Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 61
Chapter 13: Statistics
Statistics
Statistics is the study of
data. How to collect,
summarize and present it.
What is Data?
Data is a collection of facts, such as values or measurements.
It can be numbers, words, measurements, observations or even just descriptions of
things.
Qualitative vs Quantitative
Data can be qualitative or quantitative.


Qualitative data is descriptive information (it describes something)
Quantitative data, is numerical information (numbers).
13 Statistics
Page 1
Name of Lecturer: Mr. J.Agius
Course: HVAC1
And Quantitative data can also be Discrete or Continuous:


Discrete data can only take certain values (like whole numbers)
Continuous data can take any value (within a range)
Put simply: Discrete data is counted, Continuous data is measured
Example: What do we know about Arrow the Dog?
Qualitative:



He is brown and black
He has long hair
He has lots of energy
Quantitative:






Discrete:
He has 4 legs
He has 2 brothers
Continuous:
He weighs 25.5 kg
He is 565 mm tall
To help you remember think "Quantitative is about Quantity"
Discrete and Continuous Data
Data can be Descriptive (like "high" or "fast") or Numerical (numbers).
And Numerical Data can be Discrete or Continuous:
Discrete data is counted, Continuous data is measured
Discrete Data
Discrete Data can only take certain values.
Example: the number of students in a class (you can't have half a student).
13 Statistics
Page 2
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Continuous Data
Continuous Data is data that can take any value (within a range)
Examples:





A person's height: could be any value (within the range of human heights), not just
certain fixed heights,
Time in a race: you could even measure it to fractions of a second,
A dog's weight,
The length of a leaf,
Lots more!
Collecting
Data can be collected in many ways. The simplest way is direct observation.
Example: you want to find how many cars pass by a certain point on a road in a 10minute interval.
So: simply stand at that point on the road, and count the cars that pass by in that
interval.
You collect data by doing a Survey.
Census or Sample
A Census is when you collect data for every member of the group (the whole
"population").
A Sample is when you collect data just for selected members of the group.
Example: there are 120 people in your local football club.
You can ask everyone (all 120) what their age is. That is a census.
Or you could just choose the people that are there this afternoon. That is a sample.
A census is accurate, but hard to do. A sample is not as accurate, but may be good
enough, and is a lot easier.
Language
Data or Datum?
Strictly speaking, the word “data” is in the plural (the singular form is “datum”).
However, the word is often used as if it is a singular noun.
So we commonly say "the data is available" rather than the more correct way "the
data are available".
13 Statistics
Page 3
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 1
Which one of the following is quantitative data?
A She is black and white.
B
She has two ears.
C
D
She has long hair.
She has a long tail.
Question 2
Which one of the following is continuous data?
A She has two eyes.
B
She has five kittens.
C
D
She weighs 5.4 kg.
She has four paws.
Question 3
Which one of the following is continuous data?
A She has two eyes.
B
She has five kittens.
C
D
She weighs 5.4 kg.
She has four paws.
Question 4
Which one of the following is discrete data?
A She is 45.2 cm long.
B
C
D
She weighs 5.4 kg.
She is 22.3 cm high.
She has 30 teeth.
Question 5
A census collects information about:
A All members of the population.
B
C
D
A large sample of the population.
13 Statistics
All adult members of the
population.
A small sample of the population.
Page 4
Name of Lecturer: Mr. J.Agius
Course: HVAC1
How to Show Data
Bar Graphs
Bar Graph – A special graph that uses bars to show relative sizes of data
Imagine you just did a survey of your friends to find which kind of movie they liked best.
Here are the results:
Table: Favorite Type of Movie
Comedy
Action
Romance
Drama
SciFi
4
5
6
1
4
You could show that on a bar graph like this:
It is a really good way to show relative sizes: it is easy to see which types of movie are
most liked, and which are least liked, at a glance.
You can use bar graphs to show the relative sizes of many things, such as what type of
car people have, how many customers a shop has on different days and so on.
13 Statistics
Page 5
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Example: Student Grades
In a recent test, this many students got the following grades:
Grade:
A
B
C
Students:
4
12
10
D
2
And here is the bar graph:
Question 1
The bar graph shows the results when a die was thrown a number of times.
How many sixes were thrown?
A
C
2
5
13 Statistics
B
D
3
6
Page 6
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 2
The bar graph shows the favourite colours of 20 students in a class.
How many more of them favoured orange than those who favoured green?
A
C
2
4
B
D
3
5
Question 3
The bar graph shows the usual method of transport to school for the students in a
class. How many students are there altogether in the class?
A
C
20
22
13 Statistics
B
D
21
23
Page 7
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 4
The bar graph shows the marks Brett obtained in his end of year exams.
How many more percentage points did Brett score in his best subject than in his
worst subject?
A
C
25%
45%
B
D
35%
60%
Question 5
Brett's friend, Luke, scored 12 percentage points higher than Brett in Science.
What was Luke's mark for Science?
A
C
30%
52%
13 Statistics
B
D
47%
54%
Page 8
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 6
The pie chart shows the amount of time each day that Jethro spends on various
activities.
If this information were displayed using a bar graph with hours on the vertical axis,
what would be the height of the bar for sleep?
A
C
8 hours
6 hours
B
D
7 hours
2.5 hours
Question 7
If this information were displayed using a bar graph with hours on the vertical axis,
what would be the height of the bar for work?
A
C
4 hours
8 hours
13 Statistics
B
D
4.8 hours
9.6 hours
Page 9
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Pie Chart
Pie Chart - A special chart that uses "pie slices" to show relative sizes of
data.
Imagine you just did a survey of your friends to find which kind of movie they liked best.
Here are the results:
Table: Favorite Type of Movie
Comedy
Action
Romance
Drama
SciFi
4
5
6
1
4
You could show that by this pie chart:
It is a really good way to show relative sizes: it is easy to see which movie types are
most liked, and which are least liked, at a glance.
How to Make Them Yourself
First, put your data into a table (like above), then add up all the values to get a total:
Comedy
Action
Romance
Drama
SciFi
TOTAL
4
5
6
1
4
20
13 Statistics
Page 10
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Next, divide each value by the total and multiply by 100 to get a percent:
Comedy
Action
Romance
Drama
SciFi
TOTAL
4
5
6
1
4
20
4/20 = 20%
5/20 = 25%
6/20 = 30%
1/20 = 5%
4/20 = 20%
100%
Now you need to figure out how many degrees for each "pie slice" (correctly called
a sector).
A Full Circle has 360 degrees, so we do this calculation:
Comedy
Action
Romance
Drama
SciFi
TOTAL
4
5
6
1
4
20
4/20 = 20%
5/20 = 25%
6/20 = 30%
1/20 = 5%
4/20 = 20%
100%
4/20 × 360°
= 72°
5/20 × 360°
= 90°
6/20 × 360°
= 108°
1/20 × 360°
= 18°
4/20 × 360°
= 72°
360°
Now you are ready to start drawing!
Draw a circle.
Then use your protractor to measure the degrees of
each sector.
Here I show the first sector ...
... you can do the rest!
More Examples
You can use pie charts to show the relative sizes of many things, such as:



what type of car people have,
how many customers a shop has on different days and so on.
how popular are different breeds of dogs
13 Statistics
Page 11
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Example: Student Grades
Here is how many students got each grade in the recent test:
A
B
C
4
12
10
D
2
And here is the pie chart:
Question 1
In 2008 approximately what percent of the world's population lived in Asia?
A
C
50%
75%
13 Statistics
B
D
60%
90%
Page 12
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 2
The bar graph shows the scores obtained when a die was rolled a number of times.
If this information were displayed instead as a pie chart, what would be the angle
of the sector of the pie chart representing the score of 2?
A
C
18o
90o
B
D
54o
108o
Question 3
The bar graph shows the usual method of transport to school for the students in a
class.
If this information were displayed instead as a pie chart, what would be the angle
of the sector of the pie chart for the students who walk to school?
Give your answer to the nearest degree.
A
C
23o
86o
13 Statistics
B
D
82o
98o
Page 13
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 4
Anna did a survey where she asked all the children in her school to name their
favourite pet. The results are shown in the pie chart:
If there were 800 children in the school, how many said their favourite pet was
Fish?
A
C
4
14
B
D
9
32
Question 5
What is the angle for the sector of the pie chart representing Fish?
A
C
4o
14.4o
13 Statistics
B
D
9o
50.4o
Page 14
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 6
The pie chart shows the amount of time each day that Jethro spends on various
activities.
What is the angle for the sector of the pie chart representing the time he spends
playing sport?
A
C
14o
50.4o
B
D
25.7o
52o
Question 7
The pie chart shows how a family's household expenditure is broken down into
categories.
What percentage of the family's income is spent on Power?
A
C
10%
13.9%
13 Statistics
B
D
11.1%
40%
Page 15
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Question 8
This pie chart shows the Mc Creedy's household expenditure, broken down into
categories:
If their expenditure on food is €300 per week, what is the weekly expenditure on
transport?
A
C
€50
€125
B
D
€100
€150
These Notes were all taken from the website “Maths is Fun”
http://www.mathsisfun.com/data/index.html
13 Statistics
Page 16