0702-Data Presentation as Diagrams

Lecture for Yr1 Sem 2 PPSD Session on Wednesday 7th February by Professor Omar Hasan Kasule Sr.


Data grouping summarizes data but leads to loss of information due to grouping errors. The suitable number of classes is 10-20. The bigger the class interval, the bigger the grouping error. Classes should be mutually exclusive, of equal width, and cover all the data. The upper and lower class limits can be true or approximate. The approximate limits are easier to tabulate. Data can be dichotomous (2 groups), trichotomous (3 groups) or polychotomous (>3 groups).



Tabulation summarizes data in logical groupings for easy visual inspection. A table shows cell frequency (cell number), cell number as a percentage of the overall total (cell %), cell number as a row percentage (row%), cell number as a column percentage (column %), cumulative frequency, cumulative frequency%, relative (proportional) frequency, and relative frequency %. Ideal tables are simple, easy to read, correctly scaled, titled, labeled, self explanatory, with marginal and overall totals. The commonest table is the 2 x 2 contingency table. Other configurations are the 2 x k table and the r x c table.



Diagrams present data visually. An ideal diagram is self-explanatory, simple, not crowded, of appropriate size, and emphasizes data and not graphics.


The 1-way bar diagram, the stem and leaf, the pie chart, and a map are diagrams showing only 1 variable.


A bar diagram uses ‘bars’ to indicate frequency and is classified as a bar chart, a histogram, or a vertical line graph. The bar chart, with spaces between bars, and the line graph, with vertical lines instead of bars, are used for discrete, nominal or ordinal data. The histogram, with no spaces between bars, is used for continuous data. The area of the bar and not its height is proportional to frequency. If the class intervals are equal, the height of the bar is proportional to frequency. The bar diagram is intuitive for the non specialist.


The stem and leaf diagram shows actual numerical values with the aid of a key and not their representation as bars. It has equal class intervals, shows the shape of the distribution with easy identification of the minimum value, maximum value, and modal class.


The pie chart (pie diagram) shows relative frequency % converted into angles of a circle (called sector angle). The area of each sector is proportional to the frequency. Several pie charts make a doughnut chart.


Values of one variable can be indicated on a map by use of different shading, cross-hatching, dotting, and colors.


A pictogram shows pictures of the variable being measured as used instead of bars. A pictogram shows pictures of the variable being measured as used instead of bars.



Two variables can be shown on line graphs, dot plots, time series plots, 2-way bar charts, box plots, scatter diagrams (scatter-grams), and pictograms.


More than 2 variables can be shown on  scatter plots with varying dot sizes, scatter plot matrices, multiple time series plots, stacked bar charts, divided bar charts, overlay bar charts, and multiway bar charts.


Use of different colors helps clarity.


A line graph is produced when frequency is plotted against the class interval midpoint. Joining the points by straight lines produces a frequency polygon and joining them with a smoothed line produces a frequency curve. A line graph shows cumulative frequency, cumulative frequency %, moving averages, time series, trends (cyclic and non-cyclic), medians, quartiles, and percentiles. Plotting the line graph with the y-axis in logarithmic units and the x-axis as arithmetic units enables representation of a wider variation than with a linear scale.


A dot plot uses dots instead of bars.


A time series plot is a graph of the value of a variable against time.


A 2-way, 3-way, or even 4-way bar diagram, constructed using computer graphics,


The scatter diagram is also called the x-y scatter or the scatter plot.



Bar diagrams and line graphs are distributions.


The unimodal shape is the commonest shape. The 2 humps of the bimodal need not be equal. More than 2 peaks is unusual.


 A perfectly symmetrical distribution is bell-shaped and is centered on the mean. Skew to right (+ve skew) is more common than skew to the left (-ve skew).


Leptokurtosis is a narrow sharp peak. Platykurtosis is a wide flat hump.


The common shapes are the normal, the s-curve (ogive), the reverse J-curve (exponential), and the uniform.


Diagrams can be misleading due to poor labeling, inappropriate scaling, omitting the zero origin, presence of outliers, and presence of high leverage points, or using a wrong model (linear vs quadratic). Widening and narrowing the scales produces different impressions of the data. Double vertical scales can misleadingly be used to show spurious associations. Omitting zero misleads unless broken line are used to show discontinuity.

ŠProfessor Omar Hasan Kasule, Sr. February 2007