MATH 311
Statistics and probability: Study Unit 3
LECTURER DETAILS
Frequency distributions and graphical
representation
1.
Frequency distributions of continuous data
2.
Graphical representation of continuous data
3.
Cumulative frequency distributions and polygons
4.
Relative frequencies
5.
Graphical representations of discrete data
Introduction
• Data obtained by observation and measurement usually display
variation
• In order to gain insight in the pattern of variation, we need to order
and graphically represent the data
• A raw data set does not have immediate meaning
Arrays and frequency distributions of data
Know the following concepts:
Array
Frequency
Frequency table
Example p. 36
• Marks of 30 students (ungrouped data)
• Too much to make sense of
• Want to divide in classes/ intervals
• Rule of thumb: Sturge’s rule:
• 𝑘 = 1 + 1,4 ln 𝑛
• 𝑘 is the number of classes (rounded to nearest whole number)
• 𝑛 is the number of observations
Rule to determine class width:
xmax  xmin
c
k
Choose “convenient” class width (decimal make it
“clumsy”
Class width= 10
Number of classes: 7
Example: Histogram
The internet usage of 50 students during a certain week is
represented as follows:
Time spent
Number of
students
Less than 4 hours or [0;4)
2
4 and less than 8 hours or [4;8)
9
8 and less than 12 hours or [8;12) 19
12 and less than 16 hours or [12;
16)
11
16 and less than 20 hours or
[16;20)
6
20 and less than 24 hours or
[20;24)
3
Histogram
Frequency polygon
Frequency polygon
If only the polygon is shown:
Cumulative frequency polygon
Time spent (intervals
frequency
Cumulative frequency
0
0
2
2
9
11
19
30
11
41
6
47
3
50
Example: Cumulative frequency polygon
Relative frequency table
Example: Relative Frequency polygon
Graphical representation of discrete data
• Dot plots
• Pie charts
• Bar charts (different forms)
Dot plots
Divided bar chart
Pie charts
•
•
•
•
Also known as circle graphs
Compare parts to a total
Circular regions are subdivided into pie-shaped sectors
The area of each sector represents the percent of the total population associated
with each category.
© North-West University (2012)