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