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Sort, represent and interpret category data

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Last updated 26 October 2012 15:28 by NZTecAdmin
Sort, represent and interpret category data (PDF, 37 KB)

Preparing Data for Analysis progression, 3rd step; Analysing Data for Interpretation progression, 3rd step; Interpreting Data to Predict and Conclude progression, 3rd step

The purpose of the activity

In this activity, the learners sort and organise category 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

• Developing the ability to read and derive meaning from bar graphs is a developmental process, and this activity is designed to assist that development by moving from:
• the learner’s own data
• the learner’s data being represented by a sticky note placed on a graph
• the learner’s data being included in a bar on a graph.
• Working with category data (for example, favourite sport or TV programmes watched) is easier for the learners than number data (for example, number in your family, height, age, etc) and is therefore used in this initial activity.
• The learners need to choose categories in which to sort and organise the data.
• The scale chosen for a graph depends on the data.
• The purpose of statistics is to predict and tell a ‘story’, and when the learners are developing their 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.
• Discuss with the learners the connections between statistics and everyday situations.

Resources

• Sticky notes.

The guided teaching and learning sequence

Choose a ‘story to tell’ that is of interest and relevant to the learners and generates category data. To have enough data, choose a ‘story’ where there is likely to be a wide range of responses or where you can ask each learner to give two or three responses. Examples could include:

“What do you do in your leisure time?”

“What type of television programme do you enjoy watching?”

“What do you read most?” (This question could serve a literacy purpose by encouraging the learners to recognise that reading is used in a greater variety of contexts than books and newspapers.)

1. Write the question on the board and ask the learners to discuss what they think the response to the question might be. Record their predictions on the board.

2. Ask the learners to answer the question by writing their responses on sticky notes (to be used later) and also by recording their response(s) on the board.

3. Ask the learners to consider whether recording and reporting every learner’s response is the best way to answer the question. Listen for, and prompt if necessary, the idea that the responses could be summarised by sorting them into broader and fewer categories. (For example, for the question “What do you do in your leisure time?”, responses might include: karate, soccer, yoga, netball, rugby, read, go to parties, chat on the net, and broader categories might include: team sports, individual sports, internet-based activities, etc).

4. Ask the learners to choose possible categories and share their choices. Discuss until there is agreement on categories. Make sure the number of agreed categories is less than the number of learners.

Draw a horizontal line on the board with the categories listed in a row underneath. Ask the learners to place their sticky notes above the appropriate category in such a way that they can easily compare the number of notes applied to each category. You may need to prompt the learners to place the sticky notes in a vertical line. Ask:

“Can you compare the number in each category without counting them?”

Listen for and reinforce the response that the height of the line indicates the number in each category. Ask:

“Could your sticky notes be better placed to make the comparison more accurate?”

Listen for and reinforce the response that the sticky notes and the spaces between them need to be the same size for accurate comparison.

Ask the learners to adjust the positioning of the sticky notes if necessary.

6. Explain you are going to draw a bar graph that uses bars instead of the sticky notes to represent the responses.

Draw bars over the sticky notes. Ask:

“If I removed the sticky notes, can I still compare the number in each category?” “How could I show how many responses there are in each category?”

Listen for suggestions that you could put numbers on a vertical line (axis). Ask:

“What numbers do we need on the vertical line (axis)?”

After discussion, place appropriate numbers on the vertical axis and highlight the fact that the choice of numbers (scale) depends on the data. Remove the sticky notes.

7. Ask:

“What further information needs to be included on the graph so that a reader could understand the story it tells?”

Listen for and encourage the response that the graph and each axis need a title.

Discuss and insert appropriate titles.

8. Encourage interpretive discussion of the graph.

For example, for the question “What do you do in your leisure time?” ask:

“Which is the leisure activity that most of us do?”

“What is the least common leisure activity?”

“Do the responses agree with what we predicted?”

“If there are differences from what we predicted, can you explain why?”

Follow-up activity

Ask the learners to write a short report for another group of learners on the original question, including some comments on how sure they are of what they are saying and why.

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