Statistics and Probability, NAPX-L4-CA16 v1

Question

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Worked Solution

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Variant 0

DifficultyLevel

606

Question

This graph shows the number of people in Australia, in millions, who wear watches on their wrist, from 1998 to 2018.



Which of these statements about the graph is true?

Worked Solution

People wearing watches in 2013 ≈ 3.1 million

People wearing watches in 2018 ≈ 2.3 million

∴\therefore Decreased by more than 500 000 between 2013 and 2018.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
This graph shows the number of people in Australia, in millions, who wear watches on their wrist, from 1998 to 2018.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2020/03/NAPX-L4-16-ver1.svg 500 indent vpad
Which of these statements about the graph is true?
workedSolution
People wearing watches in 2013 ≈ 3.1 million People wearing watches in 2018 ≈ 2.3 million $\therefore$ Decreased by more than 500 000 between 2013 and 2018.
correctAnswer
The number of people wearing watches has decreased by more than 500 000 between 2013 and 2018.

Answers

Is Correct?Answer
x

The number of people wearing watches has more than halved between 1998 and 2013.

✓

The number of people wearing watches has decreased by more than 500 000 between 2013 and 2018.

x

The number of people wearing watches decreased more per year between 2003 and 2008 than at any other time.

Variant 1

DifficultyLevel

608

Question

This graph shows the number of businesses in New South Wales for the Years 2016 to 2020.



Which of these statements about the graph is true?

Worked Solution

Businesses in 2016 ≈ 729 000

Businesses in 2017 ≈ 752 000

Businesses in 2018 ≈ 781 000

Businesses in 2019 ≈ 802 000

Businesses in 2020 ≈ 820 000

∴\therefore The biggest increase of approximately 29 000 businesses occurs from 2017 to 2018.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
This graph shows the number of businesses in New South Wales for the Years 2016 to 2020.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/09/Stats_Prob_NAPX-L4-CA16-v1_v1_a.svg 520 indent vpad
Which of these statements about the graph is true?
workedSolution
Businesses in 2016 ≈ 729 000 Businesses in 2017 ≈ 752 000 Businesses in 2018 ≈ 781 000 Businesses in 2019 ≈ 802 000 Businesses in 2020 ≈ 820 000 $\therefore$ The biggest increase of approximately 29 000 businesses occurs from 2017 to 2018.
correctAnswer
The biggest increase in the number of businesses occurs from 2017 to 2018.

Answers

Is Correct?Answer
✓

The biggest increase in the number of businesses occurs from 2017 to 2018.

x

Overall the number of businesses in New South Wales increased by one hundred and sixty thousand from 2016 to 2020.

x

The number of businesses increased by 50% from 2018 to 2020.

Variant 2

DifficultyLevel

618

Question

This graph shows the number of building approvals in Victoria for the first 6 months of 2022.



Which of these statements about the graph is true?

Worked Solution

Arrange the scores in order:

3000, 4500, 5000, 5500, 5750, 6000
Median = Middle score when arranged in order
= Average of the 3rd and 4th scores
= 5000+55002\dfrac{5000+5500}{2}
= 5250 approvals

∴\therefore The median number of building approvals during the first 6 months of 2022 was 5250 approvals.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
This graph shows the number of building approvals in Victoria for the first 6 months of 2022.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/09/Stats_Prob_NAPX-L4-CA16-v1_v2b.svg 600 indent vpad
Which of these statements about the graph is true?
workedSolution
Arrange the scores in order: >>3000, 4500, 5000, 5500, 5750, 6000
| | | | ------------- | ---------- | | Median | \= Middle score when arranged in order | | | \= Average of the 3rd and 4th scores| | | \= $\dfrac{5000+5500}{2}$| | | \= 5250 approvals|

$\therefore$ The median number of building approvals during the first 6 months of 2022 was 5250 approvals.
correctAnswer
The median number of building approvals during the first 6 months of 2022 was 5250 approvals.

Answers

Is Correct?Answer
x

The greatest increase in approvals was between February and March.

✓

The median number of building approvals during the first 6 months of 2022 was 5250 approvals.

x

The range of approvals was 2000.

Variant 3

DifficultyLevel

610

Question

This graph shows the estimated resident population of Tasmania from 2016 to 2021.



Which of these statements about the graph is true?

Worked Solution

Consider option 1:

Increase in population from 2020 to 2021 = 5 000 people

Increase in population from 2019 to 2020 = 10 000 people

∴\therefore The increase from 2020 to 2021 was half the increase form 2019 to 2020.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
This graph shows the estimated resident population of Tasmania from 2016 to 2021.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/09/Stats_Prob_NAPX-L4-CA16-v1_v3a.svg 450 indent vpad
Which of these statements about the graph is true?
workedSolution
Consider option 1: Increase in population from 2020 to 2021 = 5 000 people Increase in population from 2019 to 2020 = 10 000 people $\therefore$ {{{correctAnswer}}}
correctAnswer
The increase from 2020 to 2021 was half the increase form 2019 to 2020.

Answers

Is Correct?Answer
✓

The increase from 2020 to 2021 was half the increase form 2019 to 2020.

x

The estimated increase in population from 2016 to 2017 was the same as the estimated increase in population from 2019 to 2020.

x

The average population over this period was 570,000.

Variant 4

DifficultyLevel

612

Question

This graph shows a company's monthly profits for a 12 month period.

Which of these statements about the graph is true?

Worked Solution
Range = high − low
= 320 000−100 000320\ 000 - 100\ 000
= $220 000

∴\therefore The range of monthly profits for the 12 month period is $220 000.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
This graph shows a company's monthly profits for a 12 month period. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/09/Stats_Prob_NAPX-L4-CA16-v1_v4_b.svg 500 indent vpad Which of these statements about the graph is true?
workedSolution
| | | | ------------- | ---------- | | Range | \= high − low | | | \= $320\ 000 - 100\ 000$ | | | \= $220 000 |

$\therefore$ The range of monthly profits for the 12 month period is $220 000.
correctAnswer
The range of monthly profits for the 12 month period is $220 000.

Answers

Is Correct?Answer
x

The largest decrease in monthly profits was from August to September.

x

Monthly profits decreased by $50 000 from March to April.

✓

The range of monthly profits for the 12 month period is $220 000.

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