Year 7 and 8 Statistics

Candies

Image source

YEAR 7 Standards:

  • Investigate, interpret and analyse graphs from authentic data
  • Identify and investigate issues involving numerical data collected from primary and secondary sources
  • Construct and compare a range of  data displays including stem-and-leaf plots and dot plots
  • Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data.
  • Describe and interpret data displays using median, mean and range.

Resources for Year 7:

 YEAR 8 Standards:

  • Data representation and interpretation – Investigate techniques for collecting data, including census, sampling and observation
  • Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
  • Explore the variation of means and proportions of random samples drawn from the same population
  • Investigate the effect of individual data values, including outliers, on the mean and median

Resources for Year 8:

Supporting Australian Mathematics Project –

Graphs and Data

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Image created in Create-A_Graph

Last week you were working on a poster showing the results of a class survey in table and graphical form. This data is just a small sample of the school and state data. When governments and businesses want to plan for the future they need to know information about the whole population – for example, where roads, schools and hospitals need to be built. This information is obtained using a census. The national census is conducted every four years, when the Australian Bureau of Statistics asks every household to complete a survey.

Some of the data obtained in the 2011 census is recorded here. Choose one of the categories that you are interested in and create a graph of the data using “Create-A-Graph”. Email your graph to me and a copy to yourself.

Year 7 Favourites

favouritesImage Source

Learning Intention: Students will understand how to collect data using a tally and create a frequency table and bar graph using the data. They will understand how to convert fractions to decimals and percentages. They will create a pie chart using this data by converting 100% to 360 degrees.

Success Criteria: Each student will produce a poster that includes a frequency table (including fractions, decimals and percentages), bar graph and pie chart of their chosen data, collected from the Year 7 Maths Survey.

  1. First collect your data in tally form.
  2. Add each category and find the total.
  3. Represent each category as a fraction.
  4. Convert to a decimal (2/25 = 16/100)
  5. Convert to a percentage 16/100 = 16%
  6. Create a bar graph using this data
  7. Remember to add SALT to your graph – Scale, Axes, Labels, Title
  8. Turn your bar chart into a pie chart (multiply percentage by 3.6 because 100% = 360 degrees)
  9. Make sure you have a key to interpret your data.
  10. Add a beautiful title and colour to present your poster.
  11. Go to Create-A-Graph and use your data to check that your graphs are correct.
  12. Print out the computer generated graphs to add to your poster.

Interpreting Graphs

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Graph created in Excel by Jakob Linke, Year 7

Learning Intention: This week you will continue to work with line graphs, bar charts, pie charts and scatter plots. Your learning intention is to understand how to describe various graphs in words. You need to be able to interpret the information given.

Success Criteria: You will be able to look at the scale, axes, labels and title of different graphs and be able to describe what they mean. You will be able to match a graph to it’s description and draw a sketch graph from a sentence. These are the activities planned:

1. Find a graph with data in a magazine or newspaper. Cut it out and paste it into your books. Look carefully at the title, axes, labels and scale. Write a few sentences describing what the graph shows.

2. “Which graph is which” worksheet. You will be given nine small graphs and have to match scenarios to the shape of the graph.

3. Maths300: Temperature Graphs. Match the average maximum and minimum temperatures to Australia’s capital cities.

4. Match the graph to the Olympic record time/distance.

5. Which kind of graph would best represent the following situations?

  • Height of a plant growing over time?
  • The various heights of different plants of the same species in a greenhouse, over time?
  • Thousands of plants in a crop to determine which genotype was the fastest growing?
  • Percentage of different species of plants in an area of forest?

6. “Purchasing pantyhose” and “Blood Bank” graphs

7. Go to the Melbourne Grand Prix map and note the speed and distance from the start as each car makes it’s way around the track. Draw a graph that shows distance from the starting line on the horizontal axis and speed on the vertical axis.

Read more

Stem-and-Leaf Plots and Scatter plots

Learning Intention: Students will understand what data is suitable for graphing on a scatter plot and be able to describe the significance of a “line of best fit”.

Success Criteria: You will draw a correctly labelled scatter plot from our arm span and height data and determine if there is a relationship between these measurements.

Last week you learnt the definitions for mean, median, mode and range and created a stem-and-leaf plot using the height of students in Year 7. You also measured the length of seven leaves and calculated the mean, median, mode and range of this data. This week we will investigate another type of graph, the scatter plot. Use the data we collected from our Year 7 Maths Survey to graph arm span against height (in centimeters).

This week we may also get the chance to do other activities with scatter plots:
1. Barbie Bungee
How many rubber bands are needed for Barbie to safely jump from a height of 400 cm?
What is the minimum height from which Barbie should jump if 25 rubber bands are used?
How do you think the type and width of the rubber band might affect the results?
Do you think age of the rubber bands would affect the results–that is, what would happen if you used older rubber bands?
If some weight were added to Barbie, would you need to use more or fewer rubber bands to achieve the same results?
State a possible relationship between the amount of weight added and the change in the number of rubber bands needed.
(thanks to Mrs Jirkovsky at North Adams Public School for writing about this activity on her blog!)
2. Be an actuary – distance vs earthquake intensity.

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“Lies, Damn Lies and Statistics!”

Learning Intention: Students will understand that data can be displayed in various ways and they will be able to interpret different types of graphs, including bar graphs, pie charts, stem-and-leaf plots and scatter plots.

Success Criteria: Students will complete the following activites and be able to explain what the graphs tell us about the data collected.

The above quote, popularised by Mark Twain, refers to the ways that politicians can sometimes “manipulate the data” to suppport decision-making. The same data can often be used to support or disprove a theory, depending on the emphasis. Over the next couple of weeks we will use the data from the CensusAtSchool questionnaire to learn more about summary statistics and graphing. Some of the activities we will do are:

You can use the random data sampler to display the data relevant to each question.

Sketching Linear Graphs

Miss Tara Richardson has produced another video “Sketching Linear Graphs” – her blog is at “My Blog”

Learning Intention:
Students will learn how to sketch linear graphs.
Success Criteria:
There are three different methods you can use to draw a linear graph
1. You can identify the y-intercept and gradient (rise over run) from an equation.
2. You can substitute values into an equation to find at least two co-ordinates.
3. You can use the intercept method to plot two points on the x and y axis. Plot the graph by substituting x=0 (the y-intercept) into the equation as the first point and substitute y=0 into the equation to find the second point.
Tell me which method you prefer to use and why?

Column and Bar Graphs from Surveys

6-7RFavouriteTV shows

Create-A-Graph image by 6/7R student

Last lesson each of the students in both 6/7 classes completed a survey (created in Google Docs and embedded on the page with the tab “Survey2” at the top of this page) and the data was saved in a Google Docs spreadsheet. Then the students chose one of the data sets (favourite ice-cream flavours, footy teams, TV shows etc) and produced a bar chart or column graph using the class results. You can see from the graph above that “The Simpsons” is one of the most popular TV shows amongst 12 and 13 year olds at Hawkesdale P12 College!

We will use the same data to create a stem and leaf table with height data and  a scatter plot with height and foot size. Students have also been asked to collect a graph from a newspaper or magazine and will describe what the graph shows. This Voicethread, Year 6/7R Student Data and Graphs, contains some of the graphs produced in class.

Creating Graphs

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Image Source

This week in 6/7 Maths we will use out data to create bar charts, line graphs, pie charts, stem-and-leaf plots and scatter graphs. The Kids Zone has a great tool for creating different types of graphs at Create-A-GraphChartGo is another on-line tool for creating graphs. Think about which graphs are best for each purpose and the information you are trying to convey.

Choose which data you would like to graph and decide which type of graph to use. Time/Temperature graphs are usually line graphs because the data is continuous. Discrete data (favourite colour, footy teams or fast foods for example) are better represented using bar or column graphs. When you are graphing percentages of a population a pie chart is most suitable. The other thing you need to remember is that all graphs need SALT on them. Make sure you season your graphs well with the following information:

S = Scale

A= Axes

L = Labels

T = Title