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Types of Data Displays

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Types of Data Displays Powered By Docstoc
					Types of Data
  Displays
      Based on the 2008
AZ State Mathematics Standard
Pictograph
(Grades 1 and 2)
             Pictograph
              (Grades 1 and 2)

For Grade 1: the pictures/icons in the
pictograph represent a quantity of 1.


For Grade 2: The pictures/icons in the
pictograph represent more than 1 and a key
is required to interpret the graph.
Pictograph Example
            Pictographs Summary
Pictograph                   Advantages                 Disadvantages

A pictograph uses an icon to •Easy to read              •Hard to quantify partial
represent a quantity of data                            icons
values in order to decrease •Visually appealing
the size of the graph. A key                            •Icons must be of consistent
must be used to explain the                             size
icon                         •Handles large data sets
                             easily using keyed icons
                                                        •Best for only 2 – 6
                                                        categories

                                                        •Very simplistic
Tally Chart
“Favorite Pets”
   (Grade 1)
                  Frequency Table
                           “Favorite Pets”
                           (Grades 2 and 3)




Note: A frequency table may or may not have a column for the tally marks.
Pictograph made from the previous
  tally chart and frequency table
                             Bar Graphs
                             (Grades 2, 3, 4, 5)
Bar graph                     Advantages                   Disadvantages

A bar graph displays          •Visually strong             •Graph categories can be
discrete data in separate                                  reordered to emphasize
columns. A double bar         •Can easily compare two or   certain effects.
graph can be used to          three data sets.
compare two data sets.                                     •Use only with discrete data
Categories are considered
unordered and can be
rearranged alphabetically,
by size, etc.
              Bar Graphs
               (Grades 2, 3, 4, 5)


Grade 2: Single Bar Graph

Grade 3: Single Bar Graph

Grade 4: Double Bar Graph

Grade 5: Multi-Bar Graph
Bar Graph made from previous tally
       chart and pictograph
Bar Graphs Example
Horizontal Bar Graph Example
Vertical Bar Graph Example
           Which Direction?
Vertical Bar Graph
 Displays data better than horizontal bar graphs,
 and is preferred when possible.


Horizontal Bar Graph
 Useful when category names are too long to fit
 at the foot of a column.
Vertical vs. Horizontal
Double Bar Graph
     (Grade 4)
Multi-Bar Graph
     (Grade 5)
                            Line Graph
                               (Grades 3, 4, 5)


Line graph                  Advantages                  Disadvantages

A line graph plots          •Can compare multiple       •Use only with
continuous data as          continuous data sets        continuous data
points and then joins       easily
them with a line.
Multiple data sets can be
graphed together, but a     •Interim data can be
key must be used.           inferred from graph line.
             Line Graph
               (Grades 3, 4, 5)

• Grade 3: Single Line Graph

• Grade 4: Single Line Graph

• Grade 5: Double Line Graph
Single Line Graph
    (Grades 3 and 4)
Double Line Graph
      (Grade 5)
          Pie Chart – Circle Graph
                                      (Grade 4)
Pie chart                      Advantages                    Disadvantages

A pie chart displays data as   •Visually appealing           •No exact numerical data
a percentage of the whole.
Each pie section should        •Shows percent of total for   •Hard to compare 2 data
have a label and               each category.                sets
percentage. A total data
number should be included.
                                                             •“Other” category can be a
                                                             problem

                                                             •Total unknown unless
                                                             specified

                                                             •Best for 3 – 7 categories

                                                             •Use only with discrete data
Pie Chart – Circle Graph Example
   Pie (circle) charts - more info
• A way of summarizing a set of categorical data or
  displaying the different values of a given variable (e.g.
  percentage distribution).

• A circle is divided into a series of segments. Each
  segment represents a particular category.

• The area of each segment is the same proportion of a
  circle’s area as the category is of the total data set.

• Quite popular. Circle provides a visual concept of the
  whole (100%).
• Best used for displaying statistical
  information when there are no more than
  six components – otherwise, the resulting
  picture will be too complex to understand.

• Pie charts are not useful when the values
  of each component are similar because it
  is difficult to see the differences between
  slice sizes.
                    Stem and Leaf Plot
                                     (Grade 6)
Stem and Leaf Plot             Advantages                    Disadvantages

Stem and leaf plots record     •Concise representation of    •Not visually appealing
data values in rows, and can   data
easily be made into a                                        •Does not easily indicate
histogram. Large data sets     •Shows range, minimum &       measures of centrality for
can be accommodated by         maximum, gaps & clusters,     large data sets.
splitting stems.               and outliers easily

                               •Can handle extremely large
                               data sets
Stem and Leaf Plot
Stem and Leaf Plot
                               Histograms
                                       (Grade 6)
Histogram                      Advantages                    Disadvantages

A histogram is a type of bar   •Visually strong              •Cannot read exact values
graph that displays                                          because data is grouped
continuous data in ordered     •Can compare to normal        into categories.
columns. Categories are of     curve
continuous measure such                                      •More difficult to compare
as time, inches,                                             two data sets.
temperature, etc.              •Usually vertical axis is a
                               frequency count of items
                               falling into each category.   •Use only with continuous
                                                             data.
Histogram
Histogram
                                    Line Plot
                                     (Grade 4 and 5)

Line plot                         Advantages                  Disadvantages

A line plot can be used as an     •Quick analysis of data     •Not as visually appealing
initial record of discrete data
values. The range                 •Shows range, minimum &     •Best for under 50 data
determines a number line          maximum, gaps & clusters,   values
which is then plotted with X’s    and outliers easily
(or something similar) for
each data value.                                              •Needs small range of data
                                  •Exact values retained.
Line Plots (dot plot) Example
         Line Plot for the Number of M&M's™ in a Package




                                   X
                               X   X       X
                      X        X   X       X
                  X   X        X   X   X   X   X
          X       X   X   X    X   X   X   X   X       X
          12 13 14 15 16 17 18 19 20 21 22 23


 Graph paper is a good idea for it is crucial that each recorded X be
uniform in size and placed exactly across from each other (one-to-one
                          correspondence).

Notice the cluster at 17 & 18 as well as the gap at 13 and 22. The
mode is 18, the median is the second X from the bottom for number
                 18, and the mean is 17.68 or 18.
Line plot made from a Tally Chart
There are many more types of Data
             Displays
        Here are a few - - -
Stacked Vertical Bar Graph Example
 Histogram Example
(a type of bar graph)
Frequency Polygon
 Salaries of Acme
             Box and Whisker Plot
Box plot                       Advantages                 Disadvantages

A box plot is a concise        •Shows 5-point summary     •Not as visually appealing
graph showing the five point   and outliers               as other graphs
summary. Multiple box
plots can be drawn side by     •Easily compares two or    •Exact values are not
side to compare more than      more data sets             retained.
one data set.

                               •Handles extremely large
                               data sets easily.
Box & Whisker Graph Example
                           Scatter Plot

Scatter plot                   Advantages                   Disadvantages

A scatter plot displays the    •Shows a trend in the data   •Hard to visualize results in
relationship between two       relationship                 large data sets
factors of the experiment. A
trend line is used to          •Retains exact data values   •Flat trend line gives
determine positive, negative   and sample size.             inconclusive results.
or no correlation.

                               •Shows minimum/maximum       •Data on both axes should
                               and outliers                 be continuous.
Scatter Plot
Scatter Plot Example
                  No Correlation
If there is absolutely no correlation present, the value given is 0.
    Perfect linear correlation:
 A perfect positive correlation is given the value of 1.
A perfect negative correlation is given the value of -1.
 Strong linear correlation: The closer
the number is to 1 or -1, the stronger the correlation, or the
     stronger the relationship between the variables.
       Weak linear correlation:
The closer the number is to 0, the weaker the correlation.
                            Map Graph
                            Cosmograph
Map chart                   Advantages                   Disadvantages

A map chart displays data   •Good visual appeal          •Needs limited categories
by shading sections of a
map, and must include a     •Overall trends show well.   •No exact numerical values
key. A total data number
should be included.
                                                         •Color key can skew visual
                                                         interpretation.
 Map Chart
Cosmograph
               Map Graph
• Parts of whole so similar to a pie graph

• Less numerical and more graphic
Venn Diagram
Venn Diagram
Venn Diagram