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CORE, FUR1 2019 VCAA 1-3 MC

The histogram below shows the distribution of the population size of 48 countries in 2018.

Part 1

The number of these countries with a population size between 5 million and 20 million people is

  1.  11
  2.  17
  3.  23
  4.  34
  5.  35

 
Part 2

The shape of this histogram is best described as

  1. positively skewed with no outliers. 
  2. positively skewed with outliers.
  3. approximately symmetric.
  4. negatively skewed with no outliers.
  5. negatively skewed with outliers.

 
Part 3

The histogram below shows the population size for these 48 countries plotted on a `log_10` scale.

Based on this histogram, the number of countries with a population size that is less than `100\ 000` people is

  1. 1
  2. 5
  3. 7
  4. 8
  5. 48
Show Answers Only

`text(Part 1:)\ B`

`text(Part 2:)\ B`

`text(Part 3:)\ D`

Show Worked Solution

Part 1

`text{Countries (5 – 20 million)}`

`= 11 + 4 + 2`

`= 17`

`=> B`
 

Part 2

`text(Histogram is positively skewed with outliers.)`

`=> B`
 

Part 3

`log_10 100\ 000 = 5`

`text{Countries (population < 100 000)}`

`= 1 + 7`

`= 8`

`=> D`

CORE, FUR2 2007 VCAA 1

The histogram below shows the distribution of mean yearly rainfall (in mm) for Australia over 103 years.
 

CORE, FUR2 2007 VCAA 1

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

  2. Use the histogram to determine
  3.  i. the number of years in which the mean yearly rainfall was 500 mm or more.   (1 mark)

  4. ii. the percentage of years in which the mean yearly rainfall was between 500 mm and 600 mm.
  5.     Write your answer correct to one decimal place.  (1 mark)

Show Answers Only
  1. `text(Positively skewed)`
    1. `26`
    2. `text(19.4%)`
Show Worked Solution

a.   `text(Positively skewed.)`
 

b.i.   `text{Years with rainfall over 500 mm}`

`=13+7+3+1+1+1 =26`
 

b.ii.   `text{Years with rainfall between 500 and 600 mm (%)}`

`=20/103 xx 100text(%)`

`= 19.41…`

`=19.4 text{%  (1 d.p.)}`

CORE, FUR2 2014 VCAA 1

The segmented bar chart below shows the age distribution of people in three countries, Australia, India and Japan, for the year 2010.
 

Core, FUR2 2015 VCAA 1

  1. Write down the percentage of people in Australia who were aged 0 – 14 years in 2010.
  2. Write your answer, correct to the nearest percentage.  (1 mark)

  3. In 2010, the population of Japan was 128 000 000.
  4. How many people in Japan were aged 65 years and over in 2010?  (1 mark)

  5. From the graph above, it appears that there is no association between the percentage of people in the 15 – 64 age group and the country in which they live.
  6. Explain why, quoting appropriate percentages to support your explanation.  (1 mark)

Show Answers Only

  1. `text(19%)`
  2. `29\ 440\ 000`
  3. `text(The percentages of people in the 15 – 64 age group)` 
    `text(in each country is: Australia 67%, India 64%, and)` 
    `text(Japan 64%.)` 
    `text(S)text(ince the percentages are very close no matter which)`
    `text(country this age group belonged to, there is no association.)`

Show Worked Solution

a.   `text(19%)`

 

b.   `text(From the graph, 23% of Japan’s population is 65 or over.)`

`:.\ text(The number of people 65 or over)`

`=128\ 000\ 000 xx 23/100`

`= 29\ 440\ 000`

 

c.   `text(The percentages of people in the 15 – 64 age group)`

♦ Mean mark 41%.

`text(in each country is: Australia 67%, India 64%, and)`

`text(Japan 64%.)`

`text(S)text(ince the percentages are very close no matter which)`

`text(country this age group belonged to, there is no association.)`

CORE, FUR1 2011 VCAA 1-3 MC

The histogram below displays the distribution of the percentage of Internet users in 160 countries in 2007.
 

Part 1

The shape of the histogram is best described as

A.   approximately symmetric.

B.   bell shaped. 

C.   positively skewed.

D.   negatively skewed.

E.   bi-modal.

 

Part 2

The number of countries in which less than 10% of people are Internet users is closest to

A.   `10`

B.   `16`

C.   `22`

D.   `32`

E.   `54`

 

Part 3

From the histogram, the median percentage of Internet users is closest to

A.   `10text(%)`

B.   `15text(%)`

C.   `20text(%)`

D.   `30text(%)`

E.   `40text(%)`

Show Answers Only

`text(Part 1:)\ C`

`text(Part 2:)\ E`

`text(Part 3:)\ C`

Show Worked Solution

`text(Part 1)`

`text(The shape of the histogram has a definite tail)`

`text(on the right side which means it is positively)`

`text(skewed.)`

`=>  C`

 

`text(Part 2)`

`text(The histogram shows that 32% of countries fall)`

`text(between 0–5%, and 22% fall between 5–10%.)`

`:.\ text(Users below 10%)`

`= 32 + 22`

`= 54 text(%)`

`=>  E`

 

`text(Part 3)`

♦ Mean mark 45%.

`text(Total countries = 160)`

`text(Adding bars from the left hand side, there are)`

`text{80 countries in the first 4 bars (i.e. half of 160).}`

`:.\ text(Median is closest to 20%)`

`=>  C`