Math 20-3 - Unit 2 - Review
Name: ________________________________________
Reflect on Learning
Now that you have finished this chapter, you should be able to:
Determine the types of graphs that can be used to represent a given data set, and explain the advantages and
disadvantages of each;
Create, with and without technology, a graph to represent a given data set;
Describe the trends a graph represents for a given data set;
Interpolate and extrapolate values from a given graph;
Explain how the same graph can be used to justify more than one conclusion;
Explain how different graphic representations of the same data set can be used to emphasize a point of view;
Solve contextual problems that involve the interpretation of graphs; and
Critically analyze data presented graphically to determine accuracy and reliability.
Quick Review
Drawing Line Graphs
First you need a set of data. In the data there will be independent values and dependent values.
● The independent values are the intervals that you check on what is changing (This is usually time; hours,
months, years, etc.).
● The dependent values will be what is changing.
Now that you have a set of data you will then need to generally place the independent values on the x-axis, and the
dependent values on the y-axis. Label each axis with the name of each of the titles from the data. Lastly give the
graph a title that tells the reader what they are supposed to see in the graph.
Once each set of data is located on the graph you need to connect the dots by a straight line.
Advantages/Disadvantages of Line Graphs
Line graphs show continuous variation the best. This means you are able to interpolate and extrapolate data from
them. This allows you to see trends and make assumptions on the data given.
Example:
Mango rice pudding and spicy dumpling soup are some of the foods made at Chiang’s Cafe in downtown Regina. Mei
is the head cook at the cafe. Her manager has asked Mei to tell him how much money is lost each month due to food
waste, so that Mei will know when to order fewer perishable supplies such as fresh vegetables and dairy products. Mei
must record the amount and type of food waste, and then calculate and record its cost. Display Mei’s information on a
broken-line graph.
Food Waste
Month
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
Cost of
food waste
$135
$125
$92
$53
$86
$72
$97
$89
$112
$98
$82
$47
Solution:
Draw the Graph
Drawing Bar Graphs and Histograms
Example:
In his beauty salon, Gus sell eight different colours of nail polish. He used the following broken line
graph to display the number of people who chose each colour.
a) Was this the most suitable way to display the data? Explain your answer.
b) Identify and justify another type of graph that could have been used and display the data on that graph
Solution
a) This was not the most suitable display because it looks like a continuum. Like there is a colour between Red
and Green that people choose.
b) A more suitable display would have been a bar graph or a circle graph. The bar graph shows the discrete
numbers, and the circle graph shows proportions.
Example​:
While working in the forestry industry, Ray had to determine the number of trees at each height in a given area. He
displayed the information on the following chart.
a)
b)
c)
d)
e)
Discuss the suitability of this type of graph for displaying the data.
According to this chart, what is the height of the tallest tree in the area?
How many trees are 50 feet tall or more?
How many trees are shorter than 50 feet?
Could the information have been displayed effectively on a different type of graph and, if so, what type?
Solution​:
a) This is a suitable way to display the information because the trees are of differing heights and Ray
would not be able to determine their exact heights, just a range.
b) The tallest tree would be between 90 and 100 feet tall.
c) There are 32 trees taller than 50 feet.
d) We cannot be sure how many trees are less than 50 feet tall because he did not indicate how many
trees were less than 10 feet tall. However, there are 45 trees between 10 and 50 feet tall.
e) The information could have been displayed on a circle graph.
Drawing a Circle Graph:
Drawing a circle graph is done with the following steps:
Step 1)
Find the Total Amount
Step 2)
Step 3)
Find the Percentage of total amount for each piece (this will be used to label the graph)
amount = percent
total
100
Find the Amount of a circle that is used by each piece (this will be the angle that you draw with your
protractor)
amount = angle or percent = angle
total
360
100
360
Example​:
Louise has indicated that she has 45% of her farmland seeded in wheat, 20% in oats, 15% in canola, and the rest is
summer fallow. Display this data on a suitable graph and justify your choice. Are there any alternative graphs that
could be used? List them, and explain why.
Solution​:
A circle graph is a good way to display this data because we have the percentages given and it shows the distribution
clearly. A bar graph could also have been used.
Percents to Angles:
45
x
Wheat​: 100 ​= 360
x = 162o
20
x
Oats​: 100 ​= 360
x = 72o
15
x
Canola​: 100 ​= 360
x = 54o
Summer fallow​: 1
​ 00% - 45% - 20% - 15% = 20% (you will only need to label this one)