Tables, graphs, maps and central tendency

FOCUS QUESTIONS

What is central tendency? How is central tendency measured? How is data interpreted? What are pie charts, bar charts, histograms and line graphs?

A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.

Measures of central tendency are the centre values of a data set. They are also classed as summary statistics. Mean is the average of all the data.

To calculate the mean :

Add the numbers and divide the total by the number of numbers.

Mode is the data value appearing most often in the data set.

There can be more than one mode. Median is the middle value of the data set, arranged in ascending order. The median is the middle number.

You need to write the numbers in order.

To find the median number:

Put all the numbers in numerical order.

If there is an odd number of results, the median is the middle number.

If there is an even number of results, the median will be the mean of the two central numbers.

Under different conditions, some measures of central tendency become more appropriate to use than others.

INTERPRETATION OF DATA

All the information collected during research is generically named ‘data’. A set of individual data makes it possible to perform statistical analysis.

Data is collected during field work; researchers collect information by means of questions, systematic observations and imaging.

Variables are constituted by data. Variables are characteristics or attributes that:

Can be measured.

Assume different values, such as sex, age of the individuals under study. etc.

Variables are specifically divided into two large groups.

(a) The group of categorical or qualitative variables.

CATEGORICAL VARIABLES

i. Dichotomous variables, also known as binary variables, are those that have only two categories, i.e., only two response options. Typical examples of this type of variable are sex (male and female) and presence of skin cancer (yes or no).

ii. Ordinal variables are those that have three or more categories with an obvious ordering of the categories (whether in an ascending or descending order).

iii. Nominal variables are those that have three or more categories with no apparent ordering of the categories. Example: blood types A, B, AB, and O, or brown, blue or green eye colours.

(b) The group of numerical or quantitative variables.

NUMERICAL VARIABLES

i. Discrete variables are observations that can only take certain numerical values. An example of this type of variable is subjects’ age when assessed in complete years of life (1 year, 2 years, 3 years, 4 years, etc,) and the number of times a set of patients visited the dermatologist in a year.

ii. Continuous variables are those measured on a continuous scale, i.e., which have as many decimal places as the measuring instrument can record. For example, blood pressure, birth weight, height, or even age, when measured on a continuous scale.

PRESENTATION OF CATEGORICAL VARIABLES

First, it is worth emphasising that every table or graph should be self-explanatory, i.e., should be understandable without the need to read the text that refers to it.

PLEASE NOTE

It is important to point out that, depending on the objectives of the study, data may be collected as discrete or continuous variables, and be subsequently transformed into categorical variables to suit the purpose of the research and/or make interpretation easier. However, it is important to emphasise that variables measured on a numerical scale (whether discrete or continuous) are richer in information and should be preferred for statistical analyses.

PRESENTATION OF NUMERICAL VARIABLES

Frequency distributions of numerical variables can be displayed in a table, a histogram chart, or a frequency polygon chart.

BASIC RULES FOR THE PREPARATION OF TABLES AND GRAPHS

It is important to note that every table should:

Be self-explanatory.

Present values with the same number of decimal places in all its cells (standardisation).

Include a title informing what is being described and where, as well as the number of observations (N) and when data were collected.

Have a structure formed by three horizontal lines, defining table heading and the end of the table at its lower border.

Not have vertical lines at its lateral borders.

Provide additional information in table footer, when needed.

Be inserted into a document only after being mentioned in the text.

Be numbered by Arabic numerals.

Similarly to tables, graphs should:

Include, below the figure, a title providing all relevant information. Be referred to as figures in the text. Identify figure axes by the variables under analysis.

Quote the source which provided the data, if required. Demonstrate the scale being used. Be self-explanatory.

The graph’s vertical axis should always start with zero.

So, in general:

Ensure that the tables and figures in your research manuscript are self-explanatory and can be understood independent of text.

Do not repeat the contents of your tables and figures within the text. Instead, use the text to focus on the significance or key points of your tables and figures.

Present values and details consistently in tables and text (e.g., abbreviations, group names, treatment names).

Write clear, informative titles for your tables and figures, and label column heads, axis labels, figure labels, etc, clearly and appropriately.

Please Note: Well-prepared tables and figures in a research paper help you present complex data in a concise and visually appealing manner, as well as enable reviewers, examiners, and later readers to get a quick overview of your research findings.

READING DATA FROM TABLES

Tables are used as a way of describing what you are talking about in a structured format. They tend to be used to present figures, either as a summary or as a starting point for discussion. Tables are also probably the most common way of presenting data.

Tables have always been compiled by someone. In doing so, the compiler may have selected data and will have chosen a particular format, either of which may influence the reader.

INTERPRETING PERCENTAGES

Many research give information in the form of percentages.

In such research, tables and other numerical information are also often

presented in terms of percentages.

Percentages are used so often because they enable comparisons to be made more readily.

Every percentage is expressing a value as a fraction (that is, as a proportion) of a hundred. ‘Per cent’ is denoted by % and means ‘out of a hundred’, so 75% means 75 out of 100.

PIE CHARTS, BAR CHARTS, HISTOGRAMS AND LINE GRAPHS

These are all different ways of representing data and you are likely to be familiar with some, if not all of them. They usually provide a quick summary that gives you a visual image of the data being presented.

PIE CHARTS

A pie chart is a diagram in the form of a circle, with proportions of the circle clearly marked.

A pie chart is a good method of representation if we wish to compare a part of a group with the whole group. It gives an immediate idea of the relative sizes of the respondents.

BAR CHARTS

Bar charts show:

Data in the form of bars that illustrate the relationship between the items of information in terms of size; the bars get larger (generally taller) as the amounts being shown increase.

When the bars touch, they show continuous data. In other words, data that changes gradually along some sort of a scale, for example weight, height, temperature, or length (these charts are called histograms). When the bars are separate, they show discrete data. This is data that changes in whole units, such as the number of eggs, children, cars being produced.

HISTOGRAMS

Histograms are a special form of bar chart in which the bars usually touch each other, because histograms always show data collected into ‘groups’ along a continuous scale.

They tend to be used when it’s hard to see patterns in data; for example, when there are only a few variables, or the actual amounts are spread over a wide range.

LINE GRAPHS

Line graphs are most suitable when just comparing one value as it changes with another value.

They are less suitable when wanting to look at several things at once; for example, to study changes in oil prices and supermarket profits on petrol sales, the scales on the left- and right-hand sides of a graph would have to be different, and this can be very misleading. However, you can see this quite often in line graphs.

The next lesson will be on interpretation of data on bar graphs (including population pyramids), climate graphs, choropleth maps and isopleth maps.