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Extended essay Candidate code: grg 826Extended EssayGeographyIs there a difference in clustering of the chosen services in frankfurt?Word count:Introduction:The aim of this investigation is to find and compare the distribution of high and low order service types within frankfurt.I chose Frankfurt since i was born there, as well as that most of my family lives there. But i myself lived in sweden most of my life. Right now my father also owns a hospital there so this made me even more interested. I wanted to get to know frankfurt in a different way than just what is in plain sight. Frankfurt is also a economically influential city since the European Central Bank (ECB) is located there.There are two general types of services, High order and low order services. High order service are characterized by its exclusiveness. Buyers also usually want to compare the products quality and price with what the other stores have to offer. High order services are also so to say magnetic, they attract other producers of the same product. This happens because it is more beneficial for producers to build a store where they know that their customers will be rather than somewhere in the outskirt where people only come by occasionally. Another benefit of having your store close to other stores selling the same thing is that customers can easily compare which one is better. Of course this only makes sense if you are confident in that your product is better than theirs.Stores that fall under the category of low order services are often stores which sell cheaper products at high quantities, where quality either doesn’t matter or is more or less the same for every store selling this product. People usually buy Low order service items on an impulse or sudden feeling of wanting it.. Low order services are also not really affected by the magnetism effect mentioned earlier. They are usually equally distributed throughout the city.Reference:http://www.oxfordreference.com/view/10.1093/oi/authority.20110803095936128Research question:Is there a difference in clustering of the chosen services in frankfurt?Hypothesis: My hypothesis is that the High and low order service theory will hold true. So we will see a higher degree of clustering with High order services and for low order service we will see an equal distribution. Methods:The data i used was obtained from a website called Gelbe seiten (https://www.gelbeseiten.de) is a database of all, or most services provided in germany. The site provides information like the phone numbers to the companies, their websites and most importantly where the service is located. So what i did was i looked for the services i wanted to use and i plotted their locations on my own map, which i drew previously.There are two methods used to find the amount of clusterdness per service, essentially deciding to which order the two services belong to. The first one is the Nearest Neighbour Index (NNI). It is calculated by plotting the geographical position of the services on a map with a predefined investigation are that has to be a perfect square, and then as the name suggests you start to number them (i choose to do this from A to Z if i had more data points than the alphabet had letters i would Continue with AA, AB, AC and so on)  starting from the outermost point on the map and then working your way in by always going to the nearest neighbor to that point. While marking these points you write down the distance between each neighbour and also which neighbour the point has. Then you calculate the average distance (d)from neighbour to neighbour by adding all the distances (d) and then dividing by number of data (n). Your result with the rest of your collected data are then put in to the following formula NNI=2*d nA (“A”is the area of your map in kilometers squared (km2)). The result that is outputted should be within the domain of 0X2.15, the closer to 0 the result is the more clustered it will be, while, when it is close to one it means it has a random distribution and the closer we get to 2.15 the more regularly the service is distributed.The second method of finding the degree of clustering is done using the Index Of Dispersion (IOD). For this method you start, again by plotting the geographical area onto a map which has a predefined investigation area that has to be a square. Then you draw a line, that is parallel to the border of the map through the outermost point. This is repeated for each side. Giving you a new area (A). Then divide the quantity of the data points by ¼. The received value is the amount of points one moves towards the center, where you then do the same procedure again giving you another smaller square inside the first one, area (Q). plugging the two areas in to the formula IOD=QA will output a value between 0-1. Which shows, just like for the NNI a scale how clustered the service is in the area. 0means that the service is not clustered at all, it is randomly distributed. one means it is highly clustered in one small area. http://math.tutorvista.com/statistics/index-of-dispersion.html Description of frankfurt (investigation areaFrankfurts central business district (CBD) is located directly at The Main river, it divides the city into two parts. The CBD is located on the Northern side almost directly next to the river. There you also have the Römerplatz which dates back to the 15 hundreds. But the bombing during the second world war only left the facades of the Buildings around the market square. But behind the old looking facades there are modern 1950s style offices. Above that there is a long shopping street called zeil which stretches from Hauptwache to Konstablerwache. Which also are two of the most used subway stations in frankfurt and at the same time also are two “town squares”. Zeil is the main shopping alley in frankfurt where you can find almost anything. You can find things like bakeries (Low order service) all the way to jewelry shops (High order services) and rather prestigious clothing shops. To the West on the map we can find the Bankenviertel. Which basically is the financial district, here you can also find the ECB. Looking at the north part of the map we find a part of Frankfurt called Nordend. A rather rich and expensive part of frankfurt. In frankfurt there are 731.095 people living within in its defined area of the city and if you include the urban area that number rises to 2.3 million. (Numbers from 2015, most up to date at time of writing) (http://worldpopulationreview.com/world-cities/frankfurt-population/ )Picture 1: Zeil shopping streetResultsMap 1: Nail Salons distribution across Frankfurts Map 2: Plastic surgeon distribution across Frankfurts Map 3: Jewelry store distribution across Frankfurts Map 4: Pharmacy distribution across Frankfurts Map 5: Ice Cream store distribution across Frankfurts Map 6: Bakery distribution across FrankfurtsMap 7: Fast food restaurant distribution across FrankfurtMap 8: Printing House distribution across FrankfurtHigh order servicesJewellery Plastic SurgeonsNail SalonsPrinting HousesNearest Neighbour Index0.530.600.881.1Index of Dispersion0.130.060.160.11Low order servicesPharmaciesBakeriesIcecream stands Fast food RestaurantsNearest Neighbour Index0.970.601.401.13Index of Dispersion0.230.190.270.12DiscussionIn my research question i had established that i want to find the clustering for my chosen high and low order services in frankfurt. The expected outcome for this, was developed in the hypothesis which was, that High order services where to be very clustered and low order service more or less equally distributed. But if we look at the Bakeries values for the Nearest Neighbour Index, it clearly shows that the bakeries are leaning towards the clustered side. This might be because the bakeries are mostly located in the close vicinity of the city center, because most people come by there and might want to grab something to eat before, during or after work times. Since Frankfurt is my home city i know that the Bakeries frequency of occurrence falls dramatically the further out you get from the city center. The service that follows the theory and also my hypothesis the closest are the Pharmacies. They scored a Nearest Neighbour Index of 0.97, which is extremely close to one and as mentioned earlier a score of one, means random distribution. The Index of Dispersion hower shows a more subtle distribution at 0.23 which is not at all as extreme as the NNI. This might be because of the difference in the way the two methods measure the clustering. Hower The Ice Cream stores Nearest Neighbour Index values seem to show that the distribution of stores is regular which in my experience of living in Frankfurt does not hold true. There are many stores located directly at the Main river and also along the shopping alley Zeil. This inaccuracy might be because Ice Cream stores can very often be rather small businesses so they might not be listed on the Gelbe Seiten web page. Added to that, some ice cream stores might only exist for a short time since the business isn’t going well or as planned. Another reason for an inaccurate result might be because of Seasonal Unemployment (a theory from economics) which probably influences Ice Cream stores since many people enjoy Ice Cream more during the summer. This might Affect businesses in such a way that Ice Cream stores close during winter, therefore they might not be listed on the site either.Moving over to High order services, the theory of High and Low order services seem to hold true in every case. Except for Nail Salons and Printing Houses. The Nail Salons have a unusual high NNI. This could be because Nail Salons receive a lot of young visitor who do not compare prices to much. Therefore such salons don’t need to cluster upp. Nail salons also are often not owned by big companies but rather by private people resulting in them having to take whatever location is cheapest. At the same time Nail salons are, as mentioned earlier small businesses therefore they might also not be listed on Gelbe Seiten. The second service that completely defies the theory is the Printing service. The reason for them to not be clustered at all might be that nowadays most users of such facilities do it online, comparing prices from their homes. So The corporations do not need to think about where to build a their facility. Reference list:https://sites.google.com/site/geographyfais/fieldwork/6-data-analysis/statistical-tools/clustering-dispersal/interquartile-areas Waugh D. (2002) geography an integrated approach Nelson Thornes. China.https://www.gelbeseiten.dehttp://worldpopulationreview.com/world-cities/frankfurt-population/ http://math.tutorvista.com/statistics/index-of-dispersion.html Plant geography (2013) Crodrington S. (ISBN 978 0 9803436 6 3)