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Sort, represent and interpret number data


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Last updated 26 October 2012 15:30 by NZTecAdmin
Sort, represent and interpret number data (PDF, 37 KB)

Preparing Data for Analysis progression, 4th–5th steps; Analysing Data for Interpretation progression, 4th–5th steps; Interpreting Data to Predict and Conclude progression, 4th–5th steps

The purpose of the activity

In this activity, the learners sort and organise number data and represent it on graphs in order to develop the ability to read and derive meaning from graphs created by themselves or others.

The teaching points

  • First drawing a bar graph to represent ungrouped data and then a graph of grouped data helps the learners understand graphs that have two sets of numbers.
  • The grouped data graph gives information about the number of pieces of data, typical values and the spread of values.
  • There are levels of deriving meaning from graphs. Ask the learners questions that will encourage them to think at each of these levels:
    • reading the data – lifting information from the graph
    • reading between the data – interpreting information in the graph
    • reading beyond the data – predicting or inferring from the graph
    • reading behind the data – connecting the information and its context.
  • Discuss with the learners how the purpose of statistics is to predict and tell a ‘story’ and how when the learners are developing understanding of statistics it should always be in the context of a ‘story’ and that ‘story’ needs to be considered when preparing, analysing and interpreting data.

The guided teaching and learning sequence

1. Choose a ‘story to tell’ that is of interest and relevant to the learners and that generates number data, for example, “How many children do we have in our families?”.

2. Ask the learners:

“How many children do we have in our families?” Issues will arise as to whether we are meaning the family in which we are the parents or in which we are the children.

Ask:

“Is it important we all agree on what type of family we are talking about?” “Why?”
“Who are we going to include for this exercise?”

3. Once you have determined the extent of ‘family’, ask the learners to identify how many children are in their family. Find out the largest number of children in the learners’ families.

4. Draw a set of axes on the board with the vertical axis marked to the largest number. Include a title for the graph. Ask the learners to order their responses in terms of increasing family size and put their amount on the graph as a bar that is labelled along the horizontal axis with their name. (Note: this graph is representing the ungrouped data.)

Children in our families

Image of graph representing the ungrouped data.

5. Draw a second set of axes on the board.

Children in our families

Image of a second set of axes on the board.

6. Referring to the graph that shows the ungrouped data, ask:

“How many families have 1 child?” and draw a bar to show that amount on the second set of axes. “How many families have 2 children?” and draw a bar to show that amount on the second set of axes.

Continue the questions until the graph showing grouped data is complete.

Children in our families

.Image of graph showing complete grouped data.

7. Ask the learners to work in groups to discuss the questions you have prepared, using the four levels outlined in the teaching points above.

For example:

Reading the data

“How many families have 3 children?”

“What is the largest number of children in a family?”

Reading between the data

“How many families have 4 or more children?”

“What percentage of families has 2 or less children?”

(In this example, the answer is 36 percent (5 families out of 14) – encourage the learners to find this information from the grouped data graph, not just by counting the number in the class.)

Reading beyond the data

“If a new person joined our class, what do you think we could say about how many children would be in their family?”

Listen for and encourage responses such as “almost certainly between 1 and 8 children” and “unlikely to be more than 8 children”.

The learners are also likely to comment on more families having 2 and 3 children. Discuss with them that this is the case for your class but that small samples vary – the neighbouring class might be quite different – and therefore your class’s results are not a good basis on which to make judgements.

Reading behind the data

“If you went to another country or asked the question in a primary school class or elderly citizens’ club, would you get the same result?”

Follow-up activity

Find interesting and relevant bar graphs from the newspaper or internet (for example, http://www.censusatschool.org.nz/2005/data-viewer/) and prepare questions that relate to the four levels of deriving meaning for the learners to assess in relation to the graphs.

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