Introducing: Averages
Vocabulary
range
survey, representative, represents
difference, largest, smallest
Hints and Tips
Mean Median Mode (see above links to the glossary)
An average can be thought of as representing a larger set of numbers or values.
They are useful when comparing sets of data, for example, a day in September may be colder than a day in November but, on average, September days are warmer.
There are different meanings of the word average but here, we will be concentrating on the most common, mean, median and mode.
Each of these provide different sorts of information about a set of data.
Often these averages, the mean, mode and median are taught separately at different ages.
We believe they are easier to understand when taught together.
It is always useful to teach these in context using a meaningful set of data collected by your child.
Essential Prior Knowledge
Know how to arrange numbers in a sequence
Activity
A good place to start is to talk to your child about the term average.
What does your child understand by this term?
He/she may have come across the term in relation to average weight, height, speed, temperature or rainfall.
Introducing Median
Decide, with your child, a time of day to take the temperature outdoors.
Ask him/her to take the temperature over seven days and record it each day on a separate card.
Take the seven readings and ask your child to order them in ascending order.
Look at the temperatures.
Are they all different or are some the same?
Ask which temperature is in the centre of the line.
Suggest to your child that this temperature can be taken to be typical of the group. Talk to your child about how, when all values in a set of data are arranged in ascending order, the middle number or value is the median.
Introducing the Mode and Range
Buy a bag of fun size sweets, possibly Skittles, Maltesers or Smarties. (This is only a suggestion and any small bags of items can be used.)
Ask your child to count the number of sweets in each bag and write each total on a separate card.
Again, encourage your child to sort the cards into ascending order and ask which number of sweets appears most often?
Explain that this number of sweets is the mode or modal value of the data.
Introduce the term Range to your child. Ask “What is the smallest number?” and “What is the largest number?”
Explain that the difference between these numbers is known as the range, a term used to describe the difference between the largest and smallest number of sweets in the survey.
Introducing the Mean
Ask your child to make 5 towers of different heights using interlocking bricks and encourage your child to work out the range. (see above)
Introduce the term mean to your child and explain that it is a kind of average where all the values are added and then shared equally.
Ask your child to think about how this can be done.
If he/she is having difficulty working out ways, guide him/her by suggesting adding all the values (number of bricks in each tower) and dividing the total by the number of towers.
This will give the value of the mean.
Averages Activity
Using cubes or large beads (any small objects that are easily picked up by your child) you and your child can ask grab a handful and record how many objects are in each handful. repeat this until you both have a record of the number of objects picked up from 20 handfuls of objects.
From this data, ask your child to work out the mean, median, mode and range for your handfuls and the same for his/her own handfuls, following the steps from the previous activities.
Ask your child to compare the data from your handfuls and his/hers, draw conclusions and back them up with evidence.