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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.
slide4

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.
slide6

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
slide10

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)

slide11

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
slide12

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

slide13

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

slide14

-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

slide15

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

slide16

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.
slide17

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

slide18

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
slide21

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.
slide26

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
slide27

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

slide28

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?
slide29

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

slide30

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
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