Statistical Questions & Distributions — Practice
A statistical question is one that expects a spread of answers, not a single one.
What these questions cover
These questions use 9 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Mean — Two kinds of centre: the balance point, and the middle value.
- Range — The set of outputs that actually occur.
- Cluster — A group of dots bunched together.
- Outlier — A dot far away from the rest of the pattern.
- Number line — A line with numbers increasing to the right.
- Height — The perpendicular distance from the base to the opposite corner.
- Statistical question — One that anticipates variability in the answers.
- Distribution — The pattern of how the values are spread out.
- Dot plot — A chart with one dot per value, stacked above a number line.
Problem 1
Which is a statistical question?
- How tall are students in my class?
- How tall am I?
- What is 3+4?
- What day is it?
Worked answer
How tall are students in my class?
Different students have different heights
Problem 2
Which is NOT a statistical question?
- How old am I?
- How old are people in my street?
- How long do students sleep?
- How far do people travel to work?
Worked answer
How old am I?
Your own age has a single answer
Problem 3
A dot plot has dots stacked as 2, 5, 9, 5, 2. How many values are there altogether?
Worked answer
23
2+5+9+5+2 = 23
Problem 4
Which chart shows every single data value?
- A dot plot
- A histogram
- A pie chart
- A bar chart
Worked answer
A dot plot
Nothing is grouped away
Problem 5
A histogram with bars 2, 5, 9, 5, 2 is
- symmetric
- skewed right
- skewed left
- double-humped
Worked answer
symmetric
They fall away evenly on both sides
Problem 6
A histogram with bars 12, 8, 4, 2, 1 is
- skewed right
- symmetric
- skewed left
- double-humped
Worked answer
skewed right
The tail stretches to the right
Problem 7
Scores are 78, 80, 81, 82, 30. Which is the outlier?
- 30
- 82
- 78
- There is none
Worked answer
30
The others cluster near 80
Problem 8
Histogram bars touch each other because
- the intervals run into each other
- they are easier to draw
- it looks neater
- the bars are equal
Worked answer
the intervals run into each other
A number line, not separate categories
Problem 9
A dot plot runs from 4 to 19. Find the range.
Worked answer
15
19 - 4 = 15
Problem 10
Describing a distribution should mention
- centre, spread and shape
- only the mean
- only the range
- only the largest value
Worked answer
centre, spread and shape
An average alone leaves most of it unsaid
Problem 11
A dot plot of heights has two separate humps. This most likely means
- two different groups are mixed together
- the data is wrong
- everyone is the same height
- there are no outliers
Worked answer
two different groups are mixed together
Perhaps two different age groups
Problem 12
A histogram has bars of height 3, 7, 11, 6, 3. How many values are in the two tallest bars together?
Worked answer
18
11 + 7 = 18
Problem 13
An outlier should be
- noticed and investigated
- deleted at once
- ignored
- doubled
Worked answer
noticed and investigated
Only checking the source can tell you
Problem 14
A statistical question is one whose answers show
- variability
- no variability
- only whole numbers
- only positive values
Worked answer
variability
The answers differ from case to case
Problem 15
In a dot plot, 4 students have 0 pets, 6 have 1, and 2 have 3. How many students were asked?
Worked answer
12
4+6+2 = 12
Problem 16
From that same plot, how many pets are there in total?
Worked answer
12
0(4)+1(6)+3(2) = 12