SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

CORE, FUR1 2021 VCAA 5 MC

 The stem plot below shows the height, in centimetres, of 20 players in a junior football team.
 

A player with a height of 179 cm is considered an outlier because 179 cm is greater than

  1. 162 cm
  2. 169 cm
  3. 172.5 cm
  4. 173 cm
  5. 175.5 cm
Show Answers Only

`E`

Show Worked Solution

`Q_1 = (148 + 148)/2 = 148`

`Q_3 = (158 + 160)/2 = 159`

`IQR = 159 – 148 = 11`

`text{Upper fence}` `= Q_3 + 1.5 xx IQR`
  `= 159 + 1.5 xx 11`
  `= 175.5`

 
`=> E`

CORE, FUR2 2020 VCAA 1

Body mass index (BMI), in kilograms per square metre, was recorded for a sample of 32 men and displayed in the ordered stem plot below.
  

  1. Describe the shape of the distribution.   (1 mark)

  2. Determine the median BMI for this group of men.   (1 mark)

  3. People with a BMI of 25 or over are considered to be overweight.
  4. What percentage of these men would be considered to be overweight?   (1 mark)

Show Answers Only
  1. `text(Positively skewed)`
  2. `24.55`
  3. `37.5 text(%)`
Show Worked Solution

a.   `text(Positively skewed)`
 

b.   `32\ text(data points)`

`text(Median)` `= text(16th + 17th)/2`
  `= (24.5 + 24.6)/2`
  `= 24.55`

 

c.    `text(Percentage)` `= 12/32 xx 100`
    `= 37.5%`

CORE, FUR2 2019 VCAA 1

Table 1 shows the day number and the minimum temperature, in degrees Celsius, for 15 consecutive days in May 2017.
 

  1. Which of the two variables in this data set is an ordinal variable?   (1 mark)

The incomplete ordered stem plot below has been constructed using the data values for days 1 to 10.

  1. Complete the stem plot above by adding the data values for days 11 to 15.   (1 mark)

  2. The ordered stem plot below shows the maximum temperature, in degrees Celsius, for the same 15 days.

     

     

    Use this stem plot to determine

  3.  i. the value of the first quartile `(Q_1)`   (1 mark)

  4. ii. the percentage of days with a maximum temperature higher than 15.3 °C.   (1 mark)

Show Answers Only
  1. `text(Day number)`
  2. `text(See Worked Solutions)`
    1. `12.2`
    2. `text(20%)`
Show Worked Solution

a.   `text(Day number)`

b.  

 
c.i.   `15\ text(data points)`

 `Q_1 = 12.2\ text{(4th data point)}`
 

c.ii.    `text(% Days)` `= 3/15 xx 100`
    `= 20%`

CORE, FUR1 2019 VCAA 4-5 MC

The stem plot below shows the distribution of mathematics test scores for a class of 23 students.
 


 

Part 1

For this class, the range of test scores is

  1. 22
  2. 40
  3. 45
  4. 49
  5. 89

 
Part 2

For this class, the interquartile range (IQR) of test scores is

  1. 14.5
  2. 17.5
  3. 18
  4. 24
  5. 49
Show Answers Only

`text(Part 1:)\ D`

`text(Part 2:)\ C`

Show Worked Solution

`text(Part 1)`

`text(Range)` `= 89 – 40`
  `= 49`

`=> D`

 
`text(Part 2)`

`text(23 data points)`

`Q_1 =\ text(6th data point) =57`

`Q_3 =\ text(18th data point) = 75`

`text(IQR)` `= 75 – 57`
  `= 18`

 
`=>  C`

CORE, FUR2 2010 VCAA 1

Table 1 shows the percentage of women ministers in the parliaments of 22 countries in 2008.
 

CORE, FUR2 2010 VCAA 11
 

  1. What proportion of these 22 countries have a higher percentage of women ministers in their parliament than Australia?  (1 mark)

  2. Determine the median, range and interquartile range of this data.  (2 marks)

The ordered stemplot below displays the distribution of the percentage of women ministers in parliament for 21 of these countries. The value of Canada is missing.
 

    CORE, FUR2 2010 VCAA 12
 

  1. Complete the stemplot above by adding the value for Canada.  (1 mark)

  2. Both the median and the mean appropriate measures of centre for this distribution.
  3. Explain why.  (1 mark)

Show Answers Only

  1. `0.5`
  2. `text(Median= 28, Range = 56, IQR = 17)`
  3. `1 | 246`
  4. `text(S)text(ince the distribution is approximately)`

     

    `text(symmetric, the median and mean will be)`

     

    `text(appropriate measures of the centre.)`

Show Worked Solution

a.   `11/22 = 0.5`

b.   `text(22 data points,)`

`text(Median)` `=\ text{(11th + 12th)}/2`
  `= (32 + 24)/2`
  `= 28`

 

`text(Range)` `= 56 – 0`
  `= 56`

 
`Q_1=21 and Q_3=38`

`text(IQR)` `= 38 – 21`
  `= 17`

 

c.   `1 | 2 quad 4 quad 6`

♦♦ Part (d) was “poorly answered”.
MARKER’S COMMENT: The use of “symmetric” gained a mark while “evenly distributed” was deemed too vague.

 

d.   `text(S)text(ince the distribution is approximately)`

`text(symmetric, the median and mean will be)`

`text(appropriate measures of the centre.)`

CORE, FUR2 2011 VCAA 1

The stemplot in Figure 1 shows the distribution of the average age, in years, at which women first marry in 17 countries.
 

CORE, FUR2 2011 VCAA 11
 

  1. For these countries, determine
    1. the lowest average age of women at first marriage  (1 mark)

    2. the median average age of women at first marriage  (1 mark)

The stemplot in Figure 2 shows the distribution of the average age, in years, at which men first marry in 17 countries.
 

CORE, FUR2 2011 VCAA 12

  1. For these countries, determine the interquartile range (IQR) for the average age of men at first marriage.  (1 mark)

  2. If the data values displayed in Figure 2 were used to construct a boxplot with outliers, then the country for which the average age of men at first marriage is 26.0 years would be shown as an outlier.
  3. Explain why is this so. Show an appropriate calculation to support your explanation.  (2 marks)

Show Answers Only

    1. `text(25 years)`
    2. `text(28.2 years)`
  2. `text(1.1 years)`
  3. `text(See Worked Solutions)`

Show Worked Solution

a.i.   `text(Lowest age = 25 years)`

 

a.ii.   `text(Median age of 17 data point is the)`

   `text(9th point = 28.2 years)`

 

b.   `Q_L = 29.9, Q_U = 31.0,`

`:. IQR` `= Q_U − Q_L`
  `= 31.0 − 29.9`
  `= 1.1\ text(years)`

 

c.   `1.5 xx IQR = 1.5 xx 1.1 = 1.65`

MARKER’S COMMENT: Many students correctly calculated 28.25 but then failed to discuss how 26.0 related to it.

`Q_1 – IQR` `=29.9-1.65`
  `=28.25`

 

`text(S)text(ince  26.0 < 28.25,)`

`:. 26.0\ text(is an outlier.)`

CORE, FUR1 2015 VCAA 1 MC

The stem plot below displays the average number of decayed teeth in 12-year-old children from `31` countries.
 

     CORE, FUR1 2015 VCAA 1 MC
 

Based on this stem plot, the distribution of the average number of decayed teeth for these countries is best described as

  1. negatively skewed with a median of 15 decayed teeth and a range of 45
  2. positively skewed with a median of 15 decayed teeth and a range of 45
  3. approximately symmetric with a median of 1.5 decayed teeth and a range of 4.5
  4. negatively skewed with a median of 1.5 decayed teeth and a range of 4.5
  5. positively skewed with a median of 1.5 decayed teeth and a range of 4.5
Show Answers Only

`E`

Show Worked Solution

`text(Median = 16th value)\ = 1.5`

`text(Range)\ = 4.7-0.2=4.5`

`text(The clear tail to the upper end of values shows that the)`

`text(data is positively skewed.)`

`=> E`

CORE, FUR1 2014 VCAA 1 MC

The following ordered stem plot shows the areas, in square kilometres, of 27 suburbs of a large city.
 

   

The median area of these suburbs, in square kilometres, is

A.   `3.0` 

B.   `3.1` 

C.   `3.5`

D.   `30.0`

E.   `30.5`

Show Answers Only

`B`

Show Worked Solution

`text(# Data points = 27)`

`text(Median is)\ \ \ (27+1)/2 = text(14th)`

`∴ text(Median)=3.1\ text(km²)`

`=>  B`

CORE, FUR1 2012 VCAA 5 MC

The temperature of a room is measured at hourly intervals throughout the day.

The most appropriate graph to show how the temperature changes from one hour to the next is a

A.  boxplot.

B.  stem plot.

C.  histogram.

D.  time series plot.

E.  two-way frequency table.

Show Answers Only

`D`

Show Worked Solution

` text (A time series plot is best because the temperature)`

`text(is measured at regular time intervals.)`

`rArr D`

CORE, FUR1 2013 VCAA 1-2 MC

The following ordered stem plot shows the percentage of homes connected to broadband internet for 24 countries in 2007.
 

   CORE, FUR1 2013 VCAA 1-2 MC 
 

 Part 1

The number of these countries with more than 22% of homes connected to broadband internet in 2007 is

A.    `4`

B.    `5`

C.  `19`

D.  `20`

E.  `22`

 

Part 2

Which one of the following statements relating to the data in the ordered stem plot is not true?

A.  The minimum is 16%.

B.  The median is 30%.

C.  The first quartile is 23.5%

D.  The third quartile is 32%.

E.  The maximum is 38%.

Show Answers Only

`text(Part 1:)\ C`

`text(Part 2:)\ B`

Show Worked Solution

`text(Part 1)`

`text(There are 19 values greater than 22%)`

      `=>  C`

 

`text(Part 2)`

`text(24 data points.)` 

`text(Median)` `= text(12th + 13th)/2`
  `=(29+30)/2`
  `=29.5`

 

`:.\ text(B is incorrect and all other  statements can)`

`text(be verified as true.)`

`=>  B`