DATA ANALYSIS
(with GRAPHS)
Statistics is the gathering, organization, analysis,
and presentation of numerical information in an
understandable form.
Trends in a set of data and an overview of the distribution
of the values in a data set can be seen using frequency
tables and frequency diagrams.
Data may be organized and presented using frequency
diagrams such as the circle graph, bar graph, histogram,
or frequency polygon.
TERMINOLOGY
raw data:
the unprocessed information collected for a study
variable:
the quantity being measured
continuous
variables:
values in a given range ex. height, weight, temperature
discrete
variables:
specific or separate values ex. integers, colours
histogram:
a special form of the bar graph in which the areas of the
bars are proportional to the frequencies of the values of
the variable; the bars are connected
Bar graphs are used to display the data of discrete variables.
Histograms are used to display the data of continuous variables.
cumulative
frequency
graph:
shows the running total of the frequencies from the
lowest value up (also called an ogive)
FREQUENCY GRAPHS
(Examples)
HISTOGRAM
(continuous variables)
BAR GRAPH
(discrete variables)
FREQUENCY POLYGON
CUMULATIVE-FREQUENCY GRAPH
Example 
174
177
166
159
The heights of the girls in a physical education class,
measured to the nearest centimetre, are given below:
175
185
190
173
180
193
172
181
182
170
184
184
153
163
157
163
161
187
178
170
165
171
152
167
a) Use a frequency table to organize this data.
NOTE: heights range from shortest ________ to tallest ________
Height Intervals
150
160
170
180
190
–
–
–
–
–
159
169
179
189
199
Tallies
Frequency
cm
cm
cm
cm
cm
b) Describe any trends apparent from the organization of the data in
the above table.
c) Use a graph to display the information in the frequency table.
NOTE: continuous variable – use a histogram
GIRL’S PHYS. ED CLASS HEIGHTS
FREQUENCY
11 10 9 8 7 6 5 4 3 2 1 -
‘
140
‘
150
‘
160
‘
170
‘
180
‘
190
‘
200
‘
210
HEIGHT (cm)
The frequency polygon can be superimposed onto the histogram.
d)
Create a cumulative frequency column on the frequency table and
produce a cumulative frequency polygon.
Height Intervals
150
160
170
180
190
–
–
–
–
–
159
169
179
189
199
Frequency
Cumulative
Frequency
cm
cm
cm
cm
cm
Recall…cumulative frequency is a “running total”.
GIRL’S PHYS. ED CLASS HEIGHTS
30 25 CUMULATIVE
FREQUENCY
20 15 10 5
‘
140
‘
150
‘
160
‘
170
‘
180
‘
190
‘
200
‘
210
HEIGHT (cm)
How many girls have a height of 179 cm or less? ____________
e)
Create a relative frequency column on the frequency table and
produce a relative frequency polygon.
Height Intervals
Frequency
Relative
Frequency
150 – 159 cm
160 – 169 cm
170 – 179 cm
180 – 189 cm
190 – 199 cm
TOTAL:
NOTE:
relative frequency =
frequency
total
Relative frequency shows the frequency of a data
group as a fraction or percent of the whole group.
GIRL’S PHYS. ED CLASS HEIGHTS
0.4 -
RELATIVE
FREQUENCY
0.3 0.2 0.1 ‘
140
‘
150
‘
160
‘
170
‘
180
‘
190
‘
200
‘
210
HEIGHT (cm)
How does the relative frequency polygon compare to the frequency
polygon? ______________________________________________