Chapter 2
Presenting Data in Charts and Tables
Why use charts and graphs?
Visually present information that can’t easily
be read from a data table.
Many details can be shown in a small area.
Readers can see immediately major
similarities and differences without having to
compare and interpret figures.
Computer software can be used to create charts
and graphs:
SPSS
MINITAB
Ms. Excel
Ms. Visio
Others
How to present categorical data?
Categorical
data
Tabulating
data
Summary
table
Graphing
data
Bar charts
Pie charts
Bar chart
 Bar chart and pie chart are often used for
quantitative data(categorical data)
 Height of bar chart shows the frequency for
each category
 Bar graphs compare the values of different
items in specific categories or t discrete point
in time.
Bar chart example:
Populaton by urban and rural in Cambodia
45,000
40,000
35,000
30,000
2004
25,000
2007
20,000
2008
2009
15,000
10,000
5,000
0
Rural
Urban
Pie chart
 The size of pie slice shows the percentage for
each category
 It is suitable for illustrating percentage
distributions of qualitative data
 It displays the contribution of each value to a
total
 It should not contain too many sectorsmaximum 5 or 6
Pie char example:
Table example:
How to present numerical data?
Numerical
data
Ordered
array
Stem-andLeaf
Frequency
Distribution
Histogram
Polygon
Cumulative
Distributions
Ogive
The ordered array
The sequence of data in rank order:
 Shows range (min to max)
 Provides some signals about variability within the
range
 Outliers can be identified
 It is useful for small data set
Example:
Data in raw form: 23 12 32 567 45 34 32 12
Data in ordered array:12 12 23 32 32 34 45 567
(min to max)
Tabulating Numerical Data:
Frequency Distribution
 A frequency distribution is a list or a table….
 It contains class groups and
 The corresponding frequencies with which data fall within
each group or category
Why use a Frequency Distribution?
 To summarize numerical data
 To condense the raw data into a more useful form
 To visualize interpretation of data quickly
Organizing data set into a table of frequency
distribution:
Determine the number of classes
The number of classes can be determined by
using the formula: 2k>n
-k is the number of classes
-n is the number of data points
Example:
Prices of laptops sold last month at PSC:
299, 336, 450, 480, 520, 570, 650, 680, 720
765, 800, 850, 900, 920, 990, 1050, 1300, 1500
In this example, the number of data points is
n=18.
If we try k=4 which means we would use 4
classes, then 24=16 that is less than 18. So the
recommended number of classes is 5.
Determine the class interval or width
-The class interval should be the same for all
classes
-Class boundaries never overlap
-The class interval can be expressed in a formula:
Where i is the class interval, H is the highest value in the data set, L is the lowest
value in the data set, and k is the number of classes.
In the example above, H is 1500 and L is 299. So the class
interval can be at least
=240.2. The class
interval used in this data set is 250
 Determine class boundaries: 260 510 760 1010 1260 1510
 Tally the laptop selling prices into the classes:
Classes:
260 up to 510
510 up to 760
760 up to 1010
1010 up to 1260
1260 up to 1510
 Compute class midpoints: 385 635 885 1135 1385
(midpoint=(Lower bound+ Upper bound)/2)
 Count the number of items in each class. The
number of items observed in each class is called
the class frequency:
Laptop selling
Frequency Cumulative Freq.
price9($)
260 up to 510
510 up to 760
760 up to 1010
1010 up to 1260
1260 up to 1510
4
4
5
6
1
2
9
15
16
18
Step-and-leaf
A statistical technique to present a set of data.
Each numerical value is divided in two parts—
stem(leading digits), and leaf(trailing digit)
The steps are located along the y-axis, and the
leaf along the x-axis.
Stem
29
33
45
48
52
57
65
68
72
76
80
85
90
92
99
105
130
150
Leaf
9
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Histogram
A graph of the data in a frequency distribution
It uses adjoining columns to represent the
number of observations(frequency) for each
class interval in the distribution
The area of each column is proportional to the
number of observations in that interval
Example of histogram:
How can you construct the histogram in SPSS?
Polygon
A frequency polygon, like a histogram, is the
graph of a frequency distribution
In a frequency polygon, we mark the number
observations within an interval with a single
point placed at the midpoint of the interval,
and then connect each set of points with a
straight line.
Polygon example:
How can you construct the polygon in SPSS?
Ogive—a graph of cumulative frequency
Ogive example:
How can you construct the Ogive in SPSS?
Exercises
1. The price-earnings ratios for 24 stocks in the
retail store are:
8.2
9.7 9.4 8.7 11.3 12.8
9.2
11.8 10.8 10.3 9.5 12.6
8.8 8.6 10.6 12.8 11.6 9.1
10.4 12.1 11.5 9.9 11.1 12.5
a. Organize this data set into step-and-leaf
display
b. How many values are less than 10.0?
c. What are the smallest and largest values
Exercises
2. The following stem-and-leaf chart shows the
number of units produced per day in a factory.
3 8
1
4
1
5 6
2
6 01333559
9
7 0236778
16
8 59
18
9 00156
23
10 36
25
a.
b.
c.
d.
e.
How many days were studied?
How many values are in the first class?
What are the smallest and the largest values?
How many values are less than 70?
How many values are between 50 and 70?
3. The following frequency distribution
represents the number of days during a year
that employees at GDNT were absent from
work due to illness.
Number of
Days absent
Number of
Employees
0 up to 4
4 up to 8
8 up to 12
12 up to 16
16 up to 20
5
10
6
8
2
a.
b.
c.
d.
What is the midpoint of the first class?
Construct a histogram
Construct a frequency polygon
Interpret the rate of employee absenteeism
using the two charts