Organizing data

1
MATH 1530 Elements of StatisticsDr. Kirsten Boyd

• Chapter 2
• Organizing data

Slides adapted from the Weiss Text, Dr. Griffy,
and Ms. Smyth
2
(No Transcript)
3
Sec. 2.2 Grouping Data

• Why would we group data?
• So the data are in a form that makes it easier
  for a reader to give the numbers meaning.

4
Frequency Distribution(example 2.5, p. 45)
5
Important Terminology
6
How to Group?

• Guidelines
• Small enough to summarize well but large enough
  to show characteristics
• Each observation must belong to only one class
• Classes should be of the same width
• Rule of thumb number of classes should be
  between 5 and 20

7
Grouped Data Table
Use classes of equal width with 1 as the first
cutpoint and a class width of five.

• 8 1 19 3 1
• 11 18 20 6 6
• 3 2 15 1 9

8
Grouped Data Table

• Always provides
• classes,
• frequencies,
• relative freq., and
• midpoints

• 8 1 19 3 1
• 11 18 20 6 6
• 3 2 15 1 9

9
Alternative Grouping Method

• Classes are divided by lower limit (lower
  cutpoint) and upper limit (largest number that is
  still inside class), whereas with the traditional
  method the upper cutpoint is the smallest number
  inside the next class.
• Mark is used instead of midpoint but it is
  calculated the same way.

10
Alternative Grouped Data Table
Use classes of equal width with 1 as the first
limit and a class width of five.

• 8 1 19 3 1
• 11 18 20 6 6
• 3 2 15 1 9

11
Alternative Grouped Data Table

• Always provides
• classes,
• frequencies,
• relative freq., and
• mark

• 8 1 19 3 1
• 11 18 20 6 6
• 3 2 15 1 9

12
Grouping Single-Value Data(example 2.7, page 49)
The table gives the number of TV sets per
household for 50 randomly selected households.
Use classes based on a single value to construct
a grouped-data table for these data.
13
Grouping Qualitative Data (example 2.8, page 50)
Professor Weiss asked his introductory statistics
students to state their political party
affiliations as Democratic (D), Republican (R),
or Other (O). This example uses single-value
grouping, but thats not always the case for
qualitative data.
14
Sec. 2.3 Graphs and Charts

• Why are graphs important?
• For quantitative data histograms, dotplots and
  stem leaf diagrams
• For qualitative data bar charts and pie charts

15
Histograms (Example 2.10, p. 56, same data as
earlier Example 2.5)
Frequency Histogram
Relative Frequency Histogram
16
Building Histograms(Number of TVs Examples 2.7
and 2.11)
Example 2.11, page 57 TVs per Household Trends
in Television, published by the Television Bureau
of Advertising, provides information on
television ownership. The table on the left below
gives the number of TV sets per household for 50
randomly selected households, and in example 2.7
(p. 49), a table (on the right below) of
frequencies and relative frequencies was made.
Construct a frequency histogram and a
relative-frequency histogram.
17
Single-Value Histograms for TV ExampleThe
unshaded bars on these histograms are a mistake
and really should be shaded. Also notice the
slashes indicating a break in the horizontal
axis.
Frequency Histogram
Relative Frequency Histogram
18
Dotplots(this example is not in the book)

• The following data are a sample of test scores
  for a College Algebra Exam
• 76 88 65 76 99 53
• 87 86 86 72 86 98

Make a dotplot for this data.
19
Stem Leaf

• The following data are a sample of test scores
  for a College Algebra Exam.
• 76 88 65 76 99 53
• 87 86 86 72 86 98

• Do
• Stem and Leaf
• Ordered Stem and Leaf

20
Stem Leaf (Example 2.14, page 60)
A pediatrician tested the cholesterol levels of
several young patients. Given the readings of 20
patients with high levels, construct a
stem-and-leaf diagram using (a) one line per stem
and (b) two lines per stem.
21
Pie Charts Bar Charts

• Typical for qualitative data
• The percentages of each pie piece must be labeled
  and must sum to 100
• A bar chart is like a histogram, except that one
  is for qualitative data and one is for
  quantitative data, and
• The bars of qualitative data do not touch
• The bars on a bar chart and the labels on the
  horizontal axis can be placed in any order (as
  long as they match each other)
• The next slide shows Example 2.17, p. 61.

22
Bar Chart
Pie Chart
23
Sec. 2.4 Distribution Shapes
The distribution of a data set is a table, graph,
or formula that provides the values of the
observations and how often they occur.
24
Histogram Distribution Shape(Heights of
students Fig. 2.8, page 73)
25
Common Distribution Shapes
26
Describing a Distribution

• Modality unimodal, bimodal, multimodal
• Symmetry symmetrical or not
• If unimodal not symmetrical left skewed or
  right skewed

27
Shapes of Histograms(Household size, Fig. 2.10,
p. 74 what shape is this distribution?)
28
Population Sample Distributions

• Population Distribution distribution of all
  values of the variable in the population
• Sample Distribution distribution of a sample
  taken from the population
• Sample population distributions may not be
  identical but should be similar. The larger the
  sample size, the better the sample tends to
  approximate the overall population.

29
Household Size The population consists the
household size of all U.S. households. The
population distribution is (a), and (b) contains
six sample distributions. (Fig. 2.11, p. 76)
30
Sec. 2.5 Misleading Graphs

• WARNING visual images can be constructed to be
  misleading
• Watch for
• Truncated graphs
• Improperly scaled axes

31
Truncated Graphs
Images from http//wwwlb.aub.edu.lb/websmec/artic
le_1.htm
32
Truncated Graphs

• Can be extremely useful
• Appropriate if // or similar mark is made on
  truncated axis to show truncation

33
Improperly Scaled Graphs
House of Twice the size
House
Images are van Gogh