Data displays

1
Data displays

• Chapters 10, 11

2
Distribution of a variable

• The distribution of a variable tells us what
  values it takes and how often it takes them. It
  could be in table, graph, or equation form. An
  example follows.

The pie chart describes population data. It tells
the various categories and how many people fit in
each.
3
Worksheets

• Data displays provides practice making pie
  charts, bar graphs, line graphs, histograms,
  stemplots, and data tables by hand. It also
  explores other ideas including symmetry and
  outliers. Data displays help us study the
  distribution of a set of numbers.
• Minitab Assignment 1 introduces the software we
  will use in Math 111, Minitab. It covers data
  entry and basic commands. Minitab is available
  throughout the computer labs on campus. You will
  use it or another program to complete the
  Statistics project.

4
Centers and spreads

• Consider the two sets of numbers.
• Data set 1 0, 5, 10, 15, 20
• Data set 2 6, 8, 10, 12, 14
• We can find each sets center
• and spread. A sets center
• is the number all of the
• numbers are centered
• around. Its spread
• describes how far spread
• out the numbers are
• from this center.

5
Notice how the first set is more spread out than
the second set. Well quantify this idea in
chapter 12.
Both sets are centered around 10.
6
Stem plots and histograms

• Lets say we have found the ages of the 48 people
  in our organization. We could write this
  information as a list of 48 numbers, but it would
  not be easily accessible. A histogram or stem
  plot may help. Below are the 48 ages we have
  gathered. We will make a histogram and a stem
  plot using this information.

17 18 19 19 20 21 22 23
23 23 23 25 26 28 29 30
30 30 32 34 34 35 37 37
40 40 41 41 42 43 45 49
51 51 52 53 53 53 55 56
57 58 59 61 63 67 69 69
7
Histogram
A histogram groups the elements into classes. The
classes are 10 19, 20 29, 30 39, etc.
Notice the classes are labeled along the
horizontal axis using the midpoints. The number
of
elements in each class is denoted by the vertical
axis. You can use either counts or percents here.
A histogram shows us how the numbers are
distributed. It is often used to compare the
separate classes.
8
Stemplot

• Here, we record the information in a stem plot.
  Notice the similarities and differences between
  this and the histogram. You can still tell how
  the numbers are distributed. Its shape mimics
  that of the histogram.
• However, a stem plot retains each individual
  number. Whereas, a histogram groups the data and
  loses this information.

9
Outliers

• Suppose an 89-year-old man joins our group. Our
  stem plot would now look like this. Notice how
  the data value 89 sticks out. It is much larger
  than the rest of the numbers. We call it an
  outlier. We are interested in outliers because
  they deviate from the general distribution of a
  group.

10

• After chapter 12, we will complete a worksheet
  titled Minitab data displays which will show us
  how to accomplish with Minitab what we did by
  hand in Data displays. It will also add some
  concepts from chapter 12.
• Chapter 10 homework 1, 2, 5, 7, 8, 10, 11, 13,
  21, 24, 25, 27b
• Chapter 11 homework 1, 2, 5, 10, 11, 13, 15, 16