Transcript 8.1 Types of Data Displays

8.1 Types of Data Displays
Remember to Silence Your
Cell Phone and Put It In
Your Bag!
Introduction
Statistics


Descriptive Statistics
Inferential Statistics
Graphical Displays of Data
Make the display user friendly



Title
Labels
Scale
 Use a uniform scale
 When necessary use a broken line to indicate a jump in
the scale
Technology



Pencil and paper
Calculator
Computer Software
Representing Frequency and
Distribution of Data
Frequency Table
A table that organizes the data by recording the
number of times a number (score) occurs in a
set of data

To make a frequency table:
1.
Decide on the categories or intervals to use.
When making a grouped frequency table, use intervals
of equal length
2.
3.
Record the data by placing a tally mark for each
score.
Count the number of tallies and write the
number in the frequency column.
Age of Students
City Track Meet
Age of
Students
8
9
10
11
12
13
14
Tally
Frequency
||
|||
|||| |
||||
|||
|||| |
|||| |
2
3
6
4
3
6
6
Frequency Table


(cont.)
Adv
 Quick way to organize the data to get a picture
of it
 Makes it easy to identify numbers that occur
several times
 Easy to read and interpret
Dis
 When using grouped intervals some of the
specific data may be lost
Representing Frequency and
Distribution of Data
Dot Plot
A graphical display of the data using a horizontal
number line

To make a dot plot:
1.
2.
Draw a horizontal number line with scale
markings for the range of the data.
Place a dot, circle, or × above the corresponding
number line value.
Dot Plot


(cont.)
Adv
 Quick way to organize the data to get a picture
of it
 Easy to spot the extremes of the data set and
to note both outliers and clusters of points
 Can see the actual data values
Dis
 Not practical for large data sets
Representing Frequency and
Distribution of Data
Stem and Leaf Plot (Ordered)
A display of the data in a vertical format
grouping scores with the same leading digits
Use a legend


To make a stem and leaf plot:
1.
2.
3.
Decide on the number of digits in the data to be
listed under the stems.
List the stems in a column from smallest to
largest (or largest to smallest).
List the remaining digits in each data entry as
leaves, smallest to largest (or largest to
smallest).
Stem and Leaf Plot


(cont.)
Adv
 Can see the actual data values
 Makes it easy to identify numbers that occur
several times
Dis
 Can be confusing to read
 Not all data lends itself to this type of grouping
Representing Variation and
Comparing Data
Pictograph
A graph which uses icons or figures to represent
data values
Use a legend to indicate what the icon
represents
May use fractions of an icon



To make a pictograph:
1.
2.
3.
Select categories or intervals for the data.
Choose an icon and decide what it represents.
Draw the appropriate number of icons for each
category.
Pictograph


(cont.)
Adv
 Uses a visual to show differences in numerical
values
Dis
 May force the reader to make estimates of the
data
Representing Variation and
Comparing Data
Histograph (or histogram)
A graph which uses rectangles to display the
frequency of a grouped data set

To make a histograph:
1.
2.
3.
Decide on the intervals to use. Set this up on
the horizontal axis.
Find the frequency of each interval. Set this up
on the vertical axis.
Draw rectangles that touch each other on the
horizontal axis and have a height that represents
the frequency of the interval.
Histograph


(cont.)
Adv
 Can show gaps and clusters in the data
 Traditional format many are used to reading
Dis
 Usually takes more time to construct than other
graphic displays
 Specific data may be lost
 May force the reader to make estimates of the
data
Representing Variation and
Comparing Data
Bar Graph

A graph which uses rectangles to display a set of
discrete data
To make a bar graph:
1.
2.
Decide on the categories to use for each axis.
Draw equally spaced rectangles on the horizontal
axis with heights that represent the related
category.
Bar Graphs


(cont.)
Adv
 Can show gaps and clusters in the data
 Traditional format many are used to reading
Dis
 Usually takes more time to construct than other
graphic displays
 Specific data may be lost
 May force the reader to make estimates of the
data
Representing Part-to-Whole
Relationships in Data
Circle Graph (Pie Chart)
A graph in which data are represented by
disjoint sections of a circular region, with each
section representing a part of the whole

To make a circle graph
1.
2.
Find the fractional part of the total each data
category represents.
Multiply each fractional part by 360. This
number represents the measure of the central
angle for each section.
To make a circle graph:
3.
4.
5.
(cont.)
Draw a circle and mark the center.
Draw a radius to use as the initial side of the
first central angle.
Divide the circle into sections by drawing central
angles with the measures found in step 2.