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Data Analysis, GEN1 2024 NHT 4 MC

The histogram below shows the distribution of the GDP per capita, in dollars per year, for a sample of 22 countries in 2021 plotted on a logarithmic (base 10) scale.
 

Australia is one of these 22 countries, and its GDP per capita value is $56 281.

Which one of the columns marked \(\text{A, B, C, D}\) or \(\text{E}\) would contain Australia's value?

  1. \(\text{A}\)
  2. \(\text{B}\)
  3. \(\text{C}\)
  4. \(\text{D}\)
  5. \(\text{E}\)
Show Answers Only

\(C\)

Show Worked Solution

\(\log_{10}56\,281 = x\ \Rightarrow\ x=4.750…\)

\(\text{Column C includes \(x\) between 4.6 – 4.8.}\)

\(\Rightarrow C\)

Data Analysis, GEN1 2024 VCAA 3-4 MC

The histogram below displays the population density, in people per km\(^{2}\), of the 27 countries in the European Union in 2021. The histogram has a logarithmic (base 10) scale.
 

 
Part 1

The median value occurs in a column with a frequency of

  1. 2
  2. 3
  3. 6
  4. 9

 
Part 2

There is one outlier at the upper end of the histogram. This value could be

  1. 330
  2. 1330
  3. 2030
  4. 2730
Show Answers Only

Part 1: \(D\)

Part 2: \(C\)

Show Worked Solution

Part 1

\(\text{There are 27 scores}\ \ \rightarrow\ \ \text{median is 14th score.}\)

\(\text{Column frequency }= 9\)

\(D\)

 
Part 2

\(10^{3.2} <\log\text{(Population Density)}<10^{3.4}\)

\(1585 <\log\text{(Population Density)}<2512\)

\(\Rightarrow C\)

Data Analysis, GEN1 2022 VCAA 6 MC

The histogram below displays the distribution of spleen weight for a sample of 32 seals.

The histogram has a \(\log _{10}\) scale.
 

The number of seals in this sample with a spleen weight of 1000 g or more is

  1. 7
  2. 8
  3. 17
  4. 25
  5. 27
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Given}\ \log_{10} 1000 = 3\ \ (10^3 = 1000) \)

\(\text{Number of seals} = 8 + 9 + 7 + 1 = 25\)

\(\Rightarrow D\)

Data Analysis, GEN1 2023 VCAA 6 MC

The histogram below displays the distribution of prices, in dollars, of the cars for sale in a used-car yard.

The histogram has a logarithm (base 10) scale.
 

Six of the cars in the yard have the following prices:

\($2450, \ $3175, \ $4999, \ $8925, \ $10\ 250, \ $105\ 600\)

How many of the six car prices listed above are in the modal class interval?

  1. 1
  2. 2
  3. 3
  4. 4
  5. 6
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Modal class interval is 3.5 – 4.0}\)

\(\text{Take the log}_{10}\ \text{of each car price:}\)

\(\log_{10}2450 = 3.389\ \cross, \ \log_{10}3175 = 3.501\ \checkmark\)

\(\log_{10}4999 = 3.69\ \checkmark, \ \log_{10}8925 = 3.95\ \checkmark\)

\(\log_{10}10\ 250 = 4.01\ \cross, \ \log_{10}105\ 600 = 5.02\ \cross\)

\(\Rightarrow C\)

CORE, FUR1 2020 VCAA 5 MC

The histogram below shows the distribution of weight, in grams, for a sample of 20 animal species. The histogram has been plotted on a `log_10` scale.
 


 

The percentage of these animal species with a weight of less than 10 000 g is

  1. 17%
  2. 70%
  3. 75%
  4. 80%
  5. 85%
Show Answers Only

`E`

Show Worked Solution

`log_10 10\ 000 = 4`

`text(Animals)\ (x <= 4) = 3 + 2 + 12 = 17`

`:.\ text(Percentage)` `= 17/20`
  `= 85%`

`=>  E`

CORE, FUR1 2017 VCAA 4 MC

The histogram below shows the distribution of the log10 (area), with area in square kilometres, of 17 islands.
 

The median area of these islands, in square kilometres, is between

  1. 2 and 3
  2. 3 and 4
  3. 10 and 100
  4. 1000 and 10 000
  5. 10 000 and 100 000
Show Answers Only

`D`

Show Worked Solution

`text(17 data points)\ =>\ text(median is 9th)`

`3 < text(log)_10(text(area)) < 4`

`1000 < text(area) < 10\ 000`

`=> D`

CORE, FUR1 2016 VCAA 6-7 MC

Part 1

The histogram below shows the distribution of the number of billionaires per million people for 53 countries.
 

Using this histogram, the percentage of these 53 countries with less than two billionaires per million people is closest to

  1. `text(49%)`
  2. `text(53%)`
  3. `text(89%)`
  4. `text(92%)`
  5. `text(98%)`

 

Part 2

The histogram below shows the distribution of the number of billionaires per million people for the same 53 countries as in Part 1, but this time plotted on a `log_10` scale.
 

Based on this histogram, the number of countries with one or more billionaires per million people is

  1.   `text(1)`
  2.   `text(3)`
  3.   `text(8)`
  4.   `text(9)`
  5. `text(10)`
Show Answers Only

`text(Part 1:)\ D`

`text(Part 1:)\ E`

Show Worked Solution

`text(Part 1)`

`text(Percentage with less than 2)`

`= text(countries with less than 2)/text(total countries)`

`= 49/((49 + 2 + 1 + 1))`

`= 49/53`

`~~ 92.4text(%)`

`=> D`

 

`text(Part 2)`

`text(Let)\ \ x=\ text(number of billionaires per million,)`

`text(Number of countries where)\ \ x >= 1,`

♦ Mean mark 45%.
MARKER’S COMMENT: On a `log_10` scale, 1 is plotted as 0 because `log_10\ 1 = 0`, or `10^0=1`

`=> log_10 x >= 0`

`:.\ text(Number of countries)`

`= 9 + 1`

`= 10`

`=> E`