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Chapter 2 Presenting Data in Charts and Tables

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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?

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:

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?

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 44

510 up to 76059

760 up to 1010615

1010 up to 1260116

1260 up to 1510218

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 Leaf

299

336

450

480

520

570

650

680

720

760

800

850

900

920

990

1050

1300

1500

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

- The price-earnings ratios for 24 stocks in the retail store are:
8.29.79.48.711.312.8

9.211.810.810.39.512.6

8.88.610.612.811.69.1

10.412.111.59.911.112.5

- Organize this data set into step-and-leaf display
- How many values are less than 10.0?
- 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.

- 81
41

- 62
- 013335599
- 023677816
- 5918
- 0015623
103625

- 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 Number of

Days absentEmployees

0 up to 45

4 up to 810

8 up to 126

12 up to 168

16 up to 202

- 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