This is the fourth in a series of five articles aimed at showing the benefits of presenting tabular data in a graphical format; this considers the use of scatter and line graphs. The article looks at when they should be used, how they are constructed and the benefits that they can provide.
This type of graphical representation of data is mostly used where there is a larger quantity of sample data than that used in previous examples used in this series of articles. However, in order to demonstrate the principles of this chart and assist the reader, the same set of data will be used.
To produce a scatter graph the surveyor could determine the birth date of each of the children surveyed. If they are all in the same class or of the same age, the range of birthdays should be spread over a twelve month period.
In producing the scatter graph the day and month of the child’s birthday should be plotted along the horizontal or ‘x axis’, whilst the height of the child would be plotted along the vertical or ‘y axis’. If the child is a boy the point plotted could be in red and the girls’ could be in yellow. A series of dots will be plotted for each of the 25 children’s heights and from the scatter of the points it should be possible to determine the height of the tallest and shortest child; where their birth date fell within the year being surveyed; whereabouts within the year most children were born; and the different outcomes for the boys and girls. Clearly, if a larger survey sample was taken, then more definite and varied conclusions could be drawn about the spread of the results and how height varied across the age ranges.
This type of graph could use survey data created by averaging the height of a sample of males aged between 6 and 14 years, with preferably the same number of males in each age group.
A typical sample could produce the following results:
Age (years) / Average Height (metres)
6 / 1.18
7 / 1.23
8 / 1.275
9 / 1.33
10 / 1.39
11 / 1.44
12 / 1.485
13 / 1.55
14 / 1.63
This data is best represented using a line graph with the age represented on the horizontal axis and the average height on the vertical axis. A series of points are plotted on a graph for each of the average heights at the appropriate ages. The individual points on the graph are then joined up to their adjacent points only with straight lines, to produce a single line. It is however, sometimes preferable to join points up with the best fitting curved line. Whilst it is appreciated that this data could be represented by a vertical bar chart, a line graph would be more appropriate as the single line shows the rate at which the increase in height was either increasing or decreasing with age, as shown by the gradient of the line between two adjacent age points. From the graph plotted, the rate of growth between 6 and 11 is fairly constant at between 4.5mm to 6mm per year. However, after 12 years old male growth accelerates to about 7.5mm per year. These variations in growth rates are clearly shown on the line graph. One could carry out the same survey for the heights of girls of the same ages, which could be plotted on the same graph as the boys but with a different coloured line to differentiate which results relate to the two survey groups. You would then be able to compare the girls’ growth rates with those of the boys of the same age ranges.
The fifth and final article in this series looks at the use of pie and doughnut charts; when best to use them and how they are constructed.