Quantitative Techniques in Geography

1. Dr. Arindam Sarkar
Department of Geography
Purash Kanpur Haridas Nandi College
arindam.srkr1@gmail.com
Mean Centre
of
Population
Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com

2. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
 Mean centre population and its locational shift is an important
techniques of point pattern analysis
 Mean center can be determined by location of Geo-Centre
 In a map mean centre can be located as a point
 This techniques has been used by J.E.Hilgard (1872) for analysis of
west ward shifting tendency of population in USA
 Mean centre of population has been used to identify, determine and
analysis the concentration, distribution and shifting pattern of population
over time
 Distance of X and distance of Y coordinate of Geo-centre is determined
for calculation of mean centre of that pareticular region
 Total population (of particular census year) of an administrative unit,
location of Geo-Centre of that particular administrative unit are two main
important components have to keep in mind when you are going to
calculate mean centre of population
 Mean centre denote about average concentration of population of a
particular area

3. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Calculation Procedures
Step-1 Fit X, Y, coordinate at outside of the boundary (touching the extreme extent of
boundary in the south and west) and mark scale on it (cm).
Step-2 Locate Geo-Centre of every sub-administrative unit on the given map by X and Y
coordinate
Step-3 Calculate distance along X and Y between Geo-Centre and main axis line (X and Y
axis)
Step-4 Make a data and calculation table
Step-5 To get XP value of each sub-administrative unit do multiply Total population (P) with
X distance along X-axis of Geo-Centre
Step-6 To get YP value of each sub-administrative unit do multiply Total population (P) with
Y distance along Y-axis of Geo-Centre
Step-7 Do summation of Total population (P), XP and YP
Step-8 Calculation for mean centre. Position of mean centre represent by Xc and Yc value
Sl. No. Administrative Unit Total Population (P) X-distance (cm) Y-distance (cm) XP YP
Summation ∑P ∑XP ∑YP

4. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Mapping Procedures
Step-1 Location of Geo-Centre may be shown by black dot encircled by red circle
Step-2 Coordinate of Geo-centre may be shown by brown dotted or discontinuous
line
Step-3 Location of Mean centre may be shown by black dot encircled by red circle
Step-4 Coordinate of Mean centre shown by black continuous line
Step-5 Coordinate (main) fitted in out of the map boundary (Bottom and left hand
side) should be in black colour
Step-6 Title of the map “MEAN CENTRE OF POPULATION”
Step-7 Sub-title contain: Sub and main administrative unit, time of data (Census,
2011)
Step-8 Index content
Geo-centre
Coordinate of Geo-centre
Mean centre
Coordinate of mean centre

5. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Location of Geo-centre
 Geo-centre located by Black dot
with green circle
 Coordinate of Geo-centre
demarcated by Brown dotted or
discontinuous line
 Length also demarcated

6. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
District Population (P) X Y XP YP
Darjeeling 1024269 8.3 19 8501432.7 19461111
Jalpaiguri 2214871 10.4 18.1 23034658.4 40089165.1
Koch Bihar 1771643 11.7 17.2 20728223.1 30472259.6
Uttar Dinajpur 1415653 7.3 16 10334266.9 22650448
Dakshin
Dinajpur 989294 9 14 8903646 13850116
Maldah 2031871 7.4 13 15035845.4 26414323
Murshidabad 3697552 7.9 9.5 29210660.8 35126744
Birbhum 2095829 6.2 8.9 12994139.8 18652878.1
Bardhaman 4835388 6.7 6.9 32397099.6 33364177.2
Nadia 2964253 9 7.1 26678277 21046196.3
24 PGS (N) 5529497 9.6 4.6 53083171.2 25435686.2
Hugli 3557306 7.3 5.1 25968333.8 18142260.6
Bankura 2374815 4.4 6 10449186 14248890
Data and calculation table for Mean centre of population in the district of West Bengal (1981)

7. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
District Population (P) X Y XP YP
Purulia 1853801 2 6.5 3707602 12049706.5
Haora 2966861 7.3 3.9 21658085.3 11570757.9
Kolkata 4126846 8.5 3.9 35078191 16094699.4
24 PGS (S) 4388102 8.7 2.9 38176487.4 12725495.8
Paschim
Medinipur 3697899 5 3.4 18489495 12572856.6
Purba Medinipur 3044897 6.5 1.9 19791830.5 5785304.3
∑ 54580647 414220631.9 389753075.6
Data and calculation table for Mean centre of population in the district of West Bengal (1981)
Xc 1981 7.589148
Yc 1981 7.140866
Formula :
Xc = ∑XP/∑P
Yc = ∑YP/∑P

8. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Mean centre of
Population
Districts of West Bengal
for the Census year 1981
Xc 1981 7.589148
Yc 1981 7.140866

9. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
District Population (P) X Y XP YP
Darjeeling 1299919 8.3 19 10789327.7 24698461
Jalpaiguri 2800543 10.4 18.1 29125647.2 50689828.3
Koch Bihar 2171145 11.7 17.2 25402396.5 37343694
Uttar Dinajpur 1897045 7.3 16 13848428.5 30352720
Dakshin
Dinajpur 1230608 9 14 11075472 17228512
Maldah 2637032 7.4 13 19514036.8 34281416
Murshidabad 4740149 7.9 9.5 37447177.1 45031415.5
Birbhum 2555664 6.2 8.9 15845116.8 22745409.6
Bardhaman 6050605 6.7 6.9 40539053.5 41749174.5
Nadia 3852097 9 7.1 34668873 27349888.7
24 PGS (N) 7281881 9.6 4.6 69906057.6 33496652.6
Hugli 4355230 7.3 5.1 31793179 22211673
Bankura 2805065 4.4 6 12342286 16830390
Data and calculation table for Mean centre of population in the district of West Bengal (1991)

10. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
District Population (P) X Y XP YP
Purulia 2224577 2 6.5 4449154 14459750.5
Haora 3729644 7.3 3.9 27226401.2 14545611.6
Kolkata 4399819 8.5 3.9 37398461.5 17159294.1
24 PGS (S) 5715030 8.7 2.9 49720761 16573587
Paschim
Medinipur 4486279 5 3.4 22431395 15253348.6
Purba Medinipur 3845633 6.5 1.9 24996614.5 7306702.7
68077965 518519838.9 489307529.7
Data and calculation table for Mean centre of population in the district of West Bengal (1991)
Xc 1991 7.616559
Yc 1991 7.187458
Formula :
Xc = ∑XP/∑P
Yc = ∑YP/∑P

11. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Mean centre of
Population
Districts of West Bengal
for the Census year 1991
Xc 1991 7.616559
Yc 1991 7.187458

12. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
District Population (P) X Y XP YP
Darjeeling 1609172 8.3 19 13356127.6 30574268
Jalpaiguri 3401173 10.4 18.1 35372199.2 61561231.3
Koch Bihar 2479155 11.7 17.2 29006113.5 42641466
Uttar Dinajpur 2441794 7.3 16 17825096.2 39068704
Dakshin
Dinajpur 1503178 9 14 13528602 21044492
Maldah 3290468 7.4 13 24349463.2 42776084
Murshidabad 5866569 7.9 9.5 46345895.1 55732405.5
Birbhum 3015422 6.2 8.9 18695616.4 26837255.8
Bardhaman 6895514 6.7 6.9 46199943.8 47579046.6
Nadia 4604827 9 7.1 41443443 32694271.7
24 PGS (N) 8934286 9.6 4.6 85769145.6 41097715.6
Hugli 5041976 7.3 5.1 36806424.8 25714077.6
Bankura 3192695 4.4 6 14047858 19156170
Data and calculation table for Mean centre of population in the district of West Bengal (2001)

13. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
District Population (P) X Y XP YP
Purulia 2536516 2 6.5 5073032 16487354
Haora 4273099 7.3 3.9 31193622.7 16665086.1
Kolkata 4572876 8.5 3.9 38869446 17834216.4
24 PGS (S) 6906689 8.7 2.9 60088194.3 20029398.1
Paschim
Medinipur 5193411 5 3.4 25967055 17657597.4
Purba Medinipur 4417377 6.5 1.9 28712950.5 8393016.3
80176197 612650228.9 583543856.4
Data and calculation table for Mean centre of population in the district of West Bengal (2001)
Xc 2001 7.641298
Yc 2001 7.278268
Formula :
Xc = ∑XP/∑P
Yc = ∑YP/∑P

14. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Mean centre of
Population
Districts of West Bengal
for the Census year 2001
Xc 2001 7.641298
Yc 2001 7.278268

15. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
District Population (P) X Y XP YP
Darjeeling 1842034 8.3 19 15288882.2 34998646
Jalpaiguri 3569675 10.4 18.1 37124620 64611117.5
Koch Bihar 2822780 11.7 17.2 33026526 48551816
Uttar Dinajpur 3000849 7.3 16 21906197.7 48013584
Dakshin
Dinajpur 1670931 9 14 15038379 23393034
Maldah 3997970 7.4 13 29584978 51973610
Murshidabad 7102430 7.9 9.5 56109197 67473085
Birbhum 3502387 6.2 8.9 21714799.4 31171244.3
Bardhaman 7723663 6.7 6.9 51748542.1 53293274.7
Nadia 5168488 9 7.1 46516392 36696264.8
24 PGS (N) 10082852 9.6 4.6 96795379.2 46381119.2
Hugli 5520389 7.3 5.1 40298839.7 28153983.9
Bankura 3596292 4.4 6 15823684.8 21577752
Data and calculation table for Mean centre of population in the district of West Bengal (2011)

16. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
District Population (P) X Y XP YP
Purulia 2927965 2 6.5 5855930 19031772.5
Haora 4841638 7.3 3.9 35343957.4 18882388.2
Kolkata 4486679 8.5 3.9 38136771.5 17498048.1
24 PGS (S) 8153176 8.7 2.9 70932631.2 23644210.4
Paschim
Medinipur 5943300 5 3.4 29716500 20207220
Purba Medinipur 5094238 6.5 1.9 33112547 9679052.2
91047736 694074754.2 665231222.8
Data and calculation table for Mean centre of population in the district of West Bengal (2011)
Xc 2011 7.623196
Yc 2011 7.3064
Formula :
Xc = ∑XP/∑P
Yc = ∑YP/∑P

17. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Mean centre of
Population
Districts of West Bengal
for the Census year 2011
Xc 2011 7.623196
Yc 2011 7.3064

18. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Locational Shift of Mean
Centre of Population

19. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Quantification table of Locational Shift of Mean
Centre of Population of the district of West
Bengal During 1981-2011
Year X (cm) Y (cm)
1981 7.60 7.14
1991 7.61 7.18
2001 7.64 7.27
2011 7.62 7.31

20. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com