This document discusses various methods for organizing and displaying data, including frequency tables, stem-and-leaf plots, case tables, bar graphs, pictographs, circle graphs, and histograms. It provides examples and explanations of each method. Frequency tables, stem-and-leaf plots, and case tables are used to organize raw data into meaningful categories. Bar graphs, pictographs, circle graphs, and histograms can then be used to visually display organized data to identify trends and draw conclusions. Proper construction of graphs is also addressed.

1. DATA ANALYSISWITH GRAPHS

2. In order to draw conclusions, information must be gathered,
organized, and displayed clearly.When information is gathered
from all people in a population it is called a census.
For example, Statistics Canada takes a census of the population
every 5 years.The most recent census was conducted on May 10,
2011 (previously May 16, 2006, May 15, 2001 and May 21, 1996).

3. A poll is a method of collecting data from a sample of a
population by asking people to give their answers to a set
of questions. Once collected, the data are then organized
in a meaningful way so that conclusion can be made.

4. Ways to Organize Data
A FREQUENCYTABLE shows the
possible values of a variable and
the frequency of each value.
Example:The members of a grade 12
class were asked in which month they
were born and the results are as follows:
Organize the data into categories (i.e.
months) then, tally each category to
determine the frequency.

5. A STEM & LEAF PLOT is a data
plot that uses part of a data value
as the stem and part as the leaf to
form groups or classes.
Example: The table below gives the
number of days that rain fell in a month,
over 36 months:
In this case, the stem represents the
tens digit.The leaf will represent the
ones digit.
Note:
There are two stems that begin with a 1. One is for the
interval 10 to 15, and the second is for the interval 15
to under 20.
Ways to Organize Data

6. BACK-to-BACK STEM & LEAF
PLOT
Example: The table below shows the
examination marks in French and English
for a class of 20 students.
In this case, the stem is in the
middle of the table so that each side
can contain a leaf.
Ways to Organize Data

7. Some conclusions that can be
drawn from this data include:
• English marks are in general
higher than French marks.
• No student received a mark in the
90’s, in either subject.
• More students got a mark in the
80’s in English that in French.
• Four students failed English.

8. A CASETABLE displays data
comparing cased to different
attributes.
Example: The following are two case
tables, which display a scoring summary
for the London Knights, for the 2004-05
Memorial CupChampionTeam.
Ways to Organize Data

9. Ways to organize Data
This CASETABLE is sorted by points.

10. Ways to organize Data
This CASETABLE is sorted by penalties.

11. A BAR GRAPH displays the
relationship among a set of
numerical values using bars.
Example: The bar graph shown shows
the birth months of when grade 12
students were born
(see previous example for frequency chart).
The numerical scale should start at 0 and
accommodate the magnitude of the
numbers involved. Bar graphs are used
for comparing the values of several
categories of a variable (i.e. months)
Note:
Vertical bars are generally used when time is the
independent variable, while horizontal bars are used
when time is not a factor.
0
1
2
3
4
5
6
7
Frequency
Month
BIRTH MONTH BAR GRAPH
Ways to Display Data

12. A PICTOGRAPH uses symbols to
represent the data for a single
variable.
Example: The pictograph shows the past
& projected world population.
Ways to Display Data

13. A CIRCLE GRAPH shows the
relative sizes (proportions) of
data.
Example:
Ways to Display Data

14. A HISTOGRAM is a vertical bar
graph which contains
continuous data, grouped into
frequency intervals.
Example: The pictograph shows the past
& projected world population.
Ways to Display Data

15. Histogram Construction
• BinWidth:The width of each vertical bar.
• Different bin widths produce different
histograms.
• Small bin width may result in histogram that
does not accurately represent the data (i.e. too
many small bars).
• Bin widths should be set so they are equal.
• There should be at least five bins to have a
representative histogram.
• If a bin width has a frequency of zero, no bar
will appear.
bin width too large
bin width too small