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- CH 18|Overview & Teacher Resource Sheets
Statistics
Chapter 18 | Statistical investigation
Overview & Teacher Resource Sheets
Rich tasks
- These are problem solving open-ended questions that require students to use the Enquiry Cycle to carry out an investigation.
They can be given at the start of a topic and done as the students gain enough knowledge to complete them, inserted into a
topic at an appropriate place, or given as homework, or extension.
Note: any of these rich tasks could be used as the student’s survey topic when they reach the Enquiry Cycle section of the chapter. These tasks could be done as a group or homework project.
Social networking
- Am I like everyone else?
- Is it related?
> More on "Rich tasks for this Chapter"...
1. Social networking
- These sites might contain useful data if the search engine doesn’t return anything useful.
https://www.pewinternet.org/fact-sheets/social-networking-fact-sheet/
https://royal.pingdom.com/2012/08/21/report-social-network-demographics-in-2012/
2. Am I like everyone else?
- Students should already know points 1 to 4.
- It is important that students choose the assertions themselves so as not to highlight any embarrassing differences. Teachers need to use their own judgment as to whether this rich task should be avoided in a particular class.
- You could simplify this task by asking students to choose only three assertions to investigate.
- Encourage students to collect data about all of their assertions simultaneously, using a collection sheet suitable for multi-variate data, such as data cards.
3. Is it related?
- Once all students have finished working on this task, you could have a class discussion to predict the results and whether or not a relationship might exist. Then students could display their scatter plots on the wall and you could discuss as a class whether or not the predictions were correct.
- Students sometimes have difficulty choosing a correct scale for the axes. Encourage them to work out the highest and lowest data values for the axes and mark the axes into sensible amounts between these two values.
Displaying data
- Know how to draw a pie chart both using a spreadsheet and by calculating the angle in each sector and be able to recognise the type of data for which a pie chart is suitable.
- Know how to draw a scatter plot for two sets of measurement data and be able to recognise the type of data for which a scatter plot is suitable.
- Know how to interpret pie charts and scatter plots.
- Know how to draw and interpret a two-way table.
> More on "Displaying data"...
Teaching ideas
Watching, watching, watching ... (Teaching resource sheet 83)This link displays a large pie chart and frequency table. You will need to be able to display this onto a write-on surface.
Ask 20 or 30 students (a number that will divide evenly into 360) how many movies they watched in the last month.
Fill in the frequency table.
Ask “What fraction has watched one? two? No movies?"
Ask “How could I use these fractions to make a pie chart?”
Fill in the calculations for each sector.
Draw the pie chart using a board protractor.
This link shows a set of axes on which you can fill in data.
You need to be able to display the graph on a write-on surface or print out a copy.
Ask fifteen students to plot a point on the graph to show how many minutes of TV they watched last night and how many minutes homework they did.
Ask “What might a scatter plot be used for?”
This link displays three scatter plots and asks students to describe the relationship between the variables.
- It goes both ways.
Tell the boys to go to one corner of the room and the girls to another. Ask both groups to divide themselves into left-handed and right-handed groups so that there are four groups.
Ask “How could we show these numbers on one table?” You could get them to stand in four sections like a two-way table.
Ask a volunteer to draw the two-way table on the board.
Ask some questions about the table such as “How many left-handers are there altogether?”
This links displays some data about the height in hands and the weight in kg of 20 horses. This data can be copied and entered into a spreadsheet. Students are asked questions about the data and have to decide which is the best graph to draw out of a pie chart, scatter plot, bar chart or line graph. Discuss which graph is best for each question and why.
Teacher notes
- Notes for the practical on page 320:
- Pouring soapy water on a patch of ground brings worms to the surface.
- If it is impossible for your class to carry out this practical you could bring in leaves from two trees of the same species
growing in two different places.
- Pie charts:
- Encourage students to make the link between fractions and pie charts.
- Emphasise that the angle at the centre of the pie chart is 360º and all of the sectors have an angle that is a fraction of this.
The fraction is the same as the proportion it represents. - Encourage students to draw angles starting with the smallest as it cuts down the percentage error for the last and
largest sector. - Point out the use of pie charts in many other subject areas such as Social Studies and Science.
- Scatter plots:
- When drawing scatter plots, point out the need to plot the points accurately.
- Point out that outliers can be ignored when deciding if there is a relationship between the variables in a scatter plot.
- Encourage pupils to ask “What happens to (variable on the vertical axis) as (the variable on the horizontal axis) gets bigger?”
- Two-way tables:
- Point out that two-way tables are a good way to compare data.
The Enquiry Cycle
- Know each step of the Enquiry Cycle and be able to use it competently to carry out an investigation.
> More on "The Enquiry Cycle"...
Teaching ideas
This links displays the Getting started on page 309. This is an excellent way to generate some survey topics that interest this
age group.
Discuss what each of mean, median, mode and range is first.
You could display this sheet on a write-on surface and ask students to match the definitions and terms.
Mean = sum of the data values/number of data values
Median = is the middle number in a range of data, or the mean of the two middle values if there is an even number of data values
Mode = is the most common data value
Range = largest data value – smallest data value (range is a single number)
In common daily usage, the word average is often used to describe the mean. Students should be discouraged from doing this and use the correct term because in mathematics average refers to any of the mean, median or mode.
This link displays some sets of numbers and asks students to calculate the mean, median, mode and range of each set
of numbers.
Divide the class into two groups. Have them race each other to find the answers.
Ask for which of the data sets would the mean / median / mode be most useful.
- Number of living things in my house
Ask students to write down on a mini whiteboard or piece of paper the number of living things that live in their house –
this includes pets.
Ask 10 students to come and stand in a row and hold up their number. Ask the students to put themselves in order from the largest number to the smallest number.
Ask the rest of the class to find the mean, median, mode and range of the data and then discuss these.
This link displays the means and medians for the lengths of time that two different brands of electric jug lasted and asks
students to decide which brand they would buy.
Divide the class into groups according to which brand they chose.
Have each group try to convince the other that their own choice is correct. (Note: Either could be the best to buy for
different reasons.)
This link displays cards for you to print, one with each of the graphs the students know to date (bar chart, double bar chart, pie chart, dot plot, stem and leaf plot, pictograph, strip graph, line graph and scatter plot (if you do this activity as a starter then they won’t know scatter plots).
Another set of cards has the type and an example of data such as:
categorical (month born)
discrete (data that can only have certain values eg shoe size)
grouped discrete (People who brought money to school each day for a month for lunch at the school canteen)
continuous (measurement) – time taken in seconds to skip ten times
time-series – time and temperature
two sets of data you are wanting to see if there is a relationship between, eg length and weight of snakes.
Give out the sets of cards and ask students to match an example card with a suitable type of graph so that each card has a matching graph.
Is there more than one way of doing this?
Teacher notes
- Students could either carry out their own survey once you have decided which activities students need to do as practice or students could do an activity and then carry out that part of their survey.
- Students could use the internet to gather information about their chosen survey topic or they could collect information from buddy schools via email or use http://new.censusatschool.org.nz/
- Discuss how sometimes the median is more useful than the mean when there is one or more data value that is an outlier (not close to the others). Outliers make the mean higher or lower than it would be if the outlier wasn’t there. In these cases the median might be more useful.
- Students sometimes get the mean, median and mode confused. Discuss methods that they could use to help themselves to remember the differences.
- Encourage students to look at the type of graph, the shape, clusters (data that is grouped together), outliers (data values that stand out as being different for some reason, often they are lower or higher in value than most of the other data values) and anything that is unusual about the graph.
- Point out that the same type of graph can be displayed in more than one way, for example bar charts might be vertical or horizontal. Strip graphs might be horizontal or vertical and the depth of the strips can vary. You could use a spreadsheet to experiment with different types of graphs for the same data.
- Point out that a graph might look complicated when it really isn’t.
These sites might be useful to you.
New Statistics about pollution
https://www.stats.govt.nz/searchresults.aspx?q=pollution
World statistics about pollution
A good place to find misleading statistics
http://www.remedialthoughts.com/
The Olympic games site with a lot of useful statistics
A site you can use to create a digital survey
Starter ideas for surveys
1 You are planning a school disco, class camp or end of year class party, singing competition or gaming night.
2 Compare your ecological footprint with others.
3 Compare the population/energy usage/production of goods etc of some countries of your choice.
4 Investigate whether some statements are myths or truth.
Example: If you put warm water into ice cube trays it freezes faster than cold water.
5 Investigate if left-handed and right-handed people have different abilities.
6 Is there a relationship between age and when people gain ownership of items, for example bikes, mobile phones etc?
7 Does listening to different types of music affect memory, reaction etc?
8 Does gender affect the level of commitment to community and environmental awareness, for example recycling?
9 Does gender affect ability in taste tests, for example water and bottled water, Marmite and Vegemite, Coke and Pepsi etc?
10 Does age affect nutritional choices?
11 Does gender affect mobile phone usage patterns?
12 How accurate are two different sources at predicting the weather?
13 Does eating breakfast affect mental and physical ability?
14 Does the time of day affect the length of the TV or radio advertisement break?
15 Is there more male or female sport reported in the sports section of the news?
16 Is there is a difference between gender and strength or gender and aerobic capacity at different ages?
17 Does price relate to quality?
18 Investigate physical relationships, for example the relationship between the volume of a person’s fist (as measured by
immersing it in a jug of water) and the length of their little finger, or the relationship between the length of someone’s stride
and their foot length.
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