In this unit we use measurements of our classmates to find the average (mean and mode) of our features. We use our findings to create a 3-dimensional "class head".
See Planning a Statistical Investigation (Level 3) for general information related to planning a statistical enquiry/. Data detective posters showing the PPDAC (problem, plan, data, analysis, conclusion) cycle are available to download from Census At School in English and te reo Māori.
In this unit we plan an investigation to find out what the average student in our class might look like. In doing this we consider whether use two different measures of central tendency: mean and mode. 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 (mode) is brown.
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.
Although we don't use it in this investigation, the other way to measure the central tendency, is finding the "middle" number in a set of data when all the numbers are arranged in order (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. 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.
Mode, mean and median all 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 median is literally in the middle. However, the point of the mode is that its central tendency is the sameness of data (what is the most common "same" number). The mean states 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.
Although the focus of the unit is on creating the "average head" it also provides an opportunity for the practising measuring skills.
The learning opportunities in this unit can be differentiated by providing or removing supports to students and by varying the task requirments. Ways to support students include:
The context for this unit could be adpated to further suit the interests and experiences of your students. For example, instead of measuring head size and eye colour, you might choose to measure hand size and hair colour. Alternatively, you might be able to investigate variables related to students' favourite animals.
Te reo Māori kupu such as toharite (average, mean), tau tānui (mode), ine (measure), taura ine (tape measure), tūhuratanga tauanga (statistical investigation), and kauwhata (graph) could be introduced in this unit and used throughout other mathematical learning
This session provides an introduction and purpose to statistical investigations. The teacher will need to provide the students with plenty of magazines, newspapers and websites that have some good examples of how data can be presented effectively and perhaps some examples of poorly displayed data. This could be collated into a chart or slideshow. Prior to the session, ask the students to spend some time at home looking through magazines and newspapers to find examples of statistics to bring in for the session.
Over the next 2-3 days the students will work in small groups to create their own "average looking" head.
Get the students to discuss with a partner how they are alike and different to the model of the average head. They could write a letter to their parents explaining how they are alike and different to the model of the average head. Encourage the use of the terms mean and mode.
During the year; leave your model on display. Re-do some of the measurements to see if any of the average measurements have changed. Ask why things have changed, haven’t changed? What things will stay the same? Why? When we measure next month what things might change? Why?
Dear families and whānau
This week we have been collecting data to find out what the average head in our class looks like. Come and along and look at the models that we have made – do they look like anyone you know?
This week we are to find out and record the head circumference of each member in our family using centimetres and millimetres (we might use a piece of string and then measure this with a school ruler). We then need to figure out the average head circumference for our family
We also need to work out the most common (the mode) eye colour in our family.
We hope that you will be happy to help.
Thank you.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/average-looking at 8:46pm on the 26th February 2024