Grouping continuous data

Part ofMathsCollecting and recording data

Key points

A series of two images. The first image is a grouped frequency tally chart. The second image is an open left hand, palm side up. A horizontal orange arrow extends the distance between the tip of the thumb and the tip of the small finger. Written below: hand span.
Continuous data can be grouped using a frequency tally.
  • Continuous data is that can take any value. Usually, continuous data can be measured. Some examples of continuous data include:
    • time
    • height
    • weight
  • Because continuous data can take any value, it must be grouped before it can be represented in a table or chart. Continuous data is grouped into .
  • It can be useful to remember notation as this is used when writing class intervals:
    • ≤ less than or equal to
    • < less than
    • > greater than
    • ≥ greater than or equal to
A series of two images. The first image is a grouped frequency tally chart. The second image is an open left hand, palm side up. A horizontal orange arrow extends the distance between the tip of the thumb and the tip of the small finger. Written below: hand span.
Continuous data can be grouped using a frequency tally.
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Grouping continuous data

  • Continuous data can take any value so before representing it in a table or chart, it must be grouped into distinct .
  • Class intervals can be any size that suits the data, but they must not have any overlapping values:
    • The class interval 0 ≤ \(x\) < 10 can have any values greater than or equal to 0 but less than 10 in it.
    • This group includes anything exactly equal to 0 but does not include anything exactly equal to 10
    • To avoid any overlaps, the next class interval would be 10 ≤ \(x\) < 20. Any pieces of data which are greater than or equal to 10 but less than 20 fall in this interval.
  • Once continuous data has been sorted into class intervals, it can be represented in a frequency chart, or a range of other types of graphs. These charts help to interpret the data.
  • It is useful to remember that tallies are used to count pieces of data, and they count in fives.

Examples

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  1. Example one. A series of two images. The first image is a grid of raw data. The grid has four columns and four rows. Each cell is populated with a decimal number, measured in centimetres. The first row is: fifteen point one, fourteen point zero, twelve point one, fifteen point one. The second row is: fifteen point zero, thirteen point six, sixteen point one, thirteen point nine. The third row is: fourteen point one, fifteen point nine, thirteen point one, sixteen point nine. The fourth row is: twelve point six, fifteen point four, sixteen point three, thirteen point six. The second image is an open left hand, palm side up. A horizontal orange arrow extends the distance between the tip of the thumb and the tip of the small finger. Written below: hand span.

    The hand spans of a group of students are measured. Hand span is an example of continuous data, as it can take any value. The data collected is shown in this table.

Question

Which class interval should 30 m be put into?

An image of a table with three columns and six rows. The first column is labelled, height, and is populated with the groups, ten metres is less than, h, is less than or equal to twenty metres. Twenty metres is less than, h, is less than or equal to thirty metres. Thirty metres is less than, h, is less than or equal to forty metres. Forty metres is less than, h, is less than or equal to fifty metres. Fifty metres is less than, h, is less than or equal to sixty metres. The second column is labelled, tally. The cells have been populated with tally marks, three, a group of five, three, a group of five and a single tally mark, one. The third column is labelled, frequency. The cells have been populated with the numbers, three, five, three, six, one. Written below: thirty metres. The cells for the labels are highlighted purple.

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Practise grouping continuous data

Quiz

Practise grouping continuous data and using tally charts with this quiz. You may need a pen and paper to help you with your answers.

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Real-life maths

Class intervals are used for the bands of paid by working adults in the UK.

This frequency chart shows the level of income, and the frequency of adults who paid that rate.

A table showing the bands of income tax. The table has four columns and five rows. The first column is labelled, income, and is populated with the groups, zero to twelve thousand five hundred and seventy pounds. Twelve thousand five hundred and seventy pounds to fifty thousand two hundred and seventy pounds. Fifty thousand two hundred and seventy pounds to one hundred and fifty thousand pounds. More than one hundred and fifty thousand pounds. The second column is labelled, band, and is populated with the names, personal allowance, basic rate, higher rate, additional rate. The third column is labelled, rate, and is populated with the percentages, zero percent, twenty percent, forty percent, forty five percent. The fourth column is labelled number of adults and is populated with the numbers, twenty two point one million, twenty seven point six million, four point two million, four hundred and eighty one thousand.

Anything up to, and including, £12,750 is taxed at 0%. This could also be expressed as 0 < £ ≤ 12,750

Any amount between £12,750 and £50,270 is taxed at 20%. Mathematically, this class interval can be written as 12,750 < £ ≤ 50,270

These groups vary slightly each year.

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