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Interpreting Data, SM-Bank 017

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)

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Interpreting Data, SM-Bank 016 MC

A single back-to-back stem-and-leaf plot would be an appropriate graphical tool to investigate the association between a car’s speed, in kilometres per hour, and the

  1. driver’s age, in years. 
  2. car’s colour (white, red, grey, other). 
  3. average distance travelled, in kilometres.
  4. driver’s sex (female, male).
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Interpreting Data, SM-Bank 015 MC

The back-to-back ordered stem-and-leaf plot below shows the distribution of maximum temperatures (in °Celsius) of two towns, Beachside and Flattown, over 21 days in January.
 


 

For this distribution, which of the following is not true?

  1. The range of temperatures for Flattown is greater than the range of temperatures for Beachside.
  2. The median temperature for Beachside is lower than the median temperature for Flatttown.
  3. The distribution of temperatures for Beachside is positively skewed.
  4. The maximum temperatures for Flattown are generally lower than those of Beachside.
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Interpreting Data, SM-Bank 013 MC

The back-to-back ordered stem plot below shows the female and male smoking rates, expressed as a percentage, in 18 countries.
 

  

For these 18 countries, the smoking rates for females are generally

  1. lower and less variable than the smoking rates for males.
  2. lower and more variable than the smoking rates for males.
  3. higher and less variable than the smoking rates for males.
  4. higher and more variable than the smoking rates for males.
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Interpreting Data, SM-Bank 011

Table 1 shows the number of rainy days recorded in a high rainfall area for each month during 2022.
 

CORE, FUR2 2009 VCAA 11

 

The dot plot below displays the distribution of the number of rainy days for the 12 months of 2008.
 

CORE, FUR2 2009 VCAA 12
 

  1. Circle the dot on the dot plot that represents the number of rainy days in April 2008.  (1 mark)

  2. For the year 2022, determine

     

i.  the median number of rainy days per month  (1 mark)

    1. the percentage of months that have more than 10 rainy days. Write your answer correct to the nearest percent.  (2 marks) 

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CORE, FUR2 2009 VCAA 12 Answer

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Data Analysis, SM-Bank 056 MC

The dot plot below shows the times, in seconds, of 40 runners in the qualifying heats of their 800 m club championship.
 

The shape of this distribution is best described as

  1. positively skewed with one outlier.
  2. approximately symmetric with one outlier.
  3. approximately symmetric with no outliers.
  4. negatively skewed with one outlier.
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Interpreting Data, SM-Bank 009 MC

Michael wants to record how he used the data on his phone last week. He spent time on social media, playing games and listening to music.

Which type of graph would best display this data so Michael could easily see the proportion of time spent on each activity?

  1. A sector graph
  2. A stem-and-leaf plot
  3. A column graph
  4. A dot plot
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Interpreting Data, SM-Bank 006

Hannah is planning an Australian snowboarding trip this winter and is using the chart below to help decide when she should take her holidays and where she should go.
 

Hannah wishes to compare the 2 resorts using statistical information.

  1. Complete the statistical information in the table below.  (2 marks)
     

  2. Using your results in the table above (a), which resort should Hannah choose to visit for her snowboarding holiday?
    Justify your answer with at least 1 reference to the table.  (1 mark)

  3. Complete the table below, and use it to decide in which month Hannah should book her snowboarding holiday?
    Justify your answer with at least 1 reference to the table and 1 to the graph.  (3 marks)

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Interpreting Data, SM-Bank 005

While packaging cookies for the Easter show, Johnny recorded the number of broken cookies in each batch.

Broken cookies per batch

 

  1. Use the data to complete the stem-and-leaf plot below.  (1 mark)
     

  2. What is the range of broken cookies?  (1 mark)
  3. What is the median number of broken cookies?  (1 mark)
  4. Is the distribution symmetrical, positively skewed or negatively skewed?  (1 mark)
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Interpreting Data, SM-Bank 004

Bonn saved $2400 for his annual holiday.

He has drawn the graph below to represent his weekly holiday spending.

  1. What type of graph has been used to display the information?  (1 mark)
  2. Identify the two variables Bonn has used in this graph?  (1 mark)
  3. What is the amount per week that Bonn is expecting to spend on his holiday?  (1 mark)
  4. Bonn needs keep $600 for airfares to return home. With this in mind, what is the maximum number of weeks that Bonn can be on holidays?  (1 mark)
  5. Briefly describe what happens to the amount of savings as the number of weeks on holiday increases?  (1 mark)
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Interpreting Data, SM-Bank 003

Margaret is preparing a report for her supervisor regarding costs for the recent staff development day.

Below is the graph Margaret prepared summarising the cost of the staff lunch for the day.

  1. What type of graph has been used to display the information?  (1 mark)
  2. Identify the two variables Margaret has used in this graph?  (1 mark)
  3. What is the cost of lunch per attendee?  (1 mark)
  4. If the total cost for the staff lunch was $85, how many attendees were there?  (1 mark)
  5. Briefly describe what happens to the total cost of the staff lunch as the number of attendees increases?  (1 mark)
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Displaying Data, SM-Bank 043

While working at the Year 7 camp, Gene counted how many bullseyes the archery group achieved during the afternoon activity.

He summarised the data in the table below.
  

  1. How many students were in the afternoon session of archery?  (1 mark)
  2. How many students scored zero bullseyes?  (1 mark)
  3. Assuming all shots were bullseye attempts, how many shots at the bullseye were made?  (1 mark)
  4. Display this data in a vertical column graph using the grid below.  (2 marks)
     

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Displaying Data, SM-Bank 042

The marks below were recorded by Ms Smith for her students in a recent statistics quiz. The highest possible score was 5.
 


 

  1. Summarise the data using the table below.  (1 mark)

  2. Represent this data as a column graph using the grid below.  (2 marks)
     

     
  3. How many students sat for the quiz?  (1 mark)
  4. If the pass mark was 60%, how many students passed the quiz?  ( 1 mark)
  5. What was the average score achieved in the quiz? Give your answer correct to one decimal place.  (1 mark)
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Displaying Data, SM-Bank 041

Stuart collected the eggs from his free range chickens and recorded the number of eggs he collected each day for two weeks.
 


 

  1. Represent this data as a dot plot using the grid below.  (2 marks)
     

  2. How many eggs were collected altogether?  ( 1 mark)
  3. What is the average number of eggs Stuart collected?  (1 mark)
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Displaying Data, SM-Bank 040

The heights, in centimetres, of David's hockey side are as follows:
 


 

  1. Represent this data as a dot plot using the grid below.  (2 marks)
     

  2. What is the average height of the players in David's hockey team?  (2 marks)
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Displaying Data, SM-Bank 035

The graph below shows the favourite subjects of a group of 100 students.

 

   
  1. How many students in total chose either Technology or English as their favourite subject?  (1 mark)

  2. What percentage of students preferred either Science or PDHPE?  (2 marks)

  3. How many more students chose Maths as their favourite subject than History?  (1 mark)

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Displaying Data, SM-Bank 034

The graph below shows the outdoor activities chosen by students at the Year 7 camp.

 

 
  1. How many students in total chose either high ropes or abseiling?  (1 mark)

  2. What was the average number of students participating in each of the activities? Give your answer correct to the nearest whole number.  (2 marks)

  3. How many more students chose the Giant Swing than Hiking? (1 mark)

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Displaying Data, SM-Bank 033

The graph below shows the times Kerry spent, in minutes, performing different exercises at the gym over the last fortnight.

 

 
  1. How many minutes in total did Kerry spend cycling and walking? (1 mark)

  2. What was the average time per day that Kerry spent exercising over the last fortnight? Give your answer correct to the nearest minute.  (2 marks)

  3. How many more minutes did Kerry spend doing HIIT than rowing?  (1 mark)

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Displaying Data, SM-Bank 032

The graph below shows the depth of water in a sea bath from 6.00 am to 8.00 pm.
 

 

  1. What was the maximum depth, in metres, of water in the sea bath?  (1 mark)

  2. The sea bath was open to the public when the depth of water was above 1.5 m.

     

    Between which times was the sea bath open?  (1 mark)


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Displaying Data, SM-Bank 031

  1. Draw an ordered stem-and-leaf plot for the following set of scores.
     
        (2 marks)

  2. What is the median of the set of scores?   (1 mark)

  3. Comment on the skewness of the set of scores.   (1 mark)

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Data Analysis, SM-Bank 055

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


 

For this class:

  1. What was the range of test scores?  (1 mark)
  2. What was the mean test score, correct to 1 decimal place?  (2 marks)
  3. What was the median test mark?  (1 mark)
  4. What was the mode of the test scores?  (1 mark)
  5. A student sits the test late and scores a mark of 58. Describe the change, if any, in the range, the mean, the median and the mode.  (2 marks)
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Data Analysis, SM-Bank 054

The following ordered stem plot shows the areas, in square kilometres, of 27 suburbs of a large city.
  1. For these suburbs
    i.     What is the median, in square kilometres?  (1 mark)

    ii.    What is the range, in square kilometres?  (1 mark)

  2. What is the possible outlier?  (1 mark)
  3. Briefly describe the skewness of the data.  (1 mark)
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Data Analysis, SM-Bank 053

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 
 

  1. How many of these countries had more than 22% of homes connected to broadband internet in 2007?  (1 mark)
  2. What was the median percentage of homes connected to broadband?  (1 mark)
  3. For these countries, what is the modal percentage of homes connected to broadband?  (1 mark)
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Data Analysis, SM-Bank 052 MC

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

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

  1. positively skewed with a median of 15 decayed teeth and a range of 45
  2. approximately symmetric with a median of 1.5 decayed teeth and a range of 4.5
  3. negatively skewed with a median of 1.5 decayed teeth and a range of 4.5
  4. positively skewed with a median of 1.5 decayed teeth and a range of 4.5
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Displaying Data, SM-Bank 030

A random sample of people were asked what is their favourite winter sport.

The table below recorded the results.

  1. Use the information in the table to construct a divided bar graph on the template below. Remember to include a title and labels.  (2 marks)
     

     
  2. Using the data from the survey, predict how many people would choose Aussie Rules if 2000 people were surveyed. (2 marks)
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Interpreting Data, SM-Bank 002

This graph shows a company's profits over a 4 year period.
 

  1. What were the company's total profits during this period?  (1 mark)
  2. What was the average yearly profit?  (1 mark)
  3. What percentage of total profit was made in the first year? Give your answer to 1 decimal place.  (2 mark)
  4. Explain how this graph could be misleading.  (2 marks)
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Interpreting Data, SM-Bank 001

Luke picked bananas during his university holidays last summer. He counted the total number of bananas he picked everyday and created the graph shown below.
 

 

  1. For how many days in total did Luke pick bananas?  (1 mark)
  2. On how many days did he pick less than 145 bananas?  (1 mark)
  3. Explain how this graph could be misleading.  (2 marks)
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Displaying Data, SM-Bank 029

The graph shows the origin and type of all vehicles in a city.
 

  1.  Complete the table below using the graph.  (2 marks)
  2. What was the total number of Asian vehicles in the city?  (1 mark)
  3. What was the total number of Trucks and vans in the city?  (1 mark)
  4. What percentage of all vehicles in the city were Australian vehicles? Give your answer correct to 1 decimal place.  (2 marks)
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Data Analysis, SM-Bank 051

Ms Granger measured and recorded the heights of all the students in her class, to the nearest centimetre.

She made a dot plot to show the heights of these 32 children.
 

   
Student Heights (nearest cm)

 

  1. What fraction of the students' heights are greater than 145 centimetres and less than 150?  (2 marks)
  2. What is the range of the heights?  (1 mark)
  3. What is the median of the heights?  (1 mark)
  4. What would the median be if a new student arrived with a height of 135 cm?  (1 mark)
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Displaying Data, SM-Bank 028

Melinda and Cathy run the 100 metre sprint in their school athletics carnival.

A device tracks their progress and the results are shown in separate line graphs below.
 

 
Melinda starts quickly and passes the 75 metre mark after 10 seconds, slowing down as the race progresses.

Cathy is slower but runs the whole race at the same speed.

Approximately how long after Melinda did Cathy pass the 75 metre mark in the race?  (2 marks)

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Displaying Data, SM-Bank 026

Tom collected data on the number of big game animals in an African wildlife park.

This graph shows how many big game animals lived in the park.

 

 

There were 16 more elephants than rhinos in the wildlife park.

  1. What fraction of the animals were elephants?  (1 mark)
  2. What fraction of the animals were rhinos?  (1 mark)
  3. How many big game animals were in the park in total?  (2 marks)

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Displaying Data, SM-Bank 024

Kat went on her annual holiday and spent her money on accommodation, meals and shopping.

She spent $1200 in total and the pie chart below shows how she spent it.

 
 

  1. How much money did Kat spend on shopping?  (2 marks)
  2. How much money did Kat spend on meals?  (2 marks)
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Displaying Data, SM-Bank 020 MC

A store sells second hand mobile phones.

The graph below shows the price of 2 similar second-hand phones.
 

 

Which of the following is true based on the graph shown?

  1. Phone A is older and less expensive than Phone B
  2. Phone B is older and more expensive than phone A
  3. Phone A is newer and more expensive than Phone B
  4. Phone A is older and more expensive than Phone B

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