Student Resource Book |
Year 7 (4A)
Statistics
Chapter 19 | Analysing data
Overview & Teacher Resource Sheets
Rich tasks
- These are problem solving open-ended questions that require students to be able to analyse data collected by others, including internet sites. The tasks 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.
- Is it misleading?
- Have you got your cycle helmet on?
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1. Is it misleading?
- You could provide students with examples of misleading graphs or give them suitable internet sites to access.
2. Transport woes
- This task is very open-ended. You could look at the sites and give some suggestions for students who might find it difficult to choose appropriate statistics.
Mode and range
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Teaching ideas
- Mode brand of mobile phone
Establish the mode brand of mobile phone of those students in the class that have one and discuss how shops might use this data. - Range
Find out and explain the range in the shoe sizes in your class.
Teacher notes
- Students often give the range as something like 87 – 23 rather than a single number. Remind them the range is a single number.
- Sometimes, when data is given in a table and especially if the data is numerical, students mistakenly give the frequency as the mode instead of the number of the modal class.
Example:
| Age Group | ƒ |
| 1 - 5 | 8 |
| 6 - 10 | 16 |
| 11 - 15 | 27 |
| 16 - 20 | 10 |
- Students state 27 as the modal class rather than 11-15.
- Emphasise that the range gives us a measure of the spread of the data. Discuss how it might be useful to know the range of ages coming to a school family day so that suitable activities can be organized.
- Discuss when it might be useful to know the mode, such as when selling shoes it is helpful to know the mode shoe size for men and women.
Mean and median
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Teaching ideas
Beat the calculator (Teacher resource sheet 47)
This link displays some sets of numbers and asks students to calculate the means.
Divide the class into two groups. Give calculators to one group but not the other.
Get the two groups to race each other to find the mean of each set.
Discuss which questions can be done mentally and which are best done using the calculator.
Discuss the method where a mean is estimated and then each number in the list is compared to this. The difference between the number and the estimated mean is recorded as a positive or negative number and then these are added and subtracted to get a total. This total is then added to/subtracted from the estimated mean to get the actual mean.- Heights of students (Note: Be sensitive to any particularly tall or short students by not including them in the sample.)
Ask 11 students to come and stand in a row. Ask them to put themselves in order from tallest to shortest.
Find the person in the middle and discuss that this person has the median height of the 11 students. - Middle or not (Teacher resource sheet 48)
This link displays some sets of numbers and asks students to put them in order and to find the median. Discuss the best ways to do this.
Teacher notes
- Explain that the mean is what you would get if the data was shared out evenly, that is, with everyone getting equal shares.
- When finding the mean, some students think their answer is wrong because it is not one of the data values.
- Students sometimes forget to put the data in order before finding the median. Encourage them to look to see if the answer they have is sensible. For example if the answer they get for a median high jump distance is 20 metres this is not sensible.
Using mean, median, mode and range to analyse data
- Find the mode, range, mean and median of data sets and use these to analyse or compare data.
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Teaching ideas
- Magic squares (Teacher resource sheet 49)
This link displays a magic square.
Ask students to check whether it is a magic square where every row, column and diagonal adds to the same number.
Ask students to find the mean, median and range of each row, column and diagonal.
Discuss if this information is useful when making a magic square.
Teacher notes
- Discuss how sometimes the median is more useful than the mean when there is one or more data values that are outliers (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 ways that they could use to help them remember the differences.
Analysing data displays
- Answer questions and make statements about displays from investigations carried out by others.
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Teaching ideas
Teacher notes
- 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 graphs might be vertical or horizontal. Strip graphs might be horizontal or vertical and the depth of the strips can vary.
- Point out that a graph might look complicated when it really isn’t.
