GRAPHS AND CHARTS

1. Introduction

Generally speaking, DATA refers to facts that are gathered in some way, and which constitute a body of information. In order to be useful, data must not only be organized, but it should also be able to be represented in some way that comparisons, trends and or relationships may easily be visualized. Graphs and charts provide such representations. There are a wide number of types of graphs and charts, but the most common ones are line graphs, bar graphs, pie charts and histograms.

2. Line graphs

Line graphs connect data points that are somehow related. For example, a mother may measure the height of her child every year on that child's birthday. The age of the child and her height are data that are clearly related, whereas measurements of any child at any time would not be particularly meaningful. In our example, the mother's data has been entered in a table, shown here on the right. Each pair of values in the table, for example, the height (105 cm) at age 5, represents a DATA POINT.

These data point may be entered in a graph. The horizontal line is called the HORIZONTAL AXIS, and the vertical line is called the VERTICAL AXIS. Once the data points have been entered, the points may be connected by a line. The resulting line graph is shown here below on the left. The graph immediately suggests that the child undergoes a regular growth between the ages of 1 and 8. It also allows us to have a reasonable estimate of what the height of the child was at an intermediate age, say 4.5 years, when the height, read from the graph, would have been about 102 cm.


In mathematics, line graphs are routinely used to display the relationship between two variables such as x and y. The INDEPENDENT VARIABLE, x, is plotted along the horizontal axis, while the DEPENDENT VARIABLE, y (the value of y DEPENDS on the value of x) is plotted along the vertical axis. The graph above on the left shows how the value of y changes with x according to the equation y = x2 - 3x -1 over the range -2 ≤ x ≤ 7.5.

3. Bar graphs

Bar graphs are commonly used to depict the relationship between two or more series of data points. For example, the total rainfall for every month for three consecutive years in Fish Hoek was measured and tabulated. The results are shown above on the left. Using the data to construct a bar graph, the height of a bar represents the millimeters of rain that fell in a given month for each of the three years 2008-2010. By putting the bars side by side in different colours, we obtain the vertical bar graph shown above on the right. At a glance, we see observe that Fish Hoek lies in a winter rainfall area and that November 2009 was an unusually wet month, while July 2010 was unusually dry. Note that when a bar graph is plotted, a legend should be included in order to relate the colours of the bars to some series of data, the year in this case.

4. Pie charts

Pie charts are useful to show the proportion of certain types of data as parts of a whole. The "pie" represents the whole, and the segments of the pie represent the proportion of various data points to that whole. For an example, let us take a school tuckshop that is making an analysis of its sales. In a given week, it solds goods to a total of R13 414. The amounts collected for each category of items are tabulated, and the percentage contribution of each class of items worked out. The resultant pie chart is shown above on the right.

5. Histograms

Histograms display distibutions of data. Imagine a class of 26 students who have written a maths test. The score are arranged in data ranges 0-9, 10-19, and so on. Against these, the number of learners whose scores fall within these ranges are tabulated as shown in the table above on the left. A bar graph is then drawn, with the count of learners whose scores fall in each range, as shown above on the right. Histograms can be treated statistically, which is outside the scope of this topic, and can tell us much about, for example, the validity of the maths test.