Statistics 222

1
Statistics 222

• Chapter 2 Review
• 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
What is this?

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

A frequency distribution is a tabular summary of
data showing the total number of occurrences of
each unique value in a data set.
6
What is this called?

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

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.
7
What is this called?

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

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.
8
What is this called?
A bar chart.
9
What is this called?
A pie chart.
10
Tabular and graphic methods for summarizing
quantitative data

• Frequency Distribution
• Relative Frequency and Percent Frequency
  Distributions
• Histogram
• Dot Plot
• Cumulative Distributions
• Ogive

11
What is this called?

• Cost () Frequency
• 50-59 2
• 60-69 13
• 70-79 16
• 80-89 7
• 90-99 7
• 100-109 5
• Total 50

Note there are 6 classes. The class width is 10.
The upper and lower limit of the first class is
50 and 59 respectively.
A frequency distribution is a tabular summary of
data showing the total number of occurrences of
each unique value in a data set.
12
What is this called?

• Relative
• Cost () Frequency
• 50-59 .04
• 60-69 .26
• 70-79 .32
• 80-89 .14
• 90-99 .14
• 100-109 .10
• Total 1.00

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.
13
What is this called?

• Percent
• Cost () Frequency
• 50-59 4
• 60-69 26
• 70-79 32
• 80-89 14
• 90-99 14
• 100-109 10
• Total 100

The 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.
14
What is this called?
18
A histogram
16
14
12
Frequency
10
8
6
4
2
Parts Cost ()
50 60 70 80 90 100
110
What makes a histogram different than a bar
chart a histogram has no gaps between the bars.
15
What is this called?

• Cumulative
• Cost () Freq Frequency
• lt 59 2 2
• lt 69 13 15
• lt 79 16 31
• lt 89 7 38
• lt 99 7 45
• lt 109 5 50

The cumulative frequency distribution shows the
number of items with values less than or equal to
the upper limit of each class.
16
What is this called?

• Cumulative
• Relative
• Cost () Freq Frequency
• lt 59 2 .04
• lt 69 13 .30
• lt 79 16 .62
• lt 89 7 .76
• lt 99 7 .90
• lt 109 5 1.00

The cumulative relative frequency distribution
shows the proportion of items with values less
than or equal to the upper limit of each class.
17
What is this called?

• Cumulative
• Percentage
• Cost () Freq Frequency
• lt 59 2 4
• lt 69 13 30
• lt 79 16 62
• lt 89 7 76
• lt 99 7 90
• lt 109 5 100

The cumulative percent frequency distribution
shows the percentage of items with values less
than or equal to the upper limit of each class.