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Statistics, NAP-L4-CA21

Mr Squiggle bought 13 pencils.

He bought:

  • one packet of 10 pencils for $14.50, and
  • another packet of 3 pencils for $5.65

What is the mean price of the 13 pencils?

`$1.45` `$1.50` `$1.55` `$1.88`
 
 
 
 
Show Answers Only

`$1.55`

Show Worked Solution
`text(Total cost)` `= 14.50 + 5.65`
  `= $20.15`
   
`:.\ text(Mean price)` `= 20.15/13`
  `= $1.55`

Statistics, NAP-L4-CA10

In Wadonga, there are 29 538 people.

Each day, the average person uses 168 litres of water.

Which of these gives the best estimate for the total number of litres of water used in Wadonga each day?

`30\ 000 xx 200` `30\ 000 xx 100` `30\ 000 ÷ 200` `30\ 000 ÷ 100`
 
 
 
 
Show Answers Only

`30\ 000 xx 200`

Show Worked Solution
`text(Total litres)` `=\ text(litres per person × total people)`  
  `= 30\ 000 xx 200`  
     

`text{(168 is closer to 200 than 100 and}`

  `text{will give a better estimate.)}`

Statistics, NAP-K4-CA03

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.
 

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

 
 It increases
 
 It decreases
 
 There is no change
 
 It is not possible to tell
Show Answers Only

`text(Increases)`

Show Worked Solution

`text(The mean increases because the shortest distance is)`

`text(removed from the data set.)`

Statistics, NAP-A4-NC31

This graph shows the number of goals a soccer team scored in a full season.
 

 
One match incorrectly recorded the team scoring no goals when they scored one.

What effect does this have on the mean and mode of the data?

 
 The mean decreases and the mode changes.
 
 The mean increases and the mode changes.
 
 The mean decreases and the mode does not change.
 
 The mean increases and the mode does not change.
Show Answers Only

`text(The mean increases and the mode does not change.)`

Show Worked Solution

`text(Total goals scored in the season increases by one.)`

`=>\ text(mean increases.)`

`text{The mode of 2 goals scored in a match (9 times)}`

`text(remains the mode after the change.)`

`:.\ text(The mean increases and the mode does not change.)`

Statistics, NAP-A4-CA32

A survey asked 9 students in Year 7 how many times they had travelled overseas.
 

 

 
Which of the following is true for this data?

 
 mean > median > mode
 
 mean > median < mode
 
 mean = median = mode
 
 mean = median > mode
Show Answers Only

`text(mean = median > mode)`

Show Worked Solution

`text(Mode = 2)`

`text(Median = 5th number = 3)`

`text(Mean)` `= (0 + 2 + 2 + 2 + 3 + 4 + 4 + 5 + 5)/9`
  `= 27 ÷ 9`
  `= 3`

 

`:.\ text(mean = median > mode)`

Statistics, NAP-A4-CA22

Malcolm will travel by bus for 18 days during November.

A daily ticket will cost him $7.40 and a monthly ticket will cost him $109.80.

What is Malcolm's average daily saving on days he travels by bus if he buys a monthly ticket?

`$1.30` `$6.10` `$23.40` `$125.80`
 
 
 
 
Show Answers Only

`$1.30`

Show Worked Solution

`text(C)text(ost of daily tickets)`

`= 18 xx 7.40`

`= $133.20`

`text(Monthly ticket saving)`

`= 133.20 – 109.8`

`= $23.40`

 

`:.\ text(Average daily saving)`

`= 23.40/18`

`= $1.30`

Statistics, NAP-A4-CA04

This table summarises the time Tutty spent training her parrot over five days.
 

 
What was the average (mean) time for training the parrot each day?

`text(30 minutes)` `text(56 minutes)` `text(66 minutes)` `text(280 minutes)`
 
 
 
 
Show Answers Only

`text(56 minutes)`

Show Worked Solution
`text(Average)` `= (25 + 55 + 60 + 94 + 46)/5`
  `= 280/5`
  `= 56\ text(minutes)`

Statistics, NAP-B4-NC19

Here is a set of 8 scores.

  `1, \ 7, \ 8, \ 9, \ 9, \ 16, \ 16, \ 28`

What will change if score 28 is removed from the set?

 
 mean and mode
 
 mean and median
 
 mean only
 
 mean and range
Show Answers Only

`text(mean and range)`

Show Worked Solution

`text(Mean will decrease.)`

`text(Mode will remain unchanged.)`
 

`text(Median of 8 scores)`

`= {text(4th)\ +\ text(5th)}/2=(9 + 9)/2=9`

`text(Median of 7 scores)`

`= 4 text(th score)=9`
 

`text(Range of 8 scores) =28 – 1 =27`

`text(Range of 7 scores) = 16 – 1 = 15`
 

`:.\ text(Mean and range will change.)`

Statistics, NAP-B4-CA28 SA

A kindergarten class has 15 students. The average (mean) weight of a child in the class is 24 kilograms.

5 new children join the class and the average class weight increases to 26 kilograms.

What was the average weight of the 5 new children?

    kilograms
Show Answers Only

`32`

Show Worked Solution

`text(Total weight of original class)`

`= 15 xx 24`

`= 360\ text(kilograms)`

 

`text(Extra weight from 5 new children)`

`= (26 xx 20) – 360`

`= 520 – 360`

`= 160\ text(kg)`

 

`:.\ text(Average weight of new children)`

`= 160/5`

`= 32\ text(kilograms)`

Statistics, NAP-C4-CA29

The points scored by a basketball team in their first 11 games of the season is recorded.

  `62, \ 71, \ 72, \ 76, \ 63, \ 66, \ 60, \ 77, \ 72, \ 72, \ 71`

In the 12th game, they scored 58.

Which of these values would increase?

`text(mean)` `text(mode)` `text(median)` `text(range)`
 
 
 
 
Show Answers Only

`text(range)`

Show Worked Solution

`text(Consider each option:)`

`text(Mean – decreases)`

`text(Mode – unchanged as 72)`

`text(Median – unchanged at 71)`

`text{Range – increases (highest – lowest)}`

Statistics, NAP-D4-CA16

Lea collects comic books.

She sells some of them.

The selling prices are listed below.

  `$5, \ $7, \ $7, \ $7, \ $9, \ $12, \ $12, \ $14, \ $35`

What is their mean (average) price?

`$9` `$10` `$11` `$12`
 
 
 
 
Show Answers Only

`$12`

Show Worked Solution

`5 + 7 + 7 + 7 + 9 + 12 + 12 + 14 + 35 = 108`

`:.\ text(Average selling price)` `=108/9`
  `=$12`

Statistics, NAP-D4-NC17

In 4 games of netball, Finn scores 7, 14, 11 and 11 goals.

In the fifth game, she scores a season high 23 goals.

Which of these will not change after Finn's fifth game.

 
 the median of her goal scores
 
 the mean of her goal scores
 
 the range of her goal scores
 
 the total number of her goal scores
Show Answers Only

`text(the median of her goal scores)`

Show Worked Solution

`text(After 4 games,)`

`text(Median)` `= (11 + 11)/2 = 11`

 

`text(After 5 games,)`

`text(Median)` `=\ text(3rd highest score)`
  `=\ 11`

 

`:.\ text(The median will not change.)`

Statistics, NAP-C4-NC20

A vet measured the height of 21 dogs that came through his clinic.

The vet recorded the length of each dog.
  

 
What is the median length?

`52\ text(cm)` `53\ text(cm)` `56\ text(cm)` `57\ text(cm)`
 
 
 
 
Show Answers Only

`text(52 cm)`

Show Worked Solution

`text(The median of 21 data points is the 11th)`

`text(data point.)`

`:.\ text(The median is 52.)`

Statistics, NAP-F4-CA23

A college basketball team has 10 players with the following heights.

   `182, \ 172, \ 165, \ 202, \ 190, \ 207, \ 195, \ 195, \ 188, \ 195`

What is the range of heights?

 
 `30\ text(centimetres)`
 
 `35\ text(centimetres)`
 
 `37\ text(centimetres)`
 
 `42\ text(centimetres)`
Show Answers Only

`42\ text(centimetres)`

Show Worked Solution
`text(Range)` `=  207 – 165`
  `= 42\ text(centimetres)`

Statistics, NAP-F4-CA22 SA

A school's drama class puts on a play over five nights.

The play is open to the public and the numbers of tickets sold are shown in the table below.
 

 
The cost of each ticket was $15.

What was the mean amount of money collected from ticket sales per night?

$ 
Show Answers Only

`$2850`

Show Worked Solution

`text(Mean number of tickets sold)`

`= (210 + 170 + 180 + 170 + 220)/5`

`=190`

 

`:.\ text(Mean tickets sales)` `= 190 xx 15`
  `= $2850`

Statistics, NAP-F4-CA10

In 2009, an estimated 1.7 million registrations were made by Australian children to participate in organised sport outside school.

The average cost of one registration was estimated at  $392.

What was the total amount paid for registrations in 2009?

`$4\ 336\ 700` `$666\ 400` `$4\ 336\ 700\ 000` `$666\ 400\ 000`
 
 
 
 
Show Answers Only

`$666\ 400\ 000`

Show Worked Solution

`1\ 700\ 000 xx 392`

`=$666\ 400\ 000`

Statistics, NAP-F4-NC17

Riley's basketball team has 5 players.

The height of each player is listed below (in cm):

   `155, \ 180, \ 160, \ 175, \ 180`

What is the median height of these players?

`160\ text(cm)` `170\ text(cm)` `175\ text(cm)` `180\ text(cm)`
 
 
 
 
Show Answers Only

`175\ text(cm)`

Show Worked Solution

`text{Heights from shortest to tallest are:}`

`155, 160, 175, 180, 180`

`text(Median)` `= 3text(rd height)`
  `= 175\ text(cm)`

Statistics, NAP-I4-NC17

The mean height of students at a Year 9 class is 155 cm.

The median height of the same class is 145 cm.

A new student joins the class who is 165 cm tall.

Which of these is possible?

 
 The mean height stays the same and the median height increases.
 
 The mean height stays the same and the median height decreases.
 
 The mean height decreases and the median height increases.
 
 The mean height increases and the median height stays the same.
Show Answers Only

`text(It is possible for the mean height to increase and)`

`text(the median height to stay the same.)`

Show Worked Solution

`text(It is possible for the mean height to increase and)`

`text(the median height to stay the same.)`