Displaying and Graphing Data

Essentially a dot plot is a one-dimensional scatterplot of observed values of a variable.

In order to create a dot plot one needs to identify the lowest and the highest value of the data
set first, then a horizontal axis is drawn and scaled so that it covers the lowest and highest values.  A dot plot, essentially, is a simple chart where each observation is presented by a dot along the horizontal axis. If there are repeating observations (multiple occurrences), the dots are stacked up vertically. 

The dot plots will produce a simple graph of data but at the same time the data itself is never lost, you can easily identify the value of any data point in the dot plot. This is the most powerful aspect of the dot plots.

It was invented by Tukey (1977) as a method of displaying data.

A stem-and-leaf display is a type of graph for listing the numerical data and very similar to dot plot.  Basically, stem-and-leaf display divides the values into a stem and leaf using a vertical line. The “stem” represents the greatest digits on the left of the line where the right of this line displays the “leaf” with the remaining digits.

This graph can be useful to figure out the range, outliers, the most frequent values and the shape of the data. It is also useful for assessing the location and spread of the distribution of the data.

Bar chart or sometimes called bar graphs are typically used to compare counts, frequencies, total
number of categories, objectives, amounts etc.  Bar chart is the graphical representation of frequencies by rectangles (or bars) with lengths (or heights) proportional to the frequencies of observations. 

Depending on the variable type and grouping, it is possible to create many types of bar chart: Simple bar chart, stacked bar chart, grouped bar chart.

A simple bar chart is used to represent discrete values for each category for a given variable on the x-axis (horizontal). The y-axis (vertical) shows the actual numbers that are the bar heights for the corresponding category. Bars may often be of different colours to distinguish each category. The frequency distribution to be used on a simple bar chart sometimes is called a frequency table where each outcome of the variable and its frequencies are shown.

The stacked bar chart is a bar chart where each bar is divided into subgroups proportional to the contribution a subgroup makes to associated bar. Likert type items are often represented by a stacked bar chart. It helps analyzing the answers concerning to questions coming from a survey

The information about several subgroups of each category can be also shown by a grouped bar chart. It can be plotted in horizontal or vertical directions similar to a simple bar chart. In a grouped bar chart, for each main category, there are different sub-categories.

A histogram is a graph that is very similar to a bar chart except that bar charts are drawn for qualitative data but histograms are drawn for continuous data. Basically you can think histograms as bar plots of grouped frequency distributions. 

To construct a histogram, a number of steps must be followed. If you remember in bar plot, we have rectangular to represent each category, in a histogram, these rectangular are called bins. Basically, the histogram defines the number of values in the bins (classes) separated by breaks. The widths of the bars/bins are, usually, equal and the lengths/heights of the bars are defined by its frequency. There are no gaps between bins. The width of each bin represents the corresponding class interval of the variable. In order to create a histogram of the data, remember, we create the grouped frequency distribution of the data.

The frequency polygons are useful to discover the overall shape of the data (Is it symmetric or is there any asymmetry?). In order to create the frequency polygon, we use the midpoints of the bins (classes) in histogram vs the frequency of each bin. The midpoints are marked by a dot within each class interval. A straight line is used to connect the dots and so that lines are connected to each other.

A pie chart is usually used for categorical data. In pie chart components or outcomes of a total frequency is shown as sectors of a circle. The shape resembles a pie, hence the name of the chart. In pie chart, the categories are divided into slices/sectors. Each slices’ size is proportional to the total number of objects. 

A line chart is often used to display the trends in continuous data over a period of time. Line chart also works well with discrete (ordered) or categorical types of data. The chart is constructed by intersecting the points by lines on the x-axis. Some line charts are used to draw in two or three dimensions.

A scatter plot is used to investigate the relationship between two variables. They are also very helpful indicating the minimum, maximum or outliers of the variables. One of the reasons that the scatter plots may be drawn is that the scatter plot gives a good indication of the correlation between two variables.  In order to show the relationship between two variables, we may use correlation coefficient which measures of the interdependence between two variables. 

To construct a scatter plot, we need two data sets or variables, usually these two data sets or variables are named as X and Y. Once the researcher collects the data about these two variables, all pairwise values in two dimensions are plotted in Cartesian coordinates. The pair of data point for a specific observation, (X,Y), is represented by a dot or a symbol of convenience. The actual numbers are used on the plot, therefore, additional calculations is not necessary unlike pie chart.

Scatter plots have a special type for comparisons so-called the weighted scatter plots. These plots make a comparison of two sets of data easier by specifying one of the data with weights.

For a data set including numbers close to each other may create an illusion. To draw a bar chart of this data on the axis without representing the origin may lead to misunderstanding and creating big differences in numbers. Instead, the usage of a proper scaled axis starting with origin could avoid the false big differences between numbers and make them proper.