Statistics 221

1
Statistics 221

• Chapter 2 Part A
• Descriptive Statistics Tabular and Graphical
  representations

2
Summarizing Data

• The goal of statistical analysis is often to
  derive knowledge (learn something) something
  about a phenomenon.
• Statistic analysis starts by observing the
  phenomenon as it occurs and recording the outcome
  of events that signify the phenomenons
  occurrence.
• That collection of recordings, or data items is
  called a data set.
• After the data has been collected, it must first
  be summarized and then analyzed.
• This chapter is about summarizing data using both
  tabular and graphical techniques.

3
Summarization Techniques

• Recall that data can be quantitative or
  qualitative. Qualitative data are described using
  labels or names quantitative data are described
  using numeric quantities.
• Some techniques can be applied to both types of
  data and others can be applied to just one type
  of data.

4
Tabular and graphical methods of summarizing
qualitative data

• Frequency Distribution
• Relative Frequency Distribution
• Percent Frequency Distribution
• Bar Graph
• Pie Chart

5
Frequency Distribution

• A frequency distribution is a tabular summary of
  data showing the total number of occurrences of
  each unique value in a data set.
• The purpose of creating a frequency distribution
  is to provide insights about the data that cannot
  be quickly obtained by looking only at the
  original data set.

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We can create a frequency distribution to
summarize raw data

• Guests staying at Marada Inn were asked to rate
  the quality of their accommodations as being
  excellent, above average, average, below average,
  or poor. The ratings provided by a sample of 20
  guests are shown below.
• Below Average Average Above Average
• Above Average Above Average Above Average
• Above Average Below Average Below
  Average Average Poor Poor
• Above Average Excellent Above Average
• Average Above Average Average
• Above Average Average

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Data summarized by a Frequency Distribution

• Rating Frequency
• Poor 2
• Below Average 3
• Average 5
• Above Average 9
• Excellent 1
• Total 20

Guest Quality Ratings for Marada Inn
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Relative Frequency Distribution

• The relative frequency distribution is a tabular
  summary of data showing the proportion of times
  each unique value occurred out of the total
  number of values in a data set.

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Percent Frequency Distribution

• A percent frequency distribution is a tabular
  summary of data showing the percentage of times
  each unique value occurred out of the total
  number of values in a data set.

10
Expressing Frequencies as relative or percentage
frequencies

• Rating Frequency
• Poor 2
• Below Average 3
• Average 5
• Above Average 9
• Excellent 1
• Total 20

To express this value as a relative frequency,
divide 2 by the total (20) to get .10 The
percentage frequency would be 10
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Example of Relative Frequency and Percent
Frequency Distributions

• Relative Percent
• Rating Frequency Frequency
• Poor .10 10
• Below Average .15 15
• Average .25 25
• Above Average .45 45
• Excellent .05 5
• Total 1.00 100

Guest Quality Ratings for Marada Inn
Relative frequencies are expressed as
proportions percent frequencies are expressed as
percentages.
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Bar Graph

• A bar graph is a graphical device for depicting
  qualitative data that have been summarized in a
  frequency, relative frequency, or percent
  frequency distribution.
• On the horizontal axis (X) we specify the labels
  that are used for each of the classes.
• A frequency, relative frequency, or percent
  frequency scale can be used for the vertical (Y)
  axis.
• Using a bar of fixed width drawn above each class
  label, we extend the height appropriately.
• The bars are not touching each other to emphasize
  the fact that each class is a separate category.

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A bar graph presenting qualitative data as a
frequency distribution
In this case, we are plotting frequency.
Guest Quality Ratings for Marada Inn
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Pie Chart

• The pie chart is a commonly used graphical device
  for presenting relative frequency distributions
  for qualitative data.
• First draw a circle then use the relative
  frequencies to subdivide the circle into sectors
  that correspond to the relative frequency for
  each class.
• Since there are 360 degrees in a circle, a class
  with a relative frequency of .25 would consume
  .25(360) 90 degrees of the circle.

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A pie chart presenting qualitative data
Guest Quality Ratings for Marada Inn
16
Insights gained from examining descriptive
statistics

• One-half of the customers surveyed gave Marada
  Inn a quality rating of above average or
  excellent.
• For each customer who gave an excellent rating,
  there were two customers who gave a poor
  rating.

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Practice question (4 on page 28)

• According to Nielson Media Research, the top four
  TV shows at 800 pm on April 6th, 2005 were
  Millionaire, Frasier, Chicago Hope, and Charmed.
  The dataset on the next slide was derived from a
  sample of 50 TV watchers who reported what TV
  shows they were watching.

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Reported TV show watching(sample of 50 TV
viewers)

• Millionaire Millionaire Millionaire
  Fraiser Charmed
• Fraiser Fraiser Millionaire Millionaire Fraiser
• Fraiser Millionaire Millionaire
  Hope Millionaire
• Charmed Millionaire Fraiser Hope Millionaire
• Hope Charmed Fraiser Fraiser Millionaire
• Millionaire Fraiser Millionaire Millionaire Hope
• Fraiser Millionaire Millionaire Charmed Hope
• Hope Millionaire Millionaire Millionaire Milliona
  ire
• Fraiser Fraiser Millionaire Fraiser Fraiser
• Millionaire Millionaire Hope Millionaire Fraiser

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Practice questions

• A. Are these data qualitative or quantitative?
• B. Provide a frequency and percent frequency
  distribution.
• C. Construct a bar graph and a pie chart.
• D. On the basis of the sample, which show has the
  largest market share? Which one is second?

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A. Are these data qualitative or quantitative?

• Qualitative

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B. Provide a frequency and percent frequency
distribution.

• Download from WebCT and open this file in Excel
  DataSetForCh2.xls
• Select worksheet TV shows

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Open the file DataSetsForCh2 and click on the
worksheet tab TV shows See that the data has
already been entered in cells A10A59.
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• To calculate a frequency distribution, use the
  countif() formula to count the number of cells
  in the dataset that contain the label in cell A3
• B3 countif(A10A59, A3)

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2. Copy the formula in B3 down to B6.
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3. Calculate a sum for the frequency column B7
sum(B3B6)
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4. To calculate the relative frequency
distribution, divide the frequency of the first
label by the total number of values in the data
set C3 B3 / B7
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5. To calculate the other relative frequencies,
copy the formula in C3 down to C7.
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6. To calculate the percent frequency
distribution, divide the frequency of the first
label by the total number of values in the data
set (the cell has been pre-format to
percentage) D3 B3 / B7
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7. To calculate the other percent frequencies,
copy the formula in D3 down to D7.
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C. Construct a bar graph and a pie chart.
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Constructing a bar chart
1. Before starting the chart wizard, select the
cells that contain the chart data, including
column headings and row headings (A2B6). 2.
Start the Chart wizard by clicking the chart
wizard button on the standard toolbar
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3. In step 1 of the chart wizard, select column
as the chart type, select the 4th sub-type, and
click next.
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4. In step 2 of the chart wizard, the chart
source data has already been specified so just
click next
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5. In step 3 of the chart wizard, type the chart
titles indicated and click next
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6. In step 4 of the chart wizard, save as object
in existing sheet. Click Finish.
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Constructing a pie chart
1. Before starting the chart wizard, select the
cells that contain the chart data, including
column headings and row headings (A2B6). 2.
Start the Chart wizard by clicking the chart
wizard button on the standard toolbar
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3. In step 1 of the chart wizard, select pie as
the chart type, select the second sub-type, and
click next.
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4. In step 2 of the chart wizard, the chart
source data has already been specified so just
click next
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5. In step 3 of the chart wizard, type the chart
title indicated. Do NOT click next yet.
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6. While still on step 3 of the chart wizard,
click the Data Labels tab and check off
category name and percentage
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7. While still in step 3 of the chart wizard,
click the legends tab and click Show Legend
to remove the check mark. Then click next
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8. In step 4 of the chart wizard, save as object
in existing sheet. Click Finish.
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9. One by one, click each piece label and drag it
away from the pie. A leader line will appear to
connect each label with its pie piece. 10. Move
and resize the chart as appropriate.
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D. On the basis of the sample, which show has the
largest market share? Which one is second?

• Millionaire
• Fraiser

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Homework 2

• 5 on page 29
• In DataSetsForCh2.xls, use datasheet Names
• (develop relative and percent frequency
  distributions, bar graph and pie chart)
• 10 on page 30
• In DataSetsForCh2.xls, use datasheet Clients
• (develop frequency, percent frequency
  distributions and pie chart)
• Provide comments