives the alarming sign of how the rape convict numbers were increasing from
the period of 2001-2005. This alarming numbers signals the sudden action to be taken to
enhance the protective measures for women in India.
From this point we segment region wise and understand what North/South/East/West behaves
when it comes to alarming signs of rape convict number. We try to understand which region
sounds safe and also we try to figure out the states with high number of rape convicts.
North States Description
Let us try to look at the North states individual Average and total of rape convicts in the northern
region. The average rape Convicts of North States per year from the period of 2001-2010: -
2422.609
The below summary shows us how individual north region differs and Haryana having the
maximum followed by Chhattisgarh.
0
20
40
60
80
100
120
140
160
180
200
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Average Rape Convicts
Average Rape Convicts

7. Table for North State Average (2001-2010)
Groups Sum Average Variance
Chhattisgarh 3475 347.5 3690.944
Haryana 3766 376.6 10404.93
Himachal 1133 113.3 2099.344
Jammu
Kashmir 202 20.2 158.4
MP 7488 748.8 14259.51
Punjab 2248 224.8 10520.84
UP 2890.087 289.0087 100367.5
Uttarakhand 427 42.7 671.7889
Chandigarh 112 11.2 37.73333
Delhi 2485 248.5 4579.611
South States Description
The average rape convicts of South India per year from the period of 2001-2010: - 417.5
Table for South State Average (2001-2010)
Groups Sum Average Variance
Andhra
Pradesh 1728 172.8 658.8444444
Karnataka 577 57.7 371.5666667
Kerala 328 32.8 620.1777778
Tamil Nadu 1488 148.8 7087.511111
Andaman &
Nicobar 34 3.4 2.044444444
Lakshadweep 2 0.2 0.4
Puduchery 18 1.8 5.733333333
In the South region, Andhra Pradesh stands to be most unsafe region for women with highest
rape convicts found there. However when compared to northern region, South States are pretty
much safer for women with lower average than North India.

8. East States Description
The average rape convicts found in East India from the period of 2001-2010 is 1303.7
Table for East State Average (2001-2010)
Groups Sum Average Variance
Assam 2835 283.5 6521.389
Arunachal 3 1.5 0.5
Bihar 1555 155.5 647.1667
Jharkhand 3465 346.5 14090.5
WB 2039 203.9 8825.656
Odhisa 1917 191.7 1346.456
Manipur 9 0.9 0.544444
Mizoram 224 22.4 118.0444
Sikkim 79 7.9 14.1
Tripura 781 78.1 565.6556
Nagaland 41 4.1 10.54444
Meghalaya 89 8.9 56.1
Jharkhand and Assam are the most unsafe place for women in the eastern region. Assam has
for several times also been in the media radar for its highly increasing rape cases during the
past few years.
West State Description
The average of Western region states:-877.3
Table for East State Average (2001-2010)
Groups Sum Average Variance
Goa 140 14 8.444444
Gujarat 2881 288.1 31966.77
Maharashtra 2320 232 3208.889
Rajasthan 3430 343 2263.556
Daman 0 0 0
Dadra 2 0.2 0.177778

9. As the above table indicates Gujarat and Rajasthan have the highest rape convicts in the West
Region. With few states comprising the western geographical areas- Gujarat, Rajasthan and
Maharashtra have the most rape convicts which slightly increases the average of western India.
Analysis: - Analyzing the above data gives us a clear picture of Northern Region where the
rape convicts are highest and is the most unsafe region for women in India. This is followed by
Eastern India. Southern Part of India having highly low average sounds safe for Women in
India. We also conclude that Chhattisgarh, Haryana and Jharkhand are the most unsafe
place for women and measures should be taken to improve the condition of these states by
spreading education.
4. Scatter Diagram
The scatter diagram helps us to find the trend of rape convicts in each region and understand if
there is any improvement in the safety of women in those regions. We analyze each of the
geographical region to understand if the condition is getting worse or its improving thereby
understanding how safe are those region from Women point of view.
Table showing how number of rape convicts as the year progresses from 2001-2010
0
1000
2000
3000
4000
2000 2002 2004 2006 2008 2010 2012
No.ofConvicts
Time Period
North India
Total

10. 0
200
400
600
2000 2002 2004 2006 2008 2010 2012
No.ofConvicts
Time Period
South India
0
500
1000
1500
2000
2000 2002 2004 2006 2008 2010 2012
No.ofCovicts
Time Period
East India
0
200
400
600
800
1000
1200
1400
2000 2002 2004 2006 2008 2010 2012
No.ofConvicts
Time Period
West India

11. While initially the descriptive analysis of Rape Convicts in each region gave us a picture of
Northern states being most unsafe for Women, the scatter diagram gives a picture of things in
West India looks different. While the rape victim numbers for each state fell after the period of
2006, things were different for West India. After the period of 2006, the number of rape convicts
saw a sudden increase which creates a sense of concern and needs to be studied to find the
exact reason. While things are getting better when compared to the previous year, South India
shows incredible improvement in the safeties of women with number of rape convicts
decreasing and falling much below as the year passes on.
5. Correlation
This section helps us to correlate and understand how each region varies from one other. Over
here we try to observer if whenever there is an increase in number of rape victims in one of the
region is there similar increase in other region and how strongly are they bonded to each other.
Correlation of 1 state that there is a stronger relation between the variables and strong increase
in one region follows the same trend in other region .As the number decreases, the correlation
between them decreases. Negative correlation states whenever there is increase in one region,
we observer a decrement in other region.
So to proceed with the correlation, we first simplify our data showing the total rape convicts in
each region for the period of 2001-2010.
North south east west
2001 1981 465 857 600
2002 1910 334 707 627
2003 2437 375 1184 870
2004 2377 365 1412 679
2005 2669 537 1302 823
2006 3370 553 1698 806
2007 2282.198 402 1487 990
2008 2414.426 408 1592 1170
2009 2351.722 366 1524 1219
2010 2433.71 370 1274 991

12. For the above table we find the correlation between North, South, East, and West:-
North south east west
North 1
south 0.684049 1
east 0.723066 0.304197 1
west 0.177788 -0.17227 0.655837 1
So the above correlation table shows how each region behaves when compared to other region.
We see a strong positive correlation between East and North indicating the same trend of
changes being experience over the period of time. The negative correlation between South and
West indicates that the things are opposite when being compared. The correlation of south
region with other region is interesting as it shows weak relation with other region and this helps
us to understand how things were getting better for the southern region in terms of rape cases.
The correlation factor improves or strengthens our data that we represented earlier and support
the safety of women in Southern India.
6. Box plot statistics
North south east west
Upper whisker 2669.00 553.00 1698.00 1219.00
3rd quartile 2437.00 465.00 1524.00 991.00
Median 2395.71 388.50 1357.00 846.50
1st quartile 2282.20 366.00 1184.00 679.00
Lower whisker 2282.20 334.00 707.00 600.00
Nr. of data points 10.00 10.00 10.00 10.00
Mean 2422.61 417.50 1303.70 877.50

13. Box plots let us know the variations of the given data easily.
When you see from the regions point of view:
IQR of each region:
 North – IQR = Q3-Q1 = 2437-2282.5=154.8
This determines the middle 50% of the total convicts in the northern region from 2001 – 2010.
 South – IQR = Q3-Q1 = 465-366=99
This determines the middle 50% of the total convicts in the southern region from 2001 – 2010.
 East – IQR = Q3-Q1 = 1524-1184=340
This determines the middle 50% of the total convicts in the eastern region from 2001 – 2010.
 West – IQR = Q3-Q1 = 991-679=312
This determines the middle 50% of the total convicts in the western region from 2001 – 2010.
Comparing the box plots with other regions:
When comparing the convicts of north and south, the numbers of north convicts were
tremendously more (up to 2437) than the south regions (465).
Even though the variability of convicts in the west region is more when compared to the east
region, the numbers of convicts in the east region are focused between the 50% (between Q1
and Q3).
A huge number of convicts are closely found in the north and the south regions. As we can see
the convicts are closely appearing between the Q1 and Q3(50% of the total data set).

14. Looking at the 4 different regions of India, from this box plot derivation we can conclude that the
numbers of convicts in Northern regions are more compared to other 3 regions and the numbers
of convicts in Southern regions are less compared to other 3 regions.
Outliers:
Exceptions found in the box plots: Outliers are found when a huge or a smaller number is out of
range from the other values in the data set.
North: Three outliers are visible i.e. 1910, 1981 and 3370 for the year 2002, 2001 and 2006
respectively.
The reasons could be either a data entry error or an extreme period time where rape cases
happened in the northern region and were not controlled.
7. Sampling Probability
In this section we try to understand the likelihood of the sample falling within the population
range and understanding how likely the event can occur with the data given to us.
North States
Probability of mean of North States from 2001-2019 to be 242.2609
more than Population mean (146.816)
Average North = 242.2609
N(total number of states & Union Territory)= 35
n(sample of 10 states in north)= 10
population Standard Deviation(𝜎) = 181.276
Since n/N =10/35 = .28> .05 , we need to use population correction
factor
Population Correction Factor(s) = (𝜎 ÷ √ 𝑛) √{( 𝑁 − 𝑛) ÷ ( 𝑁 − 1)}
S= 49.15
𝑧 =
(242 .26−146.81)
49.15
= 1.94
Using the Z table from normal distribution, we calculate the area of
probability.
P (north mean more than population mean = 47.38%)

15. The probability of getting mean of Northern states more than that of Population mean seems to
be 47.38% which states that its very likely that the state experiences high rape convicts and the
data given in the research is a very likely event thereby endangering the safety of women in
these region.
South States
Probability of south states mean 59.64 to be lesser than population mean (146.816)
Average south = 59.64286
N(total number of states & Union Territory)= 35
n(sample of states in south)= 7
population Standard Deviation(𝜎) = 181.276
Since n/N =7/35 = .20> .05 , we need to use population correction factor
Population Correction Factor(s) = (𝜎 ÷ √ 𝑛) √{( 𝑁 − 𝑛) ÷ ( 𝑁 − 1)}
S= 62.17
𝑧 =
(59.64−146 .81)
62.17
= -1.40
P (south states mean less than population mean = 41.40%)
The probability of getting mean of Southern states less than that of Population mean seems to
be 41.40% which makes it a very likely event to occur and strengthen the data that supports the
safety of the women.

16. East States
Probability of East states mean 116.4018 to be lesser than population mean (146.816)
Average east = 116.4018
N(total number of states & Union Territory)= 35
n(sample of states in south)= 12
population Standard Deviation(𝜎) = 181.276
Since n/N =12/35 = .34> .05 , we need to use population correction factor
Population Correction Factor(s) = (𝜎 ÷ √ 𝑛) √{( 𝑁 − 𝑛) ÷ ( 𝑁 − 1)}
S= 43.03
𝑧 =
(116.4018 −146 .81)
43.03
= -.70
P(east states mean less than population mean = 25.80%)
The East states table states that there is 25.8% chance for the Eastern states mean to be lower
than the population mean.
West States
Probability of west states mean lesser than population mean
Probability of West states mean 146.2167 to be lesser than population mean (146.816)
Average west = 146.2167
N(total number of states & Union Territory)= 35
n(sample of states in south)= 6
population Standard Deviation(𝜎) = 181.276
Since n/N =6/35 = .17> .05 , we need to use population correction factor
Population Correction Factor(s) = (𝜎 ÷ √ 𝑛) √{( 𝑁 − 𝑛) ÷ ( 𝑁 − 1)}
S= 68.34
𝑧 =
(146.2167 −146 .81)
68.34
= -.0086
P (west states mean less than population mean = .2%)

17. Conclusion
As we see above that the data supports the finding of Northern states being more unsafe with
47% of rape convicts being found within the population mean and hence strengthen the facts of
steps/measures to be taken to enhance protective measures for the state.
8. Confidence Interval
In this section we try to determine an estimated range of values which is likely to include our
sample parameters. Confidence Intervals are usually calculated for 90%, 95%, 99%. In our
paper, we would try to evaluate the intervals for 99% to be more specific. The width of the
confidence interval tells us how uncertain we are about the unknown parameter.
North States:
BASIC STATISTICS
N Mean Standard deviation
10 2422.61 400.45
CONFIDENCE INTERVALS FOR THE North Sate MEAN
(With normal distribution)
Mean = 2422.6056
Standard Deviation = 400.452857
N = 10
Z (0.005) = 2.575831
(Left Interval) = 2422.6056 − 2.5758 ×
400.452
√10
= 2422.6056 - 326.18863
= 2096.41697
(Right Interval) = 2422.6056 + 2.5758 ×
400.452
√10
= 2422.6056 + 326.18863
= 2748.79423
99% Confidence Interval: (2096.41697, 2748.79423)
The above Confidence interval states that we are 99% sure that the mean of the North States
which is 2422.61 lies within the range of 2096.4169 and 2748.79423.

18. South States
BASIC STATISTICS
N Mean Standard Deviation
10 417.5 75.77
CONFIDENCE INTERVALS FOR THE South State MEAN
(With normal distribution)
Mean = 417.5
Standard Deviation = 75.770487
N = 10
Z (0.005) = 2.575831
(Left Interval) = 417.5 − 2.5758 ×
475.77048
√10
= 417.5 - 61.718804
= 355.781196
(Right Interval) = 417.5 + 2.5758 ×
475.77048
√10
= 417.5 + 61.718804
= 479.218804
99% Confidence Interval: (355.781196, 479.218804)
The above Confidence interval states that we are 99% sure that the mean of the South States
which is 417.5 lies within the range of 355.78 and 479.21
East States
BASIC STATISTICS
N Mean SD
10 1303.7 316.8
CONFIDENCE INTERVALS FOR THE East state MEAN
(With normal distribution)
Mean = 1303.7
Standard Deviation = 316.798937
N = 10
Z (0.005) = 2.575831
(Left Interval) = 1303.7 − 2.5758 ×
316.708
√10
= 1303.7 - 258.04838
= 1045.65162

19. (Right Interval) = 1303.7 + 2.5758 ×
316.708
√10
= 1303.7 + 258.04838
= 1561.74838
99% Confidence Interval: (1045.65162, 1561.74838)
The above Confidence interval states that we are 99% sure that the mean of the East States
which is 1303.7 lies within the range of 1045.651 and 1561.74. The lower range of this
confidence interval strengthens the statistic of Eastern region.
West States
BASIC STATISTICS
N Mean SD
10 877.5 214.74
CONFIDENCE INTERVALS FOR THE West State MEAN
(With normal distribution)
Mean = 877.5
Standard Deviation = 214.73873
N = 10
Z (0.005) = 2.575831
(Left Interval) = 877.5 − 2.5758 ×
214.73873
√10
= 877.5 - 174.915301
= 702.584699
(Right Interval) =877.5 + 2.5758 ×
214.73873
√10
= 877.5 + 174.915301
= 1052.415301
99% Confidence Interval: (702.584699, 1052.415301)
The above Confidence interval states that we are 99% sure that the mean of the West States
which is 877.5 lies within the range of 702.58 and1052.41.

20. 9. Anova Test
Anova Test helps us to determine regionally if the mean of the states with in each region differs
from each other. This test helps us to understand if there is any difference in the mean of the
states in the each region. If the difference is found, calculating which mean is different is beyond
the scope of this project.
North States Anova Test
H0 = All sample mean are equal
H1= At least one mean in the Northern States are different.
ANOVA
Source of
Variation SS df MS F P-value F critical
Between
Groups 4473889 9 497098.8 33.86449
3.27993E-
25 1.985595
Within
Groups 1321115 90 14679.06
Total 5795005 99
95% CONFIDENCE INTERVAL DIAGRAM
+------------------------+------------------------+
(-*--) Chhattisgarh
(---*--) Haryana
(-*) Himachal Pradesh
(* Jammu & Kashmir
(----*---) Madhya Pradesh
(---*---) Punjab
(----------*-----------) Uttar Pradesh
(*) Uttarakhand
*) Chandigarh
(-*--) Delhi
+------------------------+------------------------+
-75.94 420.51 916.96
As in the above we see in the Anova Table F lies outside the Fc, therefore we reject the Null
Hypothesis which states that the mean of the North states are equal. There is at least one mean
which differs from the rest of the north states means

21. South States Anova Test
H0 = All sample mean are equal
H1= At least one mean in the South States are different.
ANOVA
Source of
Variation SS df MS F
P-
value F crit
Between
Groups 315203.6 6 52533.93 42.04502868
3.31E-
20 2.246408
Within
Groups 78716.5 63 1249.468
Total 393920.1 69
+------------------------+------------------------+
(---*--) Andhra Pradesh
(--*-) Karnataka
(---*--) Kerala
(-----------*-----------) Tamil Nadu
* Andaman & Nicobar Isla
* Lakshadweep
(* Pondicherry
+------------------------+------------------------+
-21.18 104.39 229.95
As in the above we see F lies outside the Fc, therefore we reject the Null Hypothesis which
states that the mean of the South states are equal. There is at least one mean which differs
from the rest of the south states.
East States Anova Test
H0 = All sample mean are equal
H1= At least one mean in the East States are different.

22. ANOVA
Source of
Variation SS df MS F
P-
value F crit
Between
Groups 1579469 11 143588.1 49.55314
1.69E-
35 1.885687
Within
Groups 289765.9 100 2897.659
Total 1869235 111
+------------------------+------------------------+
(-----*----) Assam
(* Arunachal Pradesh
(*-) Bihar
(-------*-------) Jharkhand
* Manipur
*) Meghalaya
(*) Mizoram
* Nagaland
(--*-) Orissa
*) Sikkim
(-*-) Tripura
(-----*------) West Bengal
+------------------------+------------------------+
-48.48 213.28 475.04
As in the above we see F lies outside the Fc, therefore we reject the Null Hypothesis which
states that the mean of the East states are equal. There is at least one mean which differs from
the rest of the east states.
West States Anova Test
H0 = All sample mean are equal
H1= At least one mean in the West States are different.
ANOVA
Source of
Variation SS df MS F
P-
value F crit
Between
Groups 1263948 5 252789.5 40.50267
4.3E-
17 2.38607
Within Groups 337030.5 54 6241.306
Total 1600978 59

23. +------------------------+------------------------+
(* Goa
(------------*------------) Gujarat
(---*---) Maharashtra
(---*--) Rajasthan
* Dadra & Nagar Haveli
* Damman & Diu
+------------------------+------------------------+
-41.71 207.95 457.61
As in the above we see F lies outside the Fc, therefore we reject the Null Hypothesis that states
the mean of the West states are equal. There is at least one mean which differs from the rest of
the west states.

24. 10. Conclusion
The above statistical figures give us the clear picture of how each region differs in the number of
rape convicts found throughout the year of 2001-2010. We go through series of test to
understand the trend that follows in each region and to understand how safe are those region
for Women. However the number rape convicts does not states that number of rape that takes
place in India. Those figures of number of rape may be way higher than the rape convicts. The
statistical figure does not only include Indian States but at the same time includes the Union
Territories under the Indian Government regime. The test of Anova helps us to conclude that no
states in each region have same mean within the given variance of theirs. While the sampling
distribution tests strengthen our statistical data of stating the likelihood of the sample falling
under range of population. Looking at each test we conclude on the fact that Northern region
sounds more unsafe to the women of India with highest convicts per year. South India sounds
much safer in the comparison graph. Also we draw the strange graph of Western India which
shows how slowly the graph rises from the period of 2006 while other states aimed to show
certain improvement in their graph .Keeping all this in mind, we conclusively conclude that while
Northern states need more sign of concerns, each region must also not be neglected and sign f
concerns lies there as well to improve the rape convict numbers.

25. 11. References
1. http://news.harvard.edu/gazette/story/2013/09/understanding-indias-rape-crisis/
2. http://www.indialawjournal.com/volume2/issue_2/article_by_priyanka.html
3. http://citation.allacademic.com//meta/p_mla_apa_research_citation/2/4/2/6/4/pages242646/p2426
46-2.php
4. http://www.cjsonline.ca/pdf/racethsex.pdf
5. http://jcc.sagepub.com/content/12/3/284.short
6. http://onlinelibrary.wiley.com/doi/10.1111/j.1540-4560.1981.tb01068.x/abstract
7. http://ethics.journalism.wisc.edu/2013/03/19/covering-rape-the-changing-nature-of-society-and-
indian-journalism/

26. 12. Appendix
Formulas Used:-
 Variance (𝜎2 ) =
∑ (𝑥𝑖−𝜇)𝑖−𝑁
𝑖−1
𝑁
where 𝜇 = 𝑀𝑒𝑎𝑛 𝑎𝑛𝑑 𝑁 𝑖𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠
 Standard Deviation (𝜎)= √𝜎2
 Z value for sampling probability:-
𝑥−𝜇
𝜎x
√𝑛⁄
where x= Sample Mean , 𝜇 is population mean
 Population Correction Factor to be used in Z formula above if the n/N > .05 (𝜎x ):- (
𝜎
𝑁
)
x √
𝑁−𝑛
𝑁−1
where N is population number and n is sample number
 Confidence Interval :- 𝜇 + 𝑧 ×
𝜎
√𝑛
and 𝜇 − 𝑧 ×
𝜎
√𝑛
 The Anova table below shows the formula of calculating the F (Critical value). The below
table shows for both simple and regression mean, however in our paper we have used
the 1st
table for comparing the means.

27.  Formulas used for Box plot.
Mean, Standard deviation, Quartile range and the interquartile range.
 Quartile range: These tell us the position of the values for Q1, Q2 and Q3.
Q1 =
𝑛
4
𝑡ℎ
Q3 =
3𝑛
4
𝑡ℎ
Q2 = Median =
𝑛
2
𝑡ℎ
 Inter-quartile range: It tells us how much data falls between Q3 and Q1 (50%
data).
IQR = Q3 – Q1
 To find the outliers: These outliers will be beyond the whiskers of a box plot.
Low values = Q1-1.5(IQR) and High values = Q3+1.5(IQR)
The data used in our calculation –
SOUTH States 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Andhra Pradesh 166 186 191 199 160 160 216 170 153 127
Karnataka 45 29 32 46 74 66 61 67 67 90
Kerala 28 15 40 0 0 49 44 81 48 23
Tamil Nadu 226 101 109 115 300 273 73 84 88 119
Andaman&Nicobar
Island
0 3 3 4 3 4 3 5 4 5
Lakshadweep 0 0 0 0 0 0 2 0 0 0
Pondicherry 0 0 0 1 0 1 3 1 6 6
NORTH
States
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Chhattisgarh 344 339 427 337 290 307 276 357 324 474
Haryana 207 197 347 400 394 412 412 438 438 521
Himachal
Pradesh
36 65 96 90 92 122 187 147 156 142
Jammu & 11 9 15 14 16 27 18 53 21 18

28. Kashmir
Madhya
Pradesh
870 697 756 797 747 879 780 797 711 454
Punjab 70 95 169 190 168 365 252 277 313 349
Uttar
Pradesh
249 277 371 371 711 905 1198 1426 1722 1741
Uttarakhand 8 17 42 4 38 62 74 47 62 73
Chandigarh 6 7 9 4 5 13 16 23 17 12
Delhi 180 207 205 170 208 278 266 274 308 309
EAST
States
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Arunachal
Pradesh
2 1
Assam 139 176 222 298 315 343 359 371 347 256
Bihar 147 118 174 159 161 206 172 154 136 128
Jharkhand 241 146 403 435 392 571 310 392 316 259
Manipur 0 2 1 1 1 1 1 2 0 0
Meghalaya 1 2 1 5 5 15 18 6 20 16
Mizoram 13 14 16 23 14 22 18 25 30 49
Nagaland 2 0 2 2 2 4 7 5 6 11
Odhissa 161 123 151 188 198 227 233 230 209 197
Sikkim 12 7 0 11 13 9 7 7 8 5
Tripura 40 50 57 69 89 87 118 93 95 83
West
bengal
99 68 157 221 112 213 244 307 357 261
WEST
States
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Goa 14 11 11 16 18 16 11 11 14 18
Gujarat 89 114 155 162 178 230 415 525 484 529

29. Maharashtra 214 184 344 207 224 216 240 249 299 143
Rajasthan 282 318 360 294 403 344 324 384 420 301
Dadra &
Nagar
Haveli
1 0 0 0 0 0 0 1 0 0
Daman 0 0 0 0 0 0 0 0 0 0