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Grouped Data

'Grouping data' means putting it into different classes so that the number of items falling into each class are it's frequency. Each data falls within a class interval which lies between class boundaries.

Data is usually 'grouped' for a reason:
• A lot of data
• Data spread over a wide range
• Most collected values different

Grouping data should also make it easier to analyse.

Tip: Make sure you know the difference between X > 10 and X ≥ 10.
X > 10 means that X is more than 10.
X ≥ 10 means that X is more than or equal to 10.

Estimating the Mean

When we have continuous data, the individual values are lost, so we can't actually calculate the mean - only estimate it. To begin, we're going to get the mid-point of each class. You can do this by using the same method you did to calculate the mid-range - the total of the lowest and the highest value, then half it. You need to do this for every class and put the values in a column called x next to the classes. Then we have the Frequency, f column and then the x × f column at the end. Then, total the x × f and frequency columns and estimate the mean using this formula:

x̄ = ^Σxf ⁄ _Σf.

Here's an example of a table produced to estimate the mean:

Continuous Data

A frequency table constructed with continuous data looks something like the one below compared to the one above on this image:

This data is called continuous because the scale of measurement - e.g. distance - has meaning at all points between the numbers given, eg we can travel a distance of 1.2 and 1.8 miles.