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# Chapter 2 Presenting Data in Charts and Tables - PowerPoint PPT Presentation

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.

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Presentation Transcript
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.

• SPSS

• MINITAB

• Ms. Excel

• Ms. Visio

• Others

• 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.

• 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

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)

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

• 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

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

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 4 4

510 up to 760 5 9

760 up to 1010 6 15

1010 up to 1260 1 16

1260 up to 1510 2 18

• 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

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

• 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

• 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.

Ogive—a graph of cumulative frequency

Ogive example:

• 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

• Organize this data set into step-and-leaf display

• How many values are less than 10.0?

• What are the smallest and largest values

2. The following stem-and-leaf chart shows the number of units produced per day in a factory.

• 8 1

4 1

• 6 2

• 01333559 9

• 0236778 16

• 59 18

• 00156 23

10 36 25

• 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 absent Employees

0 up to 4 5

4 up to 8 10

8 up to 12 6

12 up to 16 8

16 up to 20 2

• What is the midpoint of the first class? number of days during a year that employees at GDNT were absent from work due to illness.

• Construct a histogram

• Construct a frequency polygon

• Interpret the rate of employee absenteeism using the two charts