Chapter 2 presenting data in charts and tables
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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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Chapter 2 presenting data in charts and tables
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:

  • SPSS

  • MINITAB

  • Ms. Excel

  • Ms. Visio

  • Others



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.



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





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 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


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

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


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




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.




Ogive—a graph of cumulative frequency

Ogive example:



Exercises

  • 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


Exercises

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


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