50107

Question

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Worked Solution

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Variant 0

DifficultyLevel

536

Question

Five students do a standing long jump at their athletics carnival and the length of their jumps, in centimetres, are recorded in the table below.


Student Rob Mary Stew Lenny Kath
Distance (cm) 70 75 66 95 50

If Kath's distance is removed from the data, what happens to the mean distance that is jumped from this group?

Worked Solution

The mean increases because the shortest distance is removed from the data set.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Five students do a standing long jump at their athletics carnival and the length of their jumps, in centimetres, are recorded in the table below.
>>| Student | Rob| Mary | Stew | Lenny | Kath | |:-:|:-:|:-:|:-:|:-:|:-:| | Distance (cm) | 70|75|66|95|50|

If Kath's distance is removed from the data, what happens to the mean distance that is jumped from this group?
workedSolution
The mean increases because the shortest distance is removed from the data set.
correctAnswer
It increases

Answers

Is Correct?Answer
✓

It increases

x

It decreases

x

There is no change

x

It is not possible to tell

Variant 1

DifficultyLevel

537

Question

Five competitors throw the discus at their athletics carnival and the length of their throws, in metres, are recorded in the table below.


Competitor Bill Tracey Allen Kelvin Jen
Distance (m) 9.7 10.2 10.9 12.1 9.6

If Kelvin's distance is removed from the data, what happens to the mean distance that is thrown from this group?

Worked Solution

The mean decreases because the longest distance is removed from the data set.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Five competitors throw the discus at their athletics carnival and the length of their throws, in metres, are recorded in the table below.
>>| Competitor | Bill| Tracey | Allen | Kelvin | Jen | |:-:|:-:|:-:|:-:|:-:|:-:| | Distance (m) | 9.7|10.2|10.9|12.1|9.6|

If Kelvin's distance is removed from the data, what happens to the mean distance that is thrown from this group?
workedSolution
The mean decreases because the longest distance is removed from the data set.
correctAnswer
It decreases

Answers

Is Correct?Answer
x

It increases

✓

It decreases

x

There is no change

x

It is impossible to tell

Variant 2

DifficultyLevel

538

Question

Five friends complete a fun run on the weekend and their times for the 5 kilometre event, in minutes and seconds, are recorded in the table below.


Name John Carrie Beau Zim Kelly
Times 25 m 35 s 24 m 15 s 21 m 08 s 19 m 46 s 31 m 18 s

If Kelly's time is removed from the data, what happens to the median time that is run by this group?

Worked Solution

Scores in order: 19 m 46 s, 21 m 8 s, 24 m 15 s, 25 m 35s , 31 m 18 s

The median was originally 24 m 15 s and the new median, with the highest score removed, is the average of 21 m 08 s and 24 m 15 s which will be less than the original.

Therefore, the median decreases because the 5th score is removed from the data set.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Five friends complete a fun run on the weekend and their times for the 5 kilometre event, in minutes and seconds, are recorded in the table below.
>>| Name | John| Carrie | Beau | Zim | Kelly | |:-:|:-:|:-:|:-:|:-:|:-:| | Times | 25 m 35 s|24 m 15 s|21 m 08 s|19 m 46 s|31 m 18 s|

If Kelly's time is removed from the data, what happens to the median time that is run by this group?
workedSolution
Scores in order: 19 m 46 s, 21 m 8 s, 24 m 15 s, 25 m 35s , 31 m 18 s The median was originally 24 m 15 s and the new median, with the highest score removed, is the average of 21 m 08 s and 24 m 15 s which will be less than the original. Therefore, the median decreases because the 5th score is removed from the data set.
correctAnswer
It decreases

Answers

Is Correct?Answer
x

There is no way of telling

x

It increases

✓

It decreases

x

It stays the same

Variant 3

DifficultyLevel

539

Question

Five pythons at the Reptile Park are measured and their lengths, in centimetres, are recorded in the table below.


Python Burmese Indian Sumatran Borneo Angolan
Length (cm) 270 325 166 128 183

If the Sumatran Python is removed from the data, what happens to the median length of the pythons in this group?

Worked Solution

Scores in order: 128, 166, 183, 270, 325

The median was originally 183 cm and the new median is the average of 183 cm and 270 cm which will be more than the original.

Therefore, the median increases because the 2nd shortest length is removed from the data set.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Five pythons at the Reptile Park are measured and their lengths, in centimetres, are recorded in the table below.
>>| Python| Burmese| Indian | Sumatran | Borneo | Angolan | |:-:|:-:|:-:|:-:|:-:|:-:| | Length (cm) | 270|325|166|128|183|

If the Sumatran Python is removed from the data, what happens to the median length of the pythons in this group?
workedSolution
Scores in order: 128, 166, 183, 270, 325 The median was originally 183 cm and the new median is the average of 183 cm and 270 cm which will be more than the original. Therefore, the median increases because the 2nd shortest length is removed from the data set.
correctAnswer
It increases

Answers

Is Correct?Answer
x

There is no change

x

There is no way of telling

x

It decreases

✓

It increases

Variant 4

DifficultyLevel

539

Question

Dan caught 5 fish on the weekend and their weights, in kilograms, are recorded in the table below.


Fish Bream 1 Bream 2 Kingfish Flathead Snapper
Weight (kg) 1.1 1.4 5.6 2.2 1.8

If Bream 2 is removed from the data, what happens to the range of weights for this group?

Worked Solution

Original range  5.6 −- 1.1 = 4.5

Range after Bream 2 weight removed  5.6 −- 1.1 = 4.5.

Therefore, the range stays the same if Bream 2 is removed from the data set.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Dan caught 5 fish on the weekend and their weights, in kilograms, are recorded in the table below.
>>| Fish | Bream 1| Bream 2 | Kingfish | Flathead | Snapper | |:-:|:-:|:-:|:-:|:-:|:-:| | Weight (kg) | 1.1 | 1.4 | 5.6 | 2.2 | 1.8 |

If Bream 2 is removed from the data, what happens to the range of weights for this group?
workedSolution
Original range  5.6 $-$ 1.1 = 4.5 Range after Bream 2 weight removed  5.6 $-$ 1.1 = 4.5. Therefore, the range stays the same if Bream 2 is removed from the data set.
correctAnswer
It stays the same

Answers

Is Correct?Answer
x

There is no way of telling

✓

It stays the same

x

It increases

x

It decreases

Variant 5

DifficultyLevel

540

Question

Five people measure their resting heart rate and their results, in beats per minute (BPM), are recorded in the table below.


Name Cliff Carina Cathy Clive Corinne
Resting Heart Rate (BPM) 72 55 79 45 64

If Cathy's resting heart rate is removed from the data, what happens to the range of heart rates for this group?

Worked Solution

Original range  79 −- 45 = 34

Range after Cathy's data point is removed  72 −- 45 = 27.

Therefore, the range decreases if Cathy's resting heart rate measure is removed from the data set.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Five people measure their resting heart rate and their results, in beats per minute (BPM), are recorded in the table below.
>>| Name | Cliff| Carina | Cathy | Clive | Corinne | |:-:|:-:|:-:|:-:|:-:|:-:| | Resting Heart Rate (BPM) | 72|55|79|45|64|

If Cathy's resting heart rate is removed from the data, what happens to the range of heart rates for this group?
workedSolution
Original range  79 $-$ 45 = 34 Range after Cathy's data point is removed  72 $-$ 45 = 27. Therefore, the range decreases if Cathy's resting heart rate measure is removed from the data set.
correctAnswer
It decreases

Answers

Is Correct?Answer
x

It stays the same

x

There is no way of telling

x

It increases

✓

It decreases

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