Purpose of graphs:

Having collected data as part of an investigation it is useful to summarise it in a map, diagram or graph. This is because relationships between large numbers of figures can be identified more easily and direct comparisons can be made. Trends are easier to spot this way rather than from a list of figures.

There are many types of graph that can be used to show information. It is important that every graph used is appropriate, accurate, and has a title, labels and key. Computers (spreadsheets) are helpful in drawing graphs, but be careful that the graph is meaningful. It is a good idea to add graphs to a base map of the study area to show how the data varies over space.

Main Types of graph:

• Simple Bar; Compound Bar; Histogram
• Pie; Proportional Pie
• Scatter
• Line

It is best to have an idea from the start (i.e. before the data collection) which methods of data presentation you wish to use, otherwise you may discover that the type of data you have spent hours collecting may not be suitable for anything more exciting than the simple pie/bar chart. Plan how you hope to present your results by drawing a number of sketch graphs.

Compound Bar Graph (1)	Simple Bar Graph
Compound Bar Graph (2)	Histogram
Possible Questions: Give 4 features of a well presented and appropriately used bar graph. Give an example of an occasion when you would use a histogram rather than a bar graph, and say how you would consruct it. State 2 advantages and 2 disadvantages of using bar graphs in a geographical investigation. Suggest an alternative method of presenting the data shown above.	Histograms are similar to bar charts but a continuous scale divided into groups or "classes" is used (x axis). Vertical axis shows the frequency of each class. The maximum number of classes to be used can be calculated: 5 x log n (where n is the total number of items in the data set). The class interval can also be calculated: range of values (highest - lowest) divided by the number of classes.

 

Pie Chart	Proportional Pie Chart	Proportional Pie Graphs(located on a base map)
	The diameter of each pie is proportional to the total. This method integrates data together and involves a spatial element when plotted on a suitable base map. With some thought "death by pie chart" can be avoided by using this more interesting alternative technique to present data. Notice the need for two keys explaining the size and division of the circles.	Proportional Pies use the concepts of pie graphs and proportional symbols together.
The pie chart is useful to show the total data divided into proportions. It often has good visual impact but can it is difficult to read the data accurately, particularly if there are several categories. The segments should be drawn from the largest first and the smallest last unless there is an "others" category in which case that should be last regardless of its size. Segments should be shaded in different colours and a suitable key or labels added. The raw data and percentage figures can be added to the key if appropriate.

Scatter Plot		Line Graph
Scatter plots are used to show a relationship between two data sets. The dependent data should be placed on the horizontal (x) axis. The points should not be joined up but a line of best fit showing the general trend is useful where there is an obvious correlation.		Line graphs show changes over time. All the points are joined up and the axes should normally begin at zero. Rates of change are shown well, although careful thought to the scale should be given. Unsuitable if there are only a few data points.

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Purpose of maps:
Maps are important to geographers. They are bird's eye views of the earth's surface using symbols to represent features of the land and are useful to show spatial patterns. Every geographical investigation should make use of published maps to locate the study area, and many are likely to involve base maps onto which results can be drawn. Base maps can vary from a homemade sketch maps to copies of Ordnance Survey maps and outlines of the UK.

Uses of maps:
1. Locates the study area and helps to guide sampling decisions.
2. Show changes over time when maps of different survey dates are compared.
3. Maps of urban areas show clear functional zones, building density, street patterns, transport links etc.
4. Contours indicate the shape of the land: height and gradient of slopes.
5. Patterns of urban growth and pressure on the countryside can be identified by studying the location of urban zones, golf courses, motorways etc.
6. Maps of rural areas show the intensity of agricultural use and highlight natural/undeveloped regions.

Main types of maps:
Ordnance Survey 1:125,000 (road atlas scale: shows wide area/region; useful for showing sphere of influence)
Ordnance Survey 1:50,000 Landranger (2cms = 1km scale: useful for identifying study area and broad land uses such as rural/urban)
Ordnance Survey 1:25,000 Explorer (4cms = 1km scale: useful to aid sampling decisions and can be adapted to produce a suitable base map)
Ordnance Survey 1:10,000 Landplan (10cms = 1km scale: shows patterns of land use in both urban and rural areas; street map detail)
Ordnance Survey 1:2,500 Superplan (40cms = 1km scale: very detailed showing individual buildings, pavements and shops)

GOAD Plans (very detailed plan of shopping centres of towns and cities in th UK with populations over 50,000.
Geology and Soil maps
Sketch maps, Dot maps, Choropleth maps, Topological maps, Isoline maps

1:125,000	1:50,000	1:25,000	1:10,000
GOAD Plans			Geology Maps
	Possible Questions: Suggest 2 ways you might use a map to aid a geographical investigation. How could a specialised map (not an Ordnance Survey) be used in a geographical investigation? Give 3 features of a well used map in a geographical investigation. State 2 drawbacks of using published maps in a geographical investigation. How might a sketch map be useful in a geographical investigation and give 3 features of a well-used sketch map. With reference to a geographical investigation you have carried out, justify your choice of map.

All maps should have a clear scale, north arrow, title, relevant key, and preferably be annotated.
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Sketch Maps	Dot Maps	Choropleth Maps
Sketch maps can be valuable to students completing a geographical investigation. They simplify what is shown on published maps (such as Ordnance Survey) by only showing the features that are of interest. As such unnecessary detail is ignored and the map is easier to interpret.   Accurate sketch maps can be useful to locate the study area, summarize results, and serve as important base maps.   Method for drawing sketch maps: (1) draw a box the same shape as the map area you are using; (2) sketch in the main relief features, main rivers, woodland areas, and main routeways; (3) mark and label (or add a clear key) the main features you want your map to show; (4) add a title, north direction, and use colour.	Dot maps use small dots of a fixed size to represent a variable, such as numbers of people, shops, etc. located on a base map. The value of each dot should be high enough to avoid extremes and low enough to avoid too many areas having no data plotted giving the false impression of emptiness. The dots should be drawn the same size and ideally not too large that they merge together. Different coloured dots could be used to represent different data for comparison. These maps are helpful to show distributions but they do have limitations: (a) it is very difficult to count a large number of dots so accurate reading of the map is not possible; (b) this mapping technique relies on the dots being plotted accurately on a map representing a specific location rather than a broad region - detailed knowledge of the data is therefore necessary.	In choropleth or density shading maps, areas are shaded according to a key representing a range of values. It is an easy presentation technique which gives a good visual impression of change over space. It relies on a suitable key and is limited by the following: (a) it gives a false impression of abrupt change at the boundaries; (b) variations within each area are hidden, particularly if a wide data range is used; and (c) reading exact data figures from the map isn't possible. To draw a good choropleth map a suitable base map divided into small areas is needed (this can be scanned into a computer). The number of categories can be worked out in a similar way to histogram classes. Between 4 and 8 classes is best, depending on the range of your data and what it is you are trying to show. Each class should be shaded from light (small change or low numbers) to dark (large change or high numbers). All areas should be shaded unless there is "no data" for an area. There are 3 ways the data can be grouped into classes: (i) divide the range of values into equal-size classes; (ii) rank the values in order and then divide the list into the number of groups you want; (iii) inspect the data values carefully and divide them up to reflect the distribution of the data (good with extreme values).
Topological Maps		Isoline Maps
Topological maps use area or distance to represent values. Actual distance and direction are disregarded but the relative position of places is retained. There are two types: (1) Maps of areas (e.g. countries) in which the area has been distorted to be proportional to some value (such as population, GNP etc.) (2) Maps of route networks, e.g. the London Underground Map. These maps retain the relative position of each station. They are much easier to read and understand than conventional maps.		Iolines are lines on a map that join points of equal value, e.g. contours on a relief map, isotherms of temperature, isobars of pressure, etc. The interval between the isolines should be consistent and the numerical values should be added to each line. They only work where there is plenty of data spread all over the study area and the changes across space are fairly gradual. They avoid the problems that boundary lines create on choropleth maps.s

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Selecting the right method of presenting data
Your choice of technique will depend on the type of data you have collected and what it is you want to show. Whichever method you use, it should be helpful to get across a message which a table of data would not be able to do as well, be simple to understand, and be drawn clearly. Accuracy, titles, labels, keys, northing arrows, scales, etc. are crucial!

Analysing Data: Statistics

All geographical investigations should involve detailed analysis of the data collected. Statistics can help by taking the analysis one stage beyond that which can ever be achieved with maps and diagrams. Inspecting the data mathematically provides greater precision and may give some information that might otherwise go unnoticed. It should be remembered that using statistics is only an aid to analysis and needs careful planning and interpretation.

Before attempting any statistical analysis, you should be clear what it is that you hope to achieve by using it, and be certain that the data type is appropriate. For your results to have any relevance, your data collection and sample size needs to be sound (put rubbish in, guess what comes out...!) This is why you should plan which statistical test you wish to use early in the planning stages of your project.

For AS geography, you are expected to be familiar with 4 types of statistical technique:

1. Measures of Central Tendancy (to compare and summarise data): mean, median, mode;
2. The Spread of the data: range; inter-quartile range; standard deviation;
3. Test for relationship/correlation/association between two variables: Spearman Rank Correlation Coefficient (Rs);
4. Test for difference/similarity: Mann-Whitney test.
   

1. Measures of Central Tendancy
When there is a lot of data it can be useful to find an average to summarise it, particularly when comparisons between data sets are desirable.

2. The Spread of the Data
The mean, median and mode give a useful summary value for a set of data but give no information about the spread of values around the "average" figure. As such, this summary value can be misleading and give an untrue picture of reality. The spread, or deviation, from a central value can be measured giving a fairer picture about the set of data.

3. Test for Relationship/Correlation/Association
When two things vary together (e.g. land values decreasing with distance from the CBD) there is a correlation, i.e. as one variable changes, there is a change to the other variable.

4. Test for Difference/Similarity

The Enquiry Process for Geographical Investigations (AS)
There are 5 main stages of any geographical investigation:
1. Identification of a question.
2. Development of a strategy to answer the question.
3. Collection of data.
4. Analysis, evaluation and interpretation.
5. Presentation of a summary.

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1. Identification of a question
Before conducting an enquiry, a number of points should be considered:

What are your main interests (e.g. physical or human)?
What angle could your study take (an issue, comparison with theory, etc.)?
How accessible is the study location (dependant on location & number of visits)?
The enquiry should be a small scale study.
The enquiry must be feasible for study: have a rough idea of the data collection and presentation requirements.
Many people identify a few questions before deciding on using just one in their investigation.

2. Developing a strategy
You will only be able to write a quality project if you plan well for it. The strategy is a detailed plan of action required in order to answer the original question. It may include:
A series of sub-divided questions to give the enquiry a clear focus.
An hypothesis (or a few hypotheses) to test through your fieldwork. Reference to text books, journals etc. will give your study some structure.
A list of the data sources that would help the enquiry (primary and secondary).
How easy will it be to collect reliable data in the time scale available?
A risk assessment should be carried out.
Details of the study location with a suitable map should be given.
A plan showing the links between the different stages of the enquiry should be drawn up.

3. Collection of data
Detailed planning can save a lot of wasted time later on and is a crucial part of any enquiry. Before collecting any information, be very clear about the purpose the data will serve, i.e. how will the information help you answer the main question of your enquiry?
Is your data quantitative, qualitative, or both?
What sampling framework should you use to ensure that your data is reliable? Consider sample size and methods. Many studies will use more than one type of sampling strategy. This is often the weakest part of any investigation!
Organise a pilot study and trial run before collecting all your data. Review your work and modify your enquiry if necessary.
Prepare a detailed recording sheet (possibly linked to a spreadsheet).
Consider carefully how you will present your data once you have collected it – this may influence your recording methods.

4. Analysis, evaluation and interpretation.
This is often a significant part of the enquiry and is often divided into three parts:
(i) Data organisation & presentation
Present your data in an organised way so that it is possible to describe patterns and anomalies. Use the most appropriate method(s), not as many as possible.
Attempt to explain the key trends and patterns, preferably with reference to the geographical theory used in sections 1 and 2.
Give suggested reasons for the anomalies.
(ii) Data analysis
Once you have displayed your data graphically, use a statistical technique to probe your results for particular relationships or differences. This will help you answer your geographical question with greater confidence. Any conclusion you later make is likely to be more reliable.
Descriptive statistics give a view of the typical or average situation. Mean, mode and median give quick results. The range and standard deviation may tell you more about the spread of data.
Mann-Whitney U Test can be used to test for differences between two sets of data.
Spearman Rank Correlation test can be used to see if there is a significant relationship between two sets of data.
(iii) Data interpretation & evaluation
This is the stage of any enquiry where you need to find out what your results tell you about the topic you have investigated. It should include the following:
A description of the spatial distribution of the information you have researched referring directly to your data (particularly maps).
A description and attempted explanation of any differences in the numerical data you have collected (e.g. why one area is different from another).
Identification of any relationships that might exist between data.
It is likely that you make several “mini-conclusions” relating to each strand of your investigation. Reference to some geographical theory should be made at this stage.

5. Presenting a summary (conclusion & evaluation of your work)
This is the final stage of any investigation. It is where you should draw together all the themes developed during the analysis section, and arrive at a reasoned judgement. In this section you need to draw together your “mini-conclusions” and use pieces of evidence to arrive at a firm conclusion about the answer to your original question or hypothesis. It is not uncommon to conclude that there is no straightforward answer as long as you then present the evidence to suggest that is the case.
Part of your conclusion should give:
(a) a judgement of the quality of your work by describing clearly those parts of the investigation that went well and gave good quality information.
(b) a description of any reservations about the methods you used and any limitations of the data collected.
(c) suggestions of how you could redesign the project if you were to repeat it and details of any further lines of enquiry that could be followed to improve your study.

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