Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 62
Chapter 13: Statistics
Line Graphs
Line Graph - A graph that shows information that is connected in some way
(such as change over time)
You are learning math facts, and each day you do a short test to see how good you are.
These are the results:
Table: Facts I got Correct
Day 1
Day 2
Day 3
Day 4
3
4
12
15
And here is the same data as a Line Graph:
13 Statistics
Page 1
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 1
Jerry recorded the temperature in his room (in Degrees Fahrenheit) every two
hours over a 12 hour period from noon to midnight. The results are shown in the
line graph.
What was the approximate temperature in Jerry's room at 9 p.m.?
A
C
35oF
25oF
B
D
30oF
20oF
What was the difference between the highest and the lowest temperatures Jerry
recorded?
A
C
25oF
35oF
13 Statistics
B
D
30oF
40oF
Page 2
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 2
The population of a town was recorded every twenty years from 1900 to 2000. The
results are shown in the line graph.
What was the population of the town in the year 1900?
A
C
400
900
B
D
800
8000
By how much did the population increase between 1920 and 1980?
A
C
2800
3800
B
D
3000
4000
Assuming that the trend in the population growth continues, which of the following
is most likely to be the population of the town in the year 2020?
A
C
6000
6400
13 Statistics
B
D
6800
7400
Page 3
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 3
The line graph shows how the population of parrots on an island declined over the
ten year period from 2001 to 2010. Measurements were taken at the beginning of
each year.
What was the total decline in the parrot population over that time?
A
C
14
46
B
D
42
60
Between which two years was the decline greatest?
A
C
2003-4
2006-7
B
D
2004-5
2009-10
From the information shown in the graph, how many times was the population of
parrots equal to 34?
A
C
Once
Three Times
13 Statistics
B
D
Twice
Four Times
Page 4
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Scatter Plots
A graph of plotted points that show the
relationship between two sets of data.
In this example, each dot represents one person's weight versus their
height.
(The data is plotted on the graph as "Cartesian (x,y) Coordinates")
Example:
The local ice cream shop keeps track of how much ice cream they sell versus the
temperature on that day. Here are their figures for the last 12 days:
Ice Cream Sales vs Temperature
Temperature °C Ice Cream Sales
14.2°
$215
16.4°
$325
11.9°
$185
15.2°
$332
18.5°
$406
22.1°
$522
19.4°
$412
25.1°
$614
23.4°
$544
18.1°
$421
22.6°
$445
17.2°
$408
And here is the same data as a Scatter Plot:
13 Statistics
Page 5
Name of Lecturer: Mr. J.Agius
Course: HVAC1
It is now easy to see that warmer weather leads to more sales, but the relationship
is not perfect.
Line of Best Fit
You can also draw a "Line of Best Fit" (also called a "Trend Line") on your scatter plot:
Try to have the line as close as possible to all points, and as many points above the
line as below.
13 Statistics
Page 6
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Example: Sea Level Rise
A Scatter Plot of Sea Level Rise:
And here I have drawn on a "Line of
Best Fit".
Correlation
When the two sets of data are strongly linked together we say they have a High
Correlation.
The word Correlation is made of Co- (meaning "together"), and Relation


Correlation is Positive when the values increase together, and
Correlation is Negative when one value decreases as the other increases
Like this:
13 Statistics
Page 7
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Negative Correlation
Correlations can be negative, which means there is a correlation but one value goes
down as the other value increases.
Example : Birth Rate vs Income
Country
The birth rate tends to be lower in richer countries.
Madagascar
Yearly
Birth
Production
Rate
per Person
$800 5.70
India
$3,100 2.85
Mexico
$9,600 2.49
Below is a scatter plot for about 100 different countries. Taiwan
$25,300 1.57
Norway
$40,000 1.78
It has a negative correlation (the line slopes down)
Note: I tried to fit a straight line to the data, but maybe a curve would work better,
what do you think?
13 Statistics
Page 8
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Pictographs
A Pictograph is a way of showing data using images.
Each image stands for a certain number of things.
Example: Apples Sold
Here is a pictograph of how many apples were sold at the local shop over 4 months:
Note that each picture of an apple means 10 apples (and the half-apple picture means 5
apples).
So the pictograph is showing:




In
In
In
In
January 10 apples were sold
February 40 apples were sold
March 25 apples were sold
April 20 apples were sold
It is a fun and interesting way to show data.
But it is not very accurate: in the example above we can't show just 1 apple sold, or 2
apples sold etc.
Why don't you try to make your own pictographs? Here are a few ideas:




How
How
How
How
13 Statistics
much
much
many
many
money you have (week by week)
exercise you get (each day)
hours you watch TV every week
sports stories are in each newspaper
Page 9
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 1
The pictograph shows the numbers of goals scored by four soccer teams in a
season.
How many goals did Stormers score?
A
C
15
25
B
D
20
40
How many more goals did Shooters score than Raiders?
A
C
40
20
13 Statistics
B
D
25
15
Page 10
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 2
The
pictograph
shows
the
earnings
of
four
men
in
one
week.
How much did Albert earn?
A
C
$310
$350
B
D
$325
$400
How much more did Donald earn than Bernie?
A
C
$250
$175
13 Statistics
B
D
$225
$150
Page 11
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 3
The pictograph shows the monthly sales of three rival pizza companies.
How many pizzas did PizzaHouse sell during the month?
A
C
3250
3375
B
D
3750
3500
During the month, how many more pizzas did Heaven's Pizza sell than Draught's
Pizza?
A
C
1250
1500
13 Statistics
B
D
1375
1625
Page 12
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Histograms
A Histogram is a graphical display of data using bars of different heights.
It is similar to a Bar Chart, but a histogram
groups data into ranges
And you decide what ranges to use!
Example: Dress Shop Survey
You asked customers who bought one of the "Aurora" range of skirts how old they were.
The ages were from 5 to 25 years old.
You decide to put the results into groups of 5:



The 1 to 5 years old range,
The 6 to 10 years old range,
etc...
So if someone says "I am 17" you would add 1 to the "16-20" range.
And here is the result:
You can see (for example) that there were 30 customers between 6
and 10 years old
Histograms are a great way to show results of continuous data, such as:




weight
height
how much time
etc.
13 Statistics
Page 13
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Frequency Histogram
A Frequency Histogram is a special histogram that uses vertical columns to show
frequencies (how many times each score occurs):
Here I have added up how often 1 occurs (2 times), how often 2
occurs (5 times), etc, and shown them as a histogram.
Question 1
The histogram shows the heights of 21 students in a class, grouped into 5-inch
groups.
How many students were greater than or equal to 60 inches tall?
A
C
21
11
B
D
17
6
How many students were greater than or equal to 55 inches tall but less than 70
inches tall?
A
C
13
16
13 Statistics
B
D
15
17
Page 14
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 2
A class carried out an experiment to measure the lengths of cuckoo eggs. The
length of each egg was measured to the nearest mm. The results are shown in the
following histogram:
How many eggs were measured altogether in the experiment?
A
C
25
90
B
D
40
100
How many eggs were less than 23 mm in length?
A
C
26
66
13 Statistics
B
D
40
92
Page 15
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 3
The histogram shows the birth weights of 100 new born babies.
How many babies weighed 8 lb or more?
A
C
22
30
B
D
23
45
Babies who weigh less than 5 lb are considered to have a low birth weight.
Babies who weigh 10 lb or more are considered to have a high birth weight.
What percent of the babies had neither a low or a high birth weight?
A
C
97%
85%
B
D
91%
83%
These Notes were all taken from the website “Maths is Fun”
http://www.mathsisfun.com/data/index.html
13 Statistics
Page 16