Statistics and Probability, NAPX-I4-NC17
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Variant 0
DifficultyLevel
597
Question
The median mass of a group of emperor penguins at the zoo is 23 kg.
The mean mass of the same group is 25 kg.
If a new 29 kg penguin joins the group, which of these is possible?
Worked Solution
It is possible for the mean mass to increase and
the median mass to stay the same.
Question Type
Multiple Choice (One Answer)
Variables
| Variable name | Variable value |
| question | The median mass of a group of emperor penguins at the zoo is 23 kg.
The mean mass of the same group is 25 kg.
If a new 29 kg penguin joins the group, which of these is possible? |
| workedSolution | It is possible for the mean mass to increase and
the median mass to stay the same.
|
| correctAnswer | The mean mass increases and the median mass stays the same. |
Answers
| Is Correct? | Answer |
| x | The mean mass stays the same and the median mass decreases. |
| x | The mean mass stays the same and the median mass increases. |
| x | The mean mass decreases and the median mass increases. |
| ✓ | The mean mass increases and the median mass stays the same. |
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Variant 1
DifficultyLevel
598
Question
The median high jump height of primary school students competing at the state carnival is 1.1 metres.
The mean high jump height of the same group is 0.9 metres.
If a new competitor then records a jump of 0.8 metres, which of these is possible?
Worked Solution
It is possible for the mean height to decrease and
the median height to stay the same.
Question Type
Multiple Choice (One Answer)
Variables
| Variable name | Variable value |
| question | The median high jump height of primary school students competing at the state carnival is 1.1 metres.
The mean high jump height of the same group is 0.9 metres.
If a new competitor then records a jump of 0.8 metres, which of these is possible? |
| workedSolution | It is possible for the mean height to decrease and
the median height to stay the same.
|
| correctAnswer | The mean height decreases and the median height stays the same. |
Answers
| Is Correct? | Answer |
| x | The mean height decreases and the median height increases. |
| x | The mean height stays the same and the median height decreases. |
| ✓ | The mean height decreases and the median height stays the same. |
| x | The mean height increases and the median height decreases. |
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Variant 2
DifficultyLevel
595
Question
The mean diameter of a batch of cookies is 8.5 centimetres.
The median diameter of the same batch of cookies is 8.9 centimetres.
If a new cookie with a diameter of 7 centimetres is added to the batch, which of these is possible?
Worked Solution
It is possible for the mean diameter to decrease and
the median diameter to stay the same.
Question Type
Multiple Choice (One Answer)
Variables
| Variable name | Variable value |
| question | The mean diameter of a batch of cookies is 8.5 centimetres.
The median diameter of the same batch of cookies is 8.9 centimetres.
If a new cookie with a diameter of 7 centimetres is added to the batch, which of these is possible? |
| workedSolution | It is possible for the mean diameter to decrease and
the median diameter to stay the same.
|
| correctAnswer | The mean diameter decreases and the median diameter stays the same. |
Answers
| Is Correct? | Answer |
| x | The mean diameter stays the same and the median diameter decreases. |
| ✓ | The mean diameter decreases and the median diameter stays the same. |
| x | The mean diameter increases and the median diameter increases. |
| x | The mean diameter increases and the median diameter stays the same. |
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Variant 3
DifficultyLevel
601
Question
The median wingspan of a group of wedge tailed eagles is 2.6 metres.
The mean wingspan of the same group is 2.5 metres.
If a new wedge tailed eagle joins the group with a wingspan of 2.7 metres, which of these is possible?
Worked Solution
The mean wingspan increases and the range stays the same.
Question Type
Multiple Choice (One Answer)
Variables
| Variable name | Variable value |
| question | The median wingspan of a group of wedge tailed eagles is 2.6 metres.
The mean wingspan of the same group is 2.5 metres.
If a new wedge tailed eagle joins the group with a wingspan of 2.7 metres, which of these is possible? |
| workedSolution | |
| correctAnswer | The mean wingspan increases and the range stays the same. |
Answers
| Is Correct? | Answer |
| x | The mean wingspan increases and the range decreases. |
| x | The mean wingspan stays the same and the median wingspan decreases. |
| x | The mean wingspan decreases and the median wingspan stays the same. |
| ✓ | The mean wingspan increases and the range stays the same. |
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Variant 4
DifficultyLevel
603
Question
The mean age of a group of friends is 26 years.
The median age of the same group is 28 years.
If an 18 year old joins the group, which of these is possible?
Worked Solution
It is possible for the mean age to decrease and the median age decreases
Question Type
Multiple Choice (One Answer)
Variables
| Variable name | Variable value |
| question | The mean age of a group of friends is 26 years.
The median age of the same group is 28 years.
If an 18 year old joins the group, which of these is possible? |
| workedSolution | It is possible for the mean age to decrease and the median age decreases |
| correctAnswer | The mean age decreases and the median age decreases.
|
Answers
| Is Correct? | Answer |
| x | The mean age increases and the range of ages decreases. |
| x | The median age stays the same and the mean age stays the same. |
| x | The range of ages decreases and the median age stays the same. |
| ✓ | The mean age decreases and the median age decreases. |
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Variant 5
DifficultyLevel
600
Question
The median price of houses sold in a suburb is $850 000.
The mean price of the same group of houses is $925 000.
If another house in the suburb sells for $1.2 million, which of these is possible?
Worked Solution
It is possible for the mean house price to increase and the median house price to stay the same.
Question Type
Multiple Choice (One Answer)
Variables
| Variable name | Variable value |
| question | The median price of houses sold in a suburb is $850 000.
The mean price of the same group of houses is $925 000.
If another house in the suburb sells for $1.2 million, which of these is possible? |
| workedSolution | It is possible for the mean house price to increase and the median house price to stay the same. |
| correctAnswer | The mean house price increases and the median house price stays the same.
|
Answers
| Is Correct? | Answer |
| x | The mean house price decreases and the range of house prices decreases. |
| ✓ | The mean house price increases and the median house price stays the same. |
| x | The mean house price stays the same and the median house price decreases. |
| x | The mean house price increases and the median house price decreases. |