Stem and leaf diagrams

Part of MathsCollecting and recording data

Key points

An image of a stem and leaf diagram
Stem and leaf diagrams make it easier to read lists of number
  • can be represented in many ways. Stem and leaf diagrams are a common representation of data as they are easy to read and show the shape of the data, as well as grouping the data into classes.
  • It is useful to see the shape of the data to see whether the data is or if the data is .
  • If there is a this can be clearly seen from a stem and leaf diagram.
  • Stem and leaf diagrams present the data in an ordered list to make it clearer to read, and easier to work out the highest and lowest values in the dataset.
  • There must always be a key. The key tells the user how to interpret the diagram.
An image of a stem and leaf diagram
Stem and leaf diagrams make it easier to read lists of number
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Using a Stem and leaf diagram

  • Stem and leaf diagrams are formed by splitting the number into two parts, the ‘stem’ and the ‘leaf. For example:
    • In the number 36, the tens would form the stem and the units the leaf.
    • In the number 2.1, the units would form the stem and the tenths the leaf.
  • The numbers are usually written in order, so the row

                                                             2 | 1 3 4 4 5 7

   shows the numbers 21, 23, 24, 24, 25 and 27 in order.

  • As the data is in order, it is easy to work out the highest value, lowest value and the of the data.
  • Stem and leaf diagrams must always have a key which explains how to read the data.

Examples

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  1. A grid of raw data. The grid has ten columns and three rows. Each cell is populated with a number. The first row is: seven, thirty six, forty one, thirty nine, twenty seven, twenty one, twenty four, seventeen, twenty four, thirty one. The second row is: seventeen, thirteen, forty six, fifty, twenty three, thirty one, nineteen, eight, ten, fourteen. The third row is: forty five, forty nine, thirty six, forty five, thirty two, twenty five, seventeen, eighteen, twelve, six.

    A maths test is marked out of 50. The marks awarded to different students are shown in this table. This is difficult to interpret. It is not in order, and it is hard to see the highest or lowest score.

Question

Using the stem and leaf diagram, work out:

  1. How many people got 31 marks
  2. The modal score
  3. The median score
An image of a stem and leaf diagram. The stem has rows with values, one, two, three, and four. A vertical line separates the stem and leaf parts of the diagram. The rows are separated by horizontal lines. The values for the leaf have been completed. On the one row; one, three, four, five, seven. On the two row; zero, one, one, one, eight. On the three row; one, one, two, three, seven, seven. On the four row; zero, zero, one, two, six, eight, eight. Written below the diagram: Key: one, vertical line, one, equals eleven marks. Written above the diagram: year eight scores in a French test.

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Practise stem and leaf diagrams

Quiz

Practise interpreting stem and leaf diagrams with this quiz. You may need a pen and paper to help you with your answers.

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Real-life maths

Stem and leaf diagrams can be used to make public transport timetables easier to read.

They reduce the amount of text that is needed to share information about train and bus times.

An image of a timetable, set out in a similar way to a stem and leaf diagram. The stem has rows with values, six, seven to eight, nine, ten to fifteen, sixteen and seventeen. The values for the leaf have been completed. On the six row; zero two, ten, sixteen, twenty two, thirty, thirty nine, forty five, fifty one, fifty eight. On the seven to eight row; zero two, zero nine, twelve, twenty, twenty five, twenty nine, thirty five, forty one, forty eight, fifty two, fifty six, fifty nine. On the nine row; zero two, ten, sixteen, twenty two, thirty, thirty nine, forty five, fifty one, fifty eight. On the ten to fifteen row: zero two, sixteen, thirty, forty five, fifty eight. On the sixteen row; zero two, ten, sixteen, twenty two, thirty, thirty nine, forty five, fifty one, fifty eight. On the seventeen row; zero two, zero nine, twelve, twenty, twenty five, twenty nine, thirty five, forty one, forty eight, fifty two, fifty six, fifty nine. Written below the diagram: Key: nine, vertical line, zero two, equals nine o two. The cells for the stem are highlighted purple.
Stem and leaf diagrams reduce the amount of text needed to share information.
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Game - Divided Islands

Using your maths skills, help to build bridges and bring light back to the islands in this free game from BBC Bitesize.

Play the Divided Islands game!
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