Chapter 2Presenting 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:
SPSSMINITABMs. ExcelMs. VisioOthers
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:
Rural Urban0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
45,000
Populaton by urban and rural in Cambodia
2004200720082009
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 sectors-
maximum 5 or 6
Pie char example:
Table example:
How to present numerical data?
Numerical data
Ordered array
Stem-and-Leaf
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 setExample:Data in raw form: 23 12 32 567 45 34 32 12Data 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 classesThe 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, 720765, 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 510510 up to 760760 up to 10101010 up to 12601260 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 4 4510 up to 760 5 9760 up to 1010 6 151010 up to 1260 1 161260 up to 1510 2 18
Step-and-leafA 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 Leaf
29 9 33 6 45 0 48 0 52 0 57 0 65 0 68 0 72 0 76 0 80 0 85 0 90 0 92 0 99 0 105 0 130 0 150 0
HistogramA graph of the data in a frequency distributionIt 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?
PolygonA frequency polygon, like a histogram, is the
graph of a frequency distributionIn 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 frequencyOgive example:
How can you construct the Ogive in SPSS?
Exercises1. The price-earnings ratios for 24 stocks in the
retail store are:8.2 9.7 9.4 8.7 11.3 12.89.2 11.8 10.8 10.3 9.5 12.68.88.6 10.6 12.8 11.6 9.110.4 12.1 11.5 9.9 11.1 12.5a. Organize this data set into step-and-leaf
displayb. How many values are less than 10.0?c. What are the smallest and largest values
Exercises2. The following stem-and-leaf chart shows the
number of units produced per day in a factory.3 8 14 15 6 26 01333559 97 0236778 168 59 189 00156 2310 36 25
a. How many days were studied?b. How many values are in the first class?c. What are the smallest and the largest values?d. How many values are less than 70?e. 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 Number ofDays absent Employees
0 up to 4 54 up to 8 108 up to 12 612 up to 16 816 up to 20 2
a. What is the midpoint of the first class?b. Construct a histogramc. Construct a frequency polygond. Interpret the rate of employee absenteeism
using the two charts