ESSENTIAL MATHEMATICS 1 WEEK 17 NOTES AND EXERCISES Types of Graphs Bar Graphs Bar graphs are used to present and compare data. There are two main types of bar graphs: horizontal and vertical. They are easy to understand, because they consist of rectangular bars that differ in height or length according to their value or frequency. Line Graphs Line graphs are the most popular types of graphs, because they are simple to create and easy to understand. They organize and present data in a clear manner and show relationships between the data. They are used for personal, educational, and professional reasons. Particularly popular in the fields of science and statistics, they can also forecast the results of data that is not yet gathered. While line graphs and bar graphs share the same purpose, line graphs display a change in direction, while bar graphs display a change in magnitude.
Line graphs are used to display the comparison between two variables which are plotted on the horizontal x- and vertical y-axes of a grid. The x-axis usually represents measures of time, while the y-axis usually represents percentage or measures of quantity. Pie Charts Pie charts are easy to make, easy to read, and very popular. They are used to represent categorical data or values of variables. They are basically circles that are divided into segments or categories which reflect the proportion of the variables in relation to the whole. Percentages are used to compare the segments, with the whole being equal to 100%. To make a pie chart, draw a circle with a protractor. Then, convert the measures of the variables into percentages, and divide the circle accordingly. It is best to order the segments clockwise from biggest to smallest, so that the pie chart looks neat and the variable are easy to compare. It is also recommended to write percentage and category labels next to each segment, so that users are not required to refer to the legend each time they want to identify a segment. Exercise Set 1 Q1. For the following questions select from the types of graphs above. a) Grant s marks in five subjects in his yearly examination. b) The change in temperature during the day. c) The number of litres remaining in a car s fuel tank during a trip. d) The lengths of people s arms compared with their heights. e) How Li Chin spends her money each week. f) The amount of money in Li Chin s savings account each week. g) The proportion of each colour of smarties in a packet.
Q2. In the lead-up to the Tidy Towns competition the local high school organises a clean-up day. At the end of the day the items collected are classified and weighed, as shown in this table. Sonia draws a column graph to emphasise the quantities of each type of rubbish collected. Complete the last three columns. Q3. Joseph chooses to use a divided bar chart to illustrate the rubbish composition. He makes the bar 10 cm long and he calculates that the total mass of rubbish is 200 kg. Complete the table of his calculations and then complete his bar graph shown below.
Q4. Jacob presents the rubbish information in a sector graph. Complete Jacob s table and graph. Q5. At an allergy clinic 160 people are tested for their major food allergy. a) What fraction of the people have wheat or flour as their major allergy?
b) As part of a report on the incidence of allergies, Dr Hamilton wants to present this information in a sector graph. Complete this table to calculate the angle required for each sector. c) Dr Hamilton draws this sector graph but she leaves out some of the labels. What labels should be in the sectors P, Q, R, S and T? PP P is Q is R is S is T is
Misleading Graphs We must be careful when drawing graphs that we do not give the wrong impression about the data. Some graphs are deliberately drawn to give a false impression. This can be done by: Not having a scale on the vertical axis Showing only part of the scale or an irregular scale Not showing zero on the vertical scale or only showing a small part of the vertical axis. Using pictures or three-dimensional figures on the graph to exaggerate the differences. Exercise Set 2 In each of the following graphs the data has been distorted in one or more of the ways listed above. Q1. From this graph it appears as if Joe s donuts are much more popular. Is this really the case? Explain. Food Number
Q2. Why does it appear that the interest rate has changed so much on one graph but not the other? Q3. Did Danielle actually score a much better grade than Jared and Alexi on the test? Justify your answer.
Q4. The line graphs show monthly profits of a company from October to March. Which graph suggests that the graph is extremely profitable? Is this a valid conclusion? Explain.