Worked examples
The question
Question: is "How tall are the students in my class?" a statistical question?
"How tall are the students in my class?"
A statistical question has many answers that vary.
To answer it, we collect data.
statistical = the answers vary
1 Look at who it asks about
It asks about the students.
That is a group: many people or things.
= about: the students (a group)
2 See if the answers vary
Each one can give a different answer.
For example: 150 cm, 162 cm, 147 cm, and so on.
The answers vary.
= 150 cm, 162 cm, 147 cm …
So yes: it is a statistical question.
= yes: statistical
3 Check
Let's check: to answer it, we would collect a list of cm, one for each.
That is data.
So the answer is right!
we would collect: a list of cm
Let's look back.
First: look at who it asks about.
Then: see if the answers vary.
Last: check.
Answer = yes: statistical
▶ Watch it solved
The question
Question: describe the data 3, 4, 4, 5, 7, 7, 7: its center, its spread and its shape.
3, 4, 4, 5, 7, 7, 7
1 Draw a dot plot
A number line from 3 to 7.
One dot for each number.
3 first.
And so on.
2 Find the center
There are 7 numbers.
We count in from both ends to the middle one: number 4.
= 7 numbers: middle = number 4
On the dot plot, that is 5.
The median is the center.
= center: median = 5
Careful!
The tallest stack is 7.
But the center is the middle value, 5.
Careful: the center is the middle value, not the tallest stack
3 Find the spread
The spread: biggest minus smallest.
7 minus 3 is 4.
= spread: range = 7 − 3 = 4
4 Describe the shape
The tallest stack, the peak, is at 7.
One peak, at 7.
No dots at 6: a gap.
Most dots are on the right.
A few spread out to the left: a tail to the left.
= shape: peak at 7, gap at 6, tail to the left
5 Check
Let's check: we count the dots.
7 dots for 7 numbers.
Every number is crossed out.
So the dot plot is right, and so is the answer!
7 dots, 7 numbers
Let's look back.
First: draw a dot plot.
Then: find the center.
Then: find the spread.
Then: describe the shape.
Last: check.
Answer = shape: peak at 7, gap at 6, tail to the left
▶ Watch it solved
The question
Question: describe the data 0, 1, 1, 2, 2, 2, 3, 3, 4, 8: its center, its spread and its shape.
0, 1, 1, 2, 2, 2, 3, 3, 4, 8
1 Draw a dot plot
A number line from 0 to 8.
One dot for each number.
0 first.
And so on.
2 Find the center
There are 10 numbers.
The middle is between number 5 and number 6.
= 10 numbers: middle = numbers 5 and 6
They are 2 and 2.
Halfway between is 2.
= center: median = 2
3 Find the spread
The spread: biggest minus smallest.
8 minus 0 is 8.
= spread: range = 8 − 0 = 8
4 Describe the shape
The tallest stack, the peak, is at 2.
One peak, at 2.
No dots at 5, 6 and 7: a gap.
Most dots are on the left.
A few spread out to the right: a tail to the right.
= shape: peak at 2, gap at 5, 6 and 7, tail to the right
5 Check
Let's check: we count the dots.
10 dots for 10 numbers.
Every number is crossed out.
So the dot plot is right, and so is the answer!
10 dots, 10 numbers
Let's look back.
First: draw a dot plot.
Then: find the center.
Then: find the spread.
Then: describe the shape.
Last: check.
Answer = shape: peak at 2, gap at 5, 6 and 7, tail to the right
▶ Watch it solved
