Statistical graphs and charts for data visualization
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¶ … real life example, we would compare the quarterly sales over 4 years. For this the following values would be made
Line Graphs
Pie Charts
Colum Chart
Scatter Charts
Misleading charts and graphs
Graphs and charts are tools for statistical analysis of data and information. Graphs and charts help identify and illustrate in a meaningful manner, the trends and details of the data.
Sometimes, data or information involves very large volume of data and would be too cumbersome to get them printed or to make non-technical people understand the trends and details of the data. On such occasions, using graphs and charts to represent the data in a simple and understandable manner is useful (Bhaduri and Ghosh, 2014).
Therefore it can be said that a graph or a chart shows thousands of information in a picture and help convey information quickly and easily to the user. The salient features of the data are highlighted by graphs and charts. Often relationships between various sets of data cannot easily be related. Graphs and charts helps relate and compare such data sets.
Graphs and charts therefore help to convey to the users comparisons and relationships, distribution, trends, composition, flow and/or process and location that are sought to be obtained from a data set.
Easy-to-understand formats that clearly and effectively communicate important points is enabled by graphs and charts by the condensation of large amounts of information.
The selection of the type of chart or graph to be used, the purpose of the graph or chart needs to be considered in terms of what one wants to present. For example, one could choose between expressing certain data set in the form of frequencies, percentages or categories.
Also the type of data that one is working with needs to be considered while selecting the chart or graph type.
While categorical data are grouped into non-overlapping categories such as grade, race, and yes or no responses, this can be represented by bar graphs, line graphs and pie charts. On the other hand continuous data are measured on a scale or continuum like such as weight or test scores which can be best represented through tools like histograms (Dehmer and Emmert-Streib, n.d.).
In this question we would discuss the types of charts and graphs that can be used for quantitative analysis.
There are also several types of quantitative data such as:
Discrete Data -- this is data that has distinct values or observations like 5 customers, 17 points, 12 steps etc.
Continuous Data -- this type of data is represents any value or observation within a finite or infinite interval like conversion rate, visits, page views, bounce rate, height, weight etc. (Forsyth, 2013).
Quantitative data can be summarized through mean, median, mode, standard deviation etc. And for this column chart, bar chart, line chart, Histogram etc. can be used.
In this question we would look into the usefulness of bar and line graphs and pie charts, column charts and scatter charts for analysis of quantitative data.
Types of Graph
Bar Graphs
Direct comparison of two or more sets of data is done by the use of bra graphs. This is used when the number of time intervals is small and when there is time series data.
Such graphs generally tend to have 0 as the baseline if all values are positive integers. Zero would be the midpoint of the scale in cases where the values include both positive and negative integers such as in the case of graphing differences in means.
However the scale ranges should not vary between graphs and should be standardized whenever possible. It is best not to use 3-D features in a bar graph as such graphs are complex in nature and makes them ineffective in conveying results to most audiences. It also leads to distortion of data.
Both horizontal and vertical bars can be included in bar graphs. But horizontal bar charts are rarely used to portray time series. In order to have the maximum effect of comparison of data and information in a bar graph, the columns should be sorted in some systematic order, most often according to size of value, to have visually effective schema.
The standardized grade scale is used to order findings by a particular category. Without the presence of a standard base line, stacked bar graphs that are composed of one or more segmented bars where each one of the segment represents the relative share of a total category, are not very effective in conveying data and for comparison especially in among the second, third or subsequent segments (Hsin-Yi Tsai, Yu-Lun Huang and Wagner, 2009).
It is preferable to create a bar graph that groups these values together, side by side when the graphing data from two or more different series, or different classes within the same series.
Taking a real life example, we would compare the quarterly sales over 4 years. For this the following values would be made:
The Revenue in dollars would be placed along one axis.
The time i.e. quarter number, would be plotted along another axis.
There are four categories: Q1, Q2, Q3 and Q4.
Each category will have 4 columns for years say 2006 through 2009
The data for the graph would be:
2011
2012
2013
2014
Q1
25
58
45
65
Q2
89
Q3
75
89
83
90
Q4
The resultant Bar graph would be as follows:
Line Graphs
Most often time series data is displayed by line graphs. Line graphs are more effective in presenting five or more data points when in comparison to bar graphs but do not turn out to be much effective in cases where the period of time is less and there is less emphasis on the identification of the differences.
For plotting time series online graphs, the categories should be placed on the x-axis or the horizontal axis such as the week, months, years -- depending on the data and the frequencies of data that is to be measured on the y axis or the vertical axis.
An example of a line graph can be had for representing the population trend of a country over a period of 11 years. In this graph we would plot the time in years along the X- axis and the total population of the country would be plotted along the Y-axis. There would a large number of data points or categories. A line chart is chosen to represent the above mentioned data as the number of data points is very high and a column or bar chart will look pretty cluttered and would not be able to clearly identify a trend or even fit on a computer screen or an average page. The attempt in using the line graph is to show the trend and not to show the maximum or the minimum population. The aim is to show the rate of population growth or decline or change of population which would be denoted by the steepness of the graph line instead of the actual population. Therefore to visualize trend-based data, a line chart is best suited (Hudak and Duplacey, 2008).
The data to be presented on a line chart are as below:
Year (to be plotted on X-axis)
Population (in millions) to be plotted on y-axis
2004
75
2005
80
2006
83
2007
78
2008
90
2009
92
2010
2011
2012
2013
2014
The line graph for the above data is represented a below. Here the blue line represents the change in population in a country over a period of 11 years. A user can easily get an idea about how the population of a country has changed over the 11-year period without actually requiring to know the exact population of the country at any year.
Graphs that have more than four or five lines tend is often confusing to decipher by the user unless the lines are well separated. In such cases it is the norm that, different line styles like solid line, dashed line, etc. And different colors and/or plotting symbols like asterisks, circles, etc. are used to separately identify the lines representing various data in a single graph for comparison.
If we add more values to the table above to denote the male and female population in every year of the 11-year period, the table would look as below:
Year
Population (in millions)
Male (in millions)
Female (in millions)
2004
75
35
40
2005
80
38
42
2006
83
38
45
2007
78
33
45
2008
90
42
48
2009
92
43
49
2010
47
53
2011
49
56
2012
52
58
2013
55
61
2014
57
62
Types of charts
In this section we would discuss the three types of charts that can be used for evaluation and representation of quantitative data.
Pie Charts
Though pie charts are good to view and easy to understand, the generally have limited utility. The charts are used to show parts of a whole where the whole is considered to be 100% and all the parts add up together to make 100.
While pie charts do not make small differences apparent, they are able to emphasize general findings. Generally it is advised that the pie charts should not consist of more than five or six slices and should be used to represent categorical data with a relatively small number of values (Hudak and Duplacey, 2008).
As with bar graphs, pie charts should avoid the use of 3-D features or break out of the pieces as such graphs makes it difficult to compare the relative size of the slices. The category labels should always be included in pie charts so that users can relate a slice with the category that it represents. It is also advised that the category labels should be placed directly on the pie slices for clarity and easy comprehension. For better understanding of the pie charts, value labels should be included in the charts that indicate the percentage of the pie represented by a given slice.
To differentiate various sizes of pie charts different colors for different categories is easier to identify and differentiate. Pie graphs are best suited to represent and compare just one category of data and should not be used to represent more than one category for clarity and easy understanding (Schmuller, 2013).
For practical application of a pie chart we would represent the percentage composition of the types of vehicles that ply in a city on an average day.
Category
% of total vehicle
Cars
32
Bikes
28
Lorry
15
Three wheelers
5
Bicycles
8
Walkers
12
A pie chart representing this data would look as below:
Experts of statistics advise that pie charts should essentially be used when there are no more than 6 categories and when there is this one category that clearly has values more than the rest and it is necessary to highlight that category. Pie charts are also useful in cases where two or more categories have almost the same values and for cases where there is need to sum up a couple or more categories and then compare them to another sum.
Scatter Charts
In this form of chart, the data can be plotted in a xy or scatter chart when such data is arranged in columns and rows on a worksheet. The relationships among the numeric values in several data series is shown in scatter charts as well as enable the plotting of two groups of numbers as one series of xy coordinates.
There are two value axes in a scatter chart which plots one set of numeric data along the horizontal axis or the x-axis and another set of numerical data along the vertical axis or the y-axis. The result of the data along the two axis are displayed in irregular intervals, or clusters as the chart combines both the sets of numerical values into single data points.
Numeric values, such as scientific, statistical, and engineering data is best displayed and compared by the use of scatter charts.
A scatter chart is best suited to be used when the scale of the horizontal axis is required to be changed or when the same axis a logarithmic scale. This is also useful for comparison whet the values for horizontal axis are not evenly space and in cased where there are many data points on the horizontal axis.
In practical use, scatter charts are used to effectively display worksheet data that includes pairs or grouped sets of values and more information is revealed about the grouped values by adjusting the independent scales of a scatter chart. It is used by experts to show similarities, rather than differences between large sets of data and when it is necessary to compare many data points without concern about time. This is because the comparisons in a scatter chart become better when more data is included in a scatter chart. On a worksheet to be prepared for a scatter chart, the x values are placed in one row or column and the corresponding y values in the adjacent rows or columns (Stephens, 2006).
For exhibiting the practical utility of a scatter chart we consider the situation of comparing the variation of rainfall with temperature. In this case, both the parameters are depends on another where the for every temperature value in degree centigrade ( C ), there would be a corresponding rainfall value in millimeters (mm)
The table for the Scatter chart to plot rainfall at a particular temperature is given below:
Temperature ( C)
Rainfall (mm)
25
2.7
28
3.2
27
0.8
30
1.3
32
2.5
35
6.6
27
5
38
3.2
40
2.7
41
5.5
35
4.6
40
2.8
28
5.1
32
7.6
Using the above data, a scatter is prepared as shown below:
Misleading charts and graphs
Misleading charts and graphs are primarily those that do not show the actual data representation. Misleading graphs and charts can be due to misleading data collection process or misinterpretation of data or misrepresentation and mis-visualization of the graph or chart. A misleading graph or chart can thus be both unintentional or due to lack of expertise in collecting and interpreting data or intentional -- with the intention of creating a false sense of belief from the graph or chart.
As a practical example, we take the case of a misleading representation of data in a 3-D pie chart. 3-D pie charts looks attractive and aesthetical but it can also be misleading to a great extent. Given below is an example of misrepresentation of the pie chart drawn earlier in the study.
We take the same values as taken for the earlier pie chart.
Category
% of total vehicle
Cars
32
Bikes
28
Lorry
15
Three wheelers
5
Bicycles
8
Walkers
12
Now we plot a 3-D pie chart to represent the data.
From the above pie chart, it seems that the green portion and the blue portion are almost equal. This 3-D graph looks quite good and is aesthetically pleasing to view. However this is a complete misrepresentation of the actual facts. The actual value of the green slice us is nearly half as that of the blue slice.
Conclusion
Form the above discussions it is clear that every data can be represented in the form of graphs and charts. Graphs and charts show data in a presentable and readable form that is easy to understand for the people. Quantitative data can be represented through a number of graphs and charts. However there can also be misrepresentations of charts and graphs that can result from intentional conduct or lack of expertise in categorizing or reading data.
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