# Measuring up

Purpose

In this unit the students will collect statistical data about their own class and school and learn how to compare it to data from students in the UK.

Specific Learning Outcomes
• plan an investigation;
• use spreadsheets to display and analyse data;
• discuss features of data display;
• compare features of data distributions;
Description of Mathematics

By Level 4 students are able to take increasing responsibility for the planning and conducting of statistical investigations. Students should be capable now of incorporating a computer into their work. The mathematics explored in this unit includes tally charts, the use of Microsoft Excel to collect and analyse data (especially as histograms), and measures of mid point (mean, median and mode) and spread (using box and whisker plots).

Note that measures of centre are not introduced in The New Zealand Curriculum until level 5. This material may not be suitable for all of your students.

The mode is the number or event that appears most often in a set of data. Suppose that the eye colours of the students in the class are blue, blue, blue, brown, brown, brown, brown, green, green. Then the most common eye colour is brown. This is the mode.

The number that all the numbers in a data set cluster equally around is the mean. This is calculated by adding all the numbers together and dividing by the number of numbers. It is important that students understand that the mean of a group of numbers (or measurements) in our unit represents what would happen if we equally redistributed our measurements so that everyone had the same measure.

The number that comes in the middle of a set of numbers when they are arranged in order is the median. If we had the following set of numbers (4, 4, 4, 8, 9, 10, 10), then the middle number will be the fourth one. This number is 8, so the median of the numbers is 8. Now here we are lucky that there are an odd number of numbers. Otherwise there wouldn't be a precise "middle" number. If the numbers had been 4, 4, 4, 8, 9, 10, then we have to take the "three and a half" number as the middle number. As this is halfway between 4 and 8 we take the mean of 4 and 8 to be the median. So the median in this case is 6.

The three concepts of mode, mean and median, measure central tendency in some way. That is, they give some idea of the middle number in a set. However, they are often different numbers. The point of the mode is that its central tendency is the sameness of data, what is the most common "same" number. As for the mean, that tells which number is as close as possible to all numbers. When you add all the differences, both positive and negative, between the mean and the other numbers in the set, the result is zero. Finally the median is literally in the middle. When the data set is put in order, it's the actual number that is at the halfway point of the list (or as close as we can get in the even case).

Required Resource Materials
Computers with Microsoft Excel and internet access

Paper for collecting data.

Spreadsheet Tutorial (see Related Resources if needed)

Key Vocabulary

investigation, survey, census, variables, box and whisker plots, tally charts, spreadsheet, mode, median, mean, midpoints, range, distribution, spread, histogram, similarities, differences, comparison

Activity

#### Session 1: Measuring the class

1. Tell the students that school uniform or sports wear manufacturers may be interested in information about different body sizes. Introduce differences in sizes by asking for volunteers and standing two students up to discuss what about them could be measured to inform clothing or footwear producers.

2. Brainstorm things that could be measured and compared (height, head circumference, handspan, foot length). Note that some students may be sensitive about being measured. It is not appropriate to measure weight.

3. Students to form small groups and select one attribute to measure (each group to select a different attribute). Ensure that one group selects height.

4. Discuss ways to record the data (listing, stem and leaf plots, tally chart).

5. Students to survey class and collect data. As the students gather data, the teacher should circulate and provide advice or assistance as required. Ensure that accuracy of measurements is maintained.

#### Session 2: Displaying data

Students use data from previous session to produce graphs on Microsoft Excel.

1. Discuss the data collected in the previous session and explain that the students will be using Microsoft Excel to produce graphs of the data.

2. Initially students should be given freedom to experiment with what type of graph they feel best shows the information, but some may need assistance putting the data into a spreadsheet.

3. Once groups have produced two or three graphs each bring the class together and discuss the graphs produced. Talk about strengths and weaknesses of each. Make a chart listing strengths and weaknesses that students could refer to in the future.

4. The best graph to show this type of data is a histogram, ensure that each group has produced at least one histogram of their data by the end of the session.

#### Session 3: Comparing to the school

The class will collect height data from the rest of the school to compare to their class results.

1. Depending on the size of the school and the number of other classes available to be measured, students will work in groups or individually to collect height data for the school on a tally chart.

2. All data for the school is to be brought together and entered onto one Microsoft Excel spreadsheet.

3. Students can work in small groups again to produce histograms of the whole school spreadsheet data.

4. As a class compare histograms of school heights with previously produced histogram of class heights. Focus the discussion on similarities and differences between the data.

#### Session 4: Comparing to data from the internet.

Students will produce histograms of heights of students in the UK using data from the internet.

1. Discuss the previous sessions’ work.
Who else could we compare heights with?
Would it be interesting to compare our school’s heights with heights of students from another country?

2. Explain that there is a website with information collected from students at schools in the UK that includes information about heights of students

3. As a class, visit the CensusAtSchool International site and access the results for heights of students the same age as those in class. Get the students to find the height data for the students in the UK by using the DataTool (requires Flash). After you have made each selection, click the next button at the top right of the tool.

1. Choose UK, and a year to compare with.
2. Choose age and height as the variables.
3. Choose to only use part of the database.
4. Double click on Age, and choose an appropriate age to compare with your class (you can choose a range of just one age).  You need to click save this option before continuing.
5. Drag the two variables onto the axes of the Tabulated data box (in the middle) and click the small play button. This will give you a sample randomly taken from the database of results
4. As a class compare the histograms produced with those for the class and for the school. Focus the discussion on similarities and differences between the results.

#### Session 5: Investigating midpoints/spread

Note that measures of centre are not introduced in The New Zealand Curriculum until level 5. This material may not be suitable for all of your students.

1. Students will use mean, median and mode to investigate midpoints of height data, and produce box and whisker plots to show the spread of data.

2. Discuss the results from the previous 4 sessions. Discuss what we can say to compare our class/school with the results from overseas.

3. Collect suggestions of ways we could find out more.

4. Discuss mean, median and mode, how we could find them out for this data. Find the mean, median and mode for heights of students in all three samples.

5. Discuss range, and produce box and whisker plots for all three sets of data.

6. Use the box and whisker plots to compare the three sets of data.

7. Discuss comparisons as a class.
Who is taller UK students or us?

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