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 1

4 1

5 6 2

6 01333559 9

7 0236778 16

8 59 18

9 00156 23

10 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