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# National Curriculum - Probability and statistics : Key Stage 3 : Mathematics Content Knowledge

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Key Stage 3
National Curriculum - Probability and statistics
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# 1. How confident are you that you understand:

## Example

Discrete data results from, say, counting the number of coins in pupils' pockets; number of peas in a pod, the number of lengths swum in a sponsored swim.

Non-numerical discrete data is called categorical data, e.g. pupils’ favourite colours or pupils’ pets.

Discrete data may be grouped, e.g. the numbers of pupils with shoe sizes 3–5, 6–8, 9–11, etc.

Continuous data results from measurements such as lengths of caterpillars or weights of crisp packets, and may be organised in touching but non-overlapping groups.  For example the heights of pupils (x cm) can be grouped into 130 < x ≤ 140, 140 < x ≤ 150, etc.

Discrete data only take on particular values and no values in between. Data like the number of pets a person has or the number of bikes a family owns is discrete.  You can either have 0 bikes or 1 bike or 2 bikes and so on, but you can't own 1.5 bikes.

Continuous data can take on any value in a range. Temperature and height are continuous because you can be any fraction of a meter tall (for example you can be 0.88596245... m tall.)

## What this might look like in the classroom

As a class, collect the following information for each of you:

• Height in centimetres
• Number of siblings
• Shoe size
• Eye colour
• Hand span in centimetres

Decide on a sensible way to record the information and present it in a form which makes it easy to analyse the data.

#### Outcome:

Most secondary school classes will yield a set of results for height between 120 cm and 200 cm. It is sensible for this to be grouped into class widths of 10 cm; e.g. 130 < h ≤ 140. This is spoken as “The height of the person h is greater than 130cm and less than or equal to 140cm.” As it is continuous data careful discussion might be needed about how to represent the groups and ensure that it is clear where a measurement of 130 cm should be placed. It is likely that pupils will need plenty of practice with saying the numbers and symbols relating to the groups.

A degree of sensitivity might be required when it comes to deciding who should be counted in the number of siblings. It is important for pupils to decide whether they will include step brothers and sisters or not. Once a decision has been made the information for everyone needs to be collected in the same way. Then the results can be placed into a frequency table, and could be used to calculate the average number of children in a family for the class.

The Office for National Statistics has interesting information which pupils can explore, discuss and investigate.

Shoe size is an interesting example of discrete data as it includes half sizes, and also because foot length in centimetres measures the same thing, but provides continuous data.

Eye colour, as categorical data, cannot be grouped at all, but the results should still be placed into a frequency table.

## Taking this mathematics further

It is essential for data collection to be seen as part of the complete data-handling cycle:

Learners need to appreciate that by distinguishing between the types of data this informs them how to group correctly, which then allows them to analyse the data using appropriate statistical methods. Also, distinguishing between the types of data is necessary in order to choose the correct way of representing the data. For example, if the data is discrete and a bar-graph is used to represent it, there should be a gap between the bars.

Make the work meaningful. Collect data that is relevant to the class and use it to draw conclusions that will interest them.

## Making connections

Research the history of statistics. Statistics generally developed due to the need for states to monitor socio-economic data. The Bible contains at least two accounts of censuses – the earliest in Genesis when Moses was instructed to take a census of the people. However, most statistical developments have been a comparatively recent advancement within mathematics: recent being within the last 500 years in this case!

The opportunity exists to make cross-curricular links with Science and Humanities departments.

## Related information and resources from other sites

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