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Open or closed?

This is a level 2 and 3 statistics activity from the Figure It Out series. A PDF of the student activity is included.

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Tags

  • AudienceKaiako
  • Learning AreaMathematics and Statistics
  • Resource LanguageEnglish
  • Resource typeActivity
  • SeriesFigure It Out

About this resource

Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.

This resource provides the teachers’ notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.

Specific learning outcomes:

  • Investigate open and closed survey questions.
  • Construct a graph.
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Open or closed?

Achievement objectives

S2-1: Conduct investigations using the statistical enquiry cycle: posing and answering questions; gathering, sorting, and displaying category and whole-number data; communicating findings based on the data.

S3-2: Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others.

Description of mathematics

This diagram shows the areas of statistics involved in this activity.

Investigation

Literacy

Probability

P

P

D

A

C

 

The bottom half of the diagram represents the 5 stages of the statistics investigation cycle, PPDAC (problem, plan, data, analysis, and conclusion).

Required materials

  • Figure It Out, Levels 2–3, Statistics Revised Edition, "Open and closed?", pages 10–11
  • classmates

See Materials that come with this resource to download:

  • Open or closed activity (.pdf)

Activity

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This activity helps the students differentiate between closed and open questions. The simplest closed questions are those that require a yes/no (or sometimes, a yes/no/don’t know) response. A poll of class members using a single closed question (for example, "Do you have a pet?") would immediately show the limited value of data gained in this way.

Question 1 shows that closed questions limit the kinds of responses people can make. This is often an advantage. It certainly makes the collation of category data much easier. But care needs to be taken when deciding on the options that are to be offered. If the options offered do not cover the needs of most respondents, people will get frustrated and refuse to take the survey seriously, or they will choose the "other" category. If lots of people choose the "other" option, this undermines the value of the rest of the responses.

The risk of this happening can be reduced by trialling survey questions before using them. This will usually reveal badly worded questions ("What is this question asking?") and shortcomings in the options being offered ("I can’t tick any of these answers.").

Activity 2 is designed to get students thinking about the wording of questions and the options made available.

Questions 1 and 2 illustrate the importance of identifying the purpose for which information will be used rather than haphazardly dreaming up questions and options.

The students get the opportunity to take this learning into account and consolidate their understanding when they conduct their own small surveys in the Investigation.

Activity 1

1.

The range of possible favourite colours is limited, so it would not be difficult to list them all.

2.

a. The graph from the open question data gives a clear picture of which colours are most or least popular. The problem with the graph from the closed question data is the tall "other" bar. While the graph suggests that yellow is the most popular colour, we can’t be sure. It may be, for example, that the six "other" votes were all from people who liked blue (not offered as a choice).

b. The open question was better because everybody got to name their favourite colour, and we are not left wondering what the "other" people would have chosen if they had had the chance.

Activity 2

1.

a. Open. This question may be too open and get answers such as "often" or "hardly ever". You may get better information from a closed question with carefully chosen options such as "twice a day", "once every day", "twice a week", "once a month", "only on Sunday", or "as a special treat".

b. Closed. The options could be improved. It seems odd to separate out auntie and uncle, brother and sister, but not mother and father. Also, the question could be confusing for those with family members who may buy fruit for their own eating rather than for the household as a whole. So a better question might be,

  • Who buys the fruit for your household?

c. Closed. It is unlikely that this question will get meaningful answers. Different types of fruit are plentiful and affordable at different times of the year, and most people eat what is available at the time. Also, does it make any sense to include eating "most fruit" "all year round"?

2.

The data might be useful in a class or school survey as the basis for discussion on healthy eating habits. However, it is unlikely that the data gathered using these questions would be sufficiently detailed or accurate to be of much use to producers and suppliers. Surveys are often used to find out more about the people who buy certain products. Such surveying is called market research.

Investigation

Practical activity. Results and discussion will vary.

"Open or closed?" can be used to develop these key competencies:

  • thinking
  • relating to others.

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