# Year 7 and 8 Statistics

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 –

# Probability and Percentage increases and decreases

Following our assessment task yesterday it is clear that some students need to revise certain areas of the work we have done in term 1 and 2:

Probability – Relative frequency with ten questions to complete.

Percentages – How to convert fractions and percentages to a pie chart (360 degrees) with ten questions to complete.

Percentage increases and decreases – Worked examples and five problems to solve.

Stem and Leaf plotsWorked example and thirteen questions to solve.

Problem #1: You have a list of 7 numbers. The average of the numbers is 9. If you take away one of the numbers, the average of the numbers is 8. What number did you take away?

Problem #2: Martin has completed five Maths tests and received an average score of 80%. What is the highest average he could have after the next test?

Problem #3: A Year 7 class was asked “How many goals did you shoot at lunchtime?”. The lowest answer was 5 and the highest answer was 20. The total of all the answers was 60. What is the smallest number of students who could have been asked?

# Term 3: Statistics and Probability

This term we are starting a unit of work on data and statistics and the key words you need to understand are:

• data (qualitative and quantitative)
• discrete and continuous
• census (whole population) and survey (sample)
• mean
• median
• mode

The Australian Bureau of Statistics have a range of educational resources that will assist us to explore, represent and interpret data.

# Graphs and Data

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

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.
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.

# 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.
2. Be an actuary – distance vs earthquake intensity.

# “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.

# Column and Bar Graphs from Surveys

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.

# Surveys and Data

Image Source

While I am away next week (Wednesday, Thursday and Friday) you are required to complete a class survey. Choose a topic of interest (favourite AFL football team, favourite ice-cream flavour, favourite sport etc), with at least four options, plus “Other”.

• Tally your class results in a table.
• Convert the results to percentages (use a calculator for this if necessary)
• On a 100cm strip of paper, colour each section corresponding to the data collected. For example, if 10 out of 25 people voted for Essendon, colour 40cm of the strip in essendon colours.
• Tape the ends of the paper strip together and create a pie chart on A3 paper from the paper circle.
• Colour your pie chart carefully and give it a heading. Make sure you include a key to interpret the results.

Please also complete “Survey 2” by going to the tabs at the top of this post.