LESSON NOTES

DATE: ____________________

2.1

DATA ANALYSIS WITH GRAPHS

STATISTICS is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of data. The unprocessed information collected for a study is called raw data. The quantity being measured is the variable. A continuous variable can have any value within a given range, such as the height of students in a class. A discrete variable can have only certain separate values, often integers, such as the number of students in a class.

This section introduces a variety of techniques for displaying data in graphs to help us visualize the characteristics of the data.

EXAMPLE 1 – FREQUENCY TABLES AND DIAGRAMS

The following table shows the age distribution of students at a certain secondary school. Complete the column for the cumulative frequency.

Age

Frequency

12

15

13

25

14

112

15

126

16

102

17

86

18

74

19

12

Cumulative

Frequency

We can show the frequency of the ages using a bar graph or a frequency polygon.

A frequency polygon joins the midpoints of the bars in a bar graph.

120

Where is the greatest proportion of students grouped?

Frequency

Frequency

100

80

60

40

20

12 13 14 15

16 17 18 19 20

Age

We can also graph the cumulative frequency using a polygon.

Cumulative Frequency

500

400

300

200

100

12 13 14 15 16

17 18 19 20

Age

EXAMPLE 2 – RELATIVE FREQUENCY DISTRIBUTION

The following table represents the heights of 50 players on the junior basketball team.

Heights of the Players (cm)

174

161

170

190

152

163

174

182

153

161

175

165

163

172

191

170

159

166

179

170

180

177

187

184

173

167

183

179

182

168

182

185

171

157

181

168

188

191

173

181

153

193

166

178

184

171

177

160

177

182

Complete the following table. Adjust the endpoints for your intervals for a continuous range of values.

Height

Interval

150 – 159

160 – 169

170 – 179

180 – 189

190 – 199

Midpoint

Tallies

Frequency

Relative

Frequency

Relative

Cumulative

Cumulative

Frequency

Frequency

We can show the frequency of the heights using a histogram or a frequency polygon. A histogram is a special form of bar graph in which the bars are connected and represent a continuous range of values.

The frequency polygon joins the midpoints of the histogram.

Are any trends or patterns apparent from the table?

20

Frequency

16

12

What proportion of the players was between 170 and 179 cm?

8

4

150

160

170

180

190

200

Height (cm)

Similarly, the relative and cumulative frequencies can be illustrated.

EXAMPLE 3

Below are a class’ scores on a…