Graphs and Data Presentation
Graphs are simpy a way of presenting data in a way that allows you to see what it shows; graphs help identify patterns and trends in data set, and help conclusions to be drawn from the data collected.
There are a range of different graphs that can be used. The different graphs all highlight different things and are applicable to different types of data, it also useful to display the same data in two different graphical formats to show different patterns and trends.
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Common graphs
- Scatter Graphs
These are the most useful graphs for showing the relationship between two variables that are being investigated and any correlations between them.
The independent variable of the investigation is plotted on the X-axis and the dependent variable is plotted on the Y-axis; the results are then marked on the graph with a cross. A line of best fit is drawn onto the graph, this is a line through the centre of the results with an equal number of points above and below the line.
Scatter graphs clearly highlight a correlation between two variables if it is present, and lots of points can be plotted within a small space. However the line of best fit can suggest a misleading relationship and are not accurate due to the fact they are drawn by eye. Scatter graphs are quick and easy to construct, but are much more useful when a statistical test is applied to the data.
- Line Graphs
Line graphs are most useful for displaying continuous data; they are particularly good for showing changes over time, in this way they can be used to predict future trends and "fill in gaps" where no data is present (however any predictions are only as accurate as the data plotted and the line drawn).
The independent variable (eg time, distance) is plotted on the X-axis and the dependent variable on the Y-axis, and results marked with a cross like scatter graphs. However, unlike scatter graphs, a line is then drawn freehand following th pattern of results and ignoring anomalous results, this line can curve and bend.
The scale of a line graph must be chosen carefully because the scale chosen can alter a graph dramatically. Two different line graphs can also be compared, but they can only be compared accurately if they have the same/similar scales.
There are different types of line graph showing different things:
- Simple
This is a basic line graph that displays one set of data and has only one line.
- Comparative
This shows more than one line on the same axis for comparison.
·Divergent
This is where data is displayed both sides of the X-axis, so positive and negative values are plotted on the same line. They are good for showing variation away from the mean, where the X-axis represents the mean value.
·Compound
This is where the line is split into different factors that make up different proportions of the total area under the graph. They are useful for showing percentages or proportions.
- Bar Graphs (Bar Charts)
These are graphs used to display data that is in categories; they are the simplest presentation of the number of results in a data set. These graphs can only be used to show discrete data, that has distinct intervals between the reults eg 1,2,3 or 1, 1.5, 2, 2.5 etc.
The categories in the data set are plotted on the X-axis underneath the corresponding bar, and the number in that category is plotted on the Y-axis with the bar extending up to the correct number on the X-axis.
The scale must be chosen carefully to ensure that all the data can be plotted on the same graph, and a false origin may be required to do so. When the bars are coloured differently it makes the graph aesthetically pleasing and easier to interpret.
There are also different types of bar graph that show different things:
·Simple
This is the most simple bar graph where only one set of data is plotted; there will be a number of bars from the same data set.
·Comparative
This is where more than one set of data is plotted on the same graph. Above each category on the X-axis there will be more than one bar from different sets of data, this allows comparisons to be made between data sets. For example the total rainfall at different sites over the year, the months would be the different categories on the X-axis and the results from each site the different bars.
·Divergent
This is where the bars diverge above and below the X-axis, or either side of the Y-axis. This shows positive and negative values on the same graph, and they are useful for showing difference from the mean.
·Compound
This is where each bar is divided into different categories. The bars can be different heights, representing different total values and then divided into proportions, or the same height, and divided into percentages.
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Logarithmic Scales
Logarithmic scales are useful for showing a wide range of data on the same graph, which allows comparisons to be made. Logarithmic scales can only be used on line graphs, and are very useful for comparative line graphs where the values of different lines are very different. For example total world population can be plotted on the same graph as the population of Oceania when using logarithmic scales, this allows useful comparisons. They are also very useful for showing rates of change, with a steeper line indicated a faster rate of change in the variable being measured.
However care must be taken when reading values from log graphs as it is easy to make mistakes. These scales can also make data values that are widely different seem similar because they appear close to eachother on the graph. Further disadvatages of the use of these scales is the fact that 0 cannot be plotted; they also place a greater emphasis on smaller values because they give them a larger area on the graph.
Logarithmic scales are very useful in many ways, but their use remains very limited. The introduction of a logarithmic scale to any graph alters the shape of the graph dramatically.
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Triangular Graphs
These are unique garphs that are less common, and generally seen as more complicated, than other graphs. They are useful because they have three axis which means that they can display 3 different variables on the same graph. However the 3 different categories must add up to a total of 100, meaning that these graphs are most widely used to show percentages.
http://www.geographyfieldwork.com/
The graph is always read in a clockwise direction, and any one point will have three values.
For example the graph may be used to show the percentage of people in a country working in the primary, secondary and tertiary sectors of an economy; the values may be 50%, 30% and 20% respectively. The axis on the left hand side of the graph may be labelled as the "Primary Sector" and a mark placed at 50 on the horizontal line extending from this axis. The axis on the right hand side of the graph may be labelled as the "Secondary Sector" and a mark placed at 30 on the line extending diagonally down from this axis. The axis on the bottom may be labelled as the "Tertiary Sector" and a mark placed at 20 on the line extending diagonally upwards from this axis. Where the three points intersect is where the cross is placed. Data from other countries may then be plotted on the graph for comparison.
The main advantages of these graphs are the fact that they can display a large amount of data on one graph, and clusters of poitns clearly highlight points of similar value meaning patterns in the data are clear; in fact it is only when a large amount of data is plotted that trends become visible on the graph. They are most likely to be used in conjuction with, or instead of, pie charts, because they show percentages and proportions. However these graphs are hard to construct and interpret, and only a very limited amount of data can be plotted using this type of graph.
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Radial Diagrams
Radial diagrams are graphs where values extend out from a central point; therefore they show the relationship of each variable to this central point/item.
They are useful because a number of different variables can be plotted on one graph, as more than one axis can be used. However using over four or five different variables can make a diagram quite complicated.
The most common form of this type of graph is a wind rose diagram which shows the frequency of wind direction; the axis represent North, South, East and West and the number on each of the axis is the length of time that the wind was blowing in this direction. Therefore the prevailing wind direction can be easily shown.
Radial Diagrams are most commonly used to show the relationship of a variable to compass direction, ie they are used as directional diagrams, as in the diagram above which shows the relationship of the wind to compass direction. However they can be used to plot a variety of different types of variables.
They are advantageous because trends in the data set are clearly shown, with the variable with the largest value being highlighted on the graph.
The data that is applicable to this method is limited, but data such as compass direction would be hard to present in any other way. It can also be hard to read exact values from the scale on the axis, as it often makes the diagram too crowded to include the scale; data also often has a wide range of values when plotting a number of difffrent variables, meaning that it can be hard to find a suitable scale to use.
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Pie Charts
The data must first be converted into percentages before it can be plotted onto a pie chart diagram. These percentages are then coverted into a proportion of 360 (ie the total number of degrees in a circle), this is done by multiplying the percentage values by 3.6. Remember we need to plot the percentage values that we have as a proportion of the circle, say we have a value of 13.5% we need to find out how may degrees 13.5% of 360 is. We divide 360 by 100 to find what 1% is (ie 3.6) and then multiply it by the percentage we have. This then gives us the number of degree of the circle that the category takes up, which can be plotted using a protractor.
Pie charts are useful for making comparisons in the values of different categories, when using one diagram, as well as comparing different data sets, by using more than one diagram; however it is hard to compare a lot of diagrams that are divided several times. Pie charts generally don't tend to show exact figures, unless they are written on the diagram after the pie chart is constructed, meaning it can be hard to make detailed comparisons and quote actual figures.
Proportionally Divided Circles
Both type of diagram must be large enough for the proportions of different categories to be clear and visible, small diagrams are very hard to interpret.
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Kite Diagrams
These are again more uncommon diagrams due to the limited amount of data that can be plotted using them.
Kite diagrams have two axis, and in a way are similar to bar graphs. The X-axis has one or more categories and the Y-axis the measurement sites. These graphs are most commonly used to show plant succession, with different plants forming the different categories on the X-axis. A central line is drawn up the graph from each category on the X-axis, and at each measurement site the percentage cover of each plant is plotted. However the value is divided into two, with half of the result being plotted one side of the line and half the other side of the line, thus creating a kite shape. If there was none of a particular plant present then a cross is simply marked on the line to represent 0% cover at this site. In this manner kite diagrams are divergent diagrams, as the values diverge from a central line.
An example Diagram (this simply swaps the axis around which shows just the same thing but horizontally):
http://www.geography-fieldwork.org/
These diagrams are harder to construct but generally easy to interpret, and clearly show patterns of change and allow a number of different data sets to be plotted on the same graph. They are most useful for showing a change over distance, such as plant succession; however they have a very limited use, and I have only ever seen them used to show succession.
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