1. Unit 3 - Statistics
SPECIFIC OUTCOME: SOLVE PROBLEMS THAT
INVOLVE CREATING AND INTERPRETING GRAPHS,
INCLUDING
•BAR GRAPHS
•HISTOGRAMS
•LINE GRAPHS
•CIRCLE GRAPHS
2. Achievement
Indicators
• DETERMINE THE POSSIBLE GRAPHS THAT CAN
BE USED TO REPRESENT A DATA SET, AND
EXPLAIN THE ADVANTAGES AND
DISADVANTAGES OF EACH.
• CREATE, WITH OR WITHOUT TECHNOLOGY, A
GRAPH TO REPRESENT A DATA SET.
• DESCRIBE THE TRENDS IN THE GRAPH OF A
DATA SET.
3. Achievement
Indicators
• INTERPOLATE OR EXTRAPOLATE VALUES FROM A GRAPH.
• EXPLAIN, USING EXAMPLES, HOW THE SAME GRAPH CAN
BE USED TO JUSTIFY MORE THAN ONE CONCLUSION.
• EXPLAIN, USING EXAMPLES, HOW DIFFERENT GRAPHIC
REPRESENTATIONS OF THE SAME DATA SET CAN BE USED
TO EMPHASIZE A POINT OF VIEW.
• SOLVE A CONTEXTUAL PROBLEM THAT INVOLVES THE
INTERPRETATION OF A GRAPH.
4. Warm-up: 5 mins
SEE – THINK – WONDER
•What do you see?
•What do you think?
•What do you
wonder about?
5. What do Graphs Tell You?
A graph is a way of expressing a
relationship between two different
variables.
There are several types of graphs
Line Graph
Bar Graph
Circle Graph (Pie Chart)
Histogram
6. Variables
Every scientific investigation has variables:
• Variable: factor that changes in an experiment.
• Independent variable: variable that is manipulated
(changed) in an experiment.
• Dependent variable: variable that is affected by the
independent variable.
Example: In an experiment where we are looking at the
effect of the amount of sunlight on plant growth,
since we are manipulating the amount of sunlight, it
is the independent variable and the growth of the
plant is the dependent variable.
10. Identify the Axes
Y- Axis
Dependent
Variable
(what is observed
and measured) Independent
Variable
(what is
changed by the
scientist)
X- Axis
11. DRY MIX
One way to remember which data goes on which axis is
the acronym DRY MIX.
D.R.Y. M.I.X.
D- Dependent M- Manipulated
R- Responding I- Independent
Y- Y-axis X- X-axis
12. Title
Write an appropriate title for the graph at the top.
The title should contain both the independent and
dependent variables.
13. Scale
Decide on an appropriate scale for each axis.
The scale refers to the min and max numbers used on
each axis. They may or may not begin at zero.
The min and max numbers used for the scale should be a
little lower than the lowest value and a little higher than the
highest value.
This allows you to have a smaller range which emphasizes
the comparisons/trends in the data.
14. Scale
•The Y-axis
scale is from
0-100.
•The largest
value though is
only 35.
15. Scale
•The Y-axis
scale is now
from 0-40.
•This does a
better job
emphasizing the
comparisons
between coins.
16. Intervals
Look at your minimum and maximum values you set up for
both the Y and X-axis. (For most bar graphs, the X-axis will
not have numerical values.)
Decide on an appropriate interval for the scale you have
chosen. The interval is the amount between one value and
the next.
It is highly recommended to use a common number for an
interval such as 2, 5, 10, 25, 100, etc.
18. Labels
Both axes need to be labeled so the reader knows exactly
what the independent and dependent variables are.
The dependent variable must be specific and include the
units used to measure the data (such as “number of
drops”).
20. TAILS
Another handy acronym to help you remember
everything you need to create your graphs…..
T.A.I.L.S.
Title
Axis
Interval
Labels
Scale
21. TAILS
Title: Includes both variables
Axis: IV on X-axis and DV on
Y-axis
Interval: The interval (4) is
appropriate for this scale.
Label: Both axes are labeled.
Scale: Min and max values are
appropriate.
23. Bar Graphs
•Bar graphs are descriptive.
•They compare groups of data such as amounts and
categories.
•They help us make generalizations and see
differences in the data.
26. Line Graphs
•Line graphs show a relationship between the two
variables. They show how/if the IV affects the DV.
•They are useful for showing trends in data and for
making predictions.
30. Line Graph
• A line graph shows
changes that occur
in related variables.
• The independent
variable is
generally plotted Y
on the horizontal
axis, or X-axis.
• The dependent
variable is plotted
on the vertical axis,
or Y-axis, of the
graph.
x
31. Creating a Line Graph
IMPORTANT COMPONENTS OF A GRAPH
1. Title: Tells the viewer what the graph is about.
2. X-Axis
- Independent variable
- Evenly spaced units
- Uses an appropriate scale
3. Y-Axix
- Dependent variable
- Evenly spaced units
- Uses and appropriate scale
4. Data: Data can be plotted on the graph from a DATA TABLE
5. Key: If there is more than one line on the graph, a key is needed.
32. Bar Graph
• A bar graph is used
to compare a set of
measurements
amounts or changes.
33. Circle Graph (Pie Chart)
• A circle graph or pie
chart is a divided circle
that shows how a part of
something relates to the
whole.
34. Creating a Line Graph
Find the:
1. Title
2. X-Axis
3. Y-Axis
4. Key
35. What is a Histogram?
A histogram is like a bar chart, but
there are some important differences .
It can only be used to show continuous
data
It can only be used to show numerical data
The data is always grouped.
36. Here is a histogram showing how quickly pupils could say
their twelve times tables
A histogram is made
up of a series of
bars or rectangles
The area
of each
rectangle
represent
s the
frequency
For continuous data, the class of a class
boundaries are written as part of interval.
a continuous scale
37. Histograms Example
The histogram is a tool for presenting the
distribution of a numerical variable in graphical
form.
For example, suppose the following data is the
number of hours worked in a week by a group of
nurses:
42 47 43 26 30 42 28 42 50 39
38 35 37 48 39 36 45 41 72 53
43 37 42 48 40 35 39 30 47 38
38. Histograms
These data are displayed in the following histogram:
12
The data values are grouped
10 in intervals of width five hours.
35
The first interval includes the
35
8 values from 25 to less than 30
36 40
hours. The second interval
37 41
The vertical 6 includes values from 30 to
37 42
axis is less than 35 and so on. The
38 42 45
frequency. So, 4 intervals are shown on the
38 42 47
for example, horizontal axis.
39 42 47
there are two 2
26 30 50
39 43 48
nurses who
0 28 30 39 43 48 53 72
worked from
25 30 35 40 45 50 55 60 65 70 75
25 to less than
30 hours that
Hours worked in the week
week.
39. Histograms
The choice of interval width will
12
affect the appearance of the
10 histogram.
8
6
4 6
20
2 5
0 4
25 30 35 40 45 50 55 60 65 70 75
3
10
Hours worked in the week
2
And here it is again, to the right,
To the right is the same data 1
presented in a histogram of interval 0
2.
width 10. 0
26
25
30 34
35
38 42 46
45
50 54
55
58 62
65
66 70 74
75
Hours worked in the week
Hours worked in the week
41. The table below shows the number of hours students watch
TV in one week Make a histogram of all the data.
Number of hours of TV
1 II 6 III
2 IIII 7 IIII - IIII
3 IIII - IIII 8 III
4 IIII - I 9 IIII
5 IIII - III
42. Make a frequency
table of the data. Be
sure to use equal
intervals
Number of Frequency
hours of TV
Number of hours of TV
1-3 15
1 II 6 III
4-6 17
2 IIII 7 IIII - IIII
7-9 16
3 IIII - IIII 8 III
4 IIII - I 9 IIII
5 IIII - III
43. Choose an appropriate scale and interval for the vertical axis.
The greatest value on the scale should be at least as great as
the greatest frequency.
20
Number of Frequency 16
hours of TV
12
8
1-3 15
4-6 17 4
7-9 16 0
1-3 4-6 7-9
44. Draw a bar for each interval.
The height of the bar is the Hours of Television
Stepinterval.
frequency for that
3 Watched
Bars must touch but not
overlap. 20
Label the axes and give the
Number of students
graph title 16
12
Number of Frequency 8
hours of TV
4
1-3 15 0
4-6 17 1-3 4-6 7-9
7-9 16 Hours
46. Using Circle Graphs to Represent Data
Another way to display data is in the form of a
circle graph or pie chart. Circle graphs are
useful in displaying percentages, or parts of a
whole.
47. Using Circle Graphs to Represent Data
Properties of Circle Graphs:
• They are circular shaped graphs with the entire circle
representing the whole.
• The circle is then split into parts, or sectors.
• Each sector represents a part of the whole.
• Each sector is proportional in size to the amount
each sector represents, therefore it is easy to make
generalizations and comparisons.
48. Constructing Circle Graphs
When constructing a circle graph, follow the steps below
1. Is the Data Suitable--Determine if there is a "whole" for the data. Then
determine what the different parts, or data groups, of the whole are.
2. Calculate Percentages--For data that is not already given as a
percentage, convert the amounts for each part, or data group size, into a
percentage of the whole.
3. Draw the Graph--Draw a circle and draw in a sector for each data group.
4. Title and Label the Graph--Label the sectors with the data group
name and percentage. Then add a title to the graph. This is the same as the title of
the table.
50. Constructing Circle Graphs - Example
Step 1 – Is the Data Suitable?
• There are five parts to the whole. Each data group is
a category of sneaker brands (1) Adidas, (2) Nike, (3)
Reebok, (4) Asics, (5) Other.
Step 2 – Calculate Percentages
• Calculate the whole: 150 + 192 + 60 + 108 + 90 =
600
• Calculate the percentage for each part
ex. Adidas: 150/600 = .25 or 25%
51. Constructing Circle Graphs - Example
Step 3 – Draw the Graph
• First, draw a circle. Then, draw in the sectors of
the circle using a protractor to calculate the size
of the sector.
• The percentage has to be converted to a
degrees.
ex. 25% or .25 x 360o = 90o
Step 4 – Title and Label the Graph
