Brief Description

This unit investigates broadly how children spend their leisure time. Most of the activities are summarized using data from the class, but a final section compares the class data with national figures.

Design time: 5 hours.

Aims and Objectives

On completion of this unit pupils should be able to fill in tally charts, interpret simple statistical tables and to draw and interpret pie charts and bar charts for categorical data.

They will have practised collecting data, and drawing and interpreting bar charts for continuous data.

They meet examples of a histogram, and the mode.

They should become more aware of how data are collected and some of the associated problems and of the difficulties in the interpretation and comparison of statistics.

Prerequisites

Pupils need to be able to:

1. Use tally marks.
2. Divide 360 by the number of pupils in the class to the nearest whole number (or one decimal place, if you want this accuracy).
3. Measure and draw angles (including obtuse angles).
4. Know the meaning of the words 'radius', 'sector' and 'axes'.

Equipment and Planning

Section A investigates how children spend their time and contrasts a school day with a Sunday. Section B looks at different aspects of what they like doing in their spare time. Section C compares two aspects of use of leisure time with national figures. Various alternatives are available in Section B. Different groups could do different alternatives and produce a class display for a final discussion on the unit.

'My Diary' on page Rl covers the time spent reading and watching television for seven days. It should be filled in before work on Section B is begun, so seven days warning for the class is needed.

Section B requires the completion of a questionnaire, and the recording of class results on tally charts. They can be completed after the diary and before starting work on the unit so that the flow of work is not interrupted. It may be helpful to limit the choice of television programmes in the first question on the questionnaire.

Section C2 requires the use of the Radio Tlmes, TV Times or newspapers for 'today' and Saturday. This section can be done as an individual or class activity, providing there are sufficient copies. A request on Friday will bring in copies of last week's journals.

Core material is Al, A2, B1, B2, B3, C1, C2. B4, B5, B6, B7, B8 are optionaL The various alternatives use the same techniques, and the suggestion is that different groups do the different alternatives to produce a class display giving more results with less work. C3 is optional for more able pupils.

Detailed Notes

Section A

This involves the collection of data, raises some problems of accuracy in measuring how time is spent, the presentation of data in tabular and graphic form and finishes with a simple pie chart. Pupils are asked to compare two pie charts and make commonsense observations.

If the questionnaire and tally charts are not completed before starting the unit, pupils need to work at approximately the same rate and finish this section together. The data collection in Section B can then be a class activity.

A1
With the forecast increase in leisure time because of, for example, unemployment, shorter working week and the increasing use of labour-saving gadgets, activities need to be known and provided for. There are several possible answers, for example:

2. parents, teachers, librarians, authors
3. to make proper provision for your needs, to suggest alternative books you might enjoy, broaden or deepen your reading, to order additional copies or different titles by popular authors.

A2
The clock faces are on page Rl. It is wise to avoid too many categories (use Table 1 as a guide). The problems of definitions, for example: 'What is "play"?', 'What do "breaks" count as?' can be treated informally in class discussion. The hours from the clock face are combined to give the figures in Table 1, which then give the sectors on the pie chart.

6. should show no school, more play on Sunday.
7. *shows usually more work than the pupils' school, but also less sleep. This is a reinforcement exercise and can be used for homework.

Section B

This involves simple questionnaire completion. The pupils summarize data from a questionnaire and present it in tables. Pie charts are used to show relative proportions. The questionnaire can be extended to other uses made of leisure time if desired. Two other possible items are time spent swimming last week and different indoor games played. A discussion with the class may well lead to more possibilities. These can then be used as reinforcement material to parallel B4 to B9. It can be shown that we need not be too preoccupied with accuracy for this purpose. Examples are used to show that pie charts are better for illustrating proportions, and bar charts are better for frequencies. B8 introduces a histogram.

B1
The questionnaire and completion of tally charts is probably best done as a class activity. Blank tables drawn in advance on the blackboard may help. All pupils should have the completed tables on page R2 handy for the rest of this unit. From B2 onwards, individual learning is possible. In the questionnaire completion the choice of daily newspapers needs care. If local papers are allowed, a comparison with national figures is not totally relaistic, but it is also unfair to rule out local papers. A restricted list of television programmes from which pupils can choose their favourites might help.

B2
Squared paper is helpful. Figure 3 can be used to give an example of a mode. If this is the first time these pupils have met a pie chart and their arithmetical ability is low, it may be helpful to give fictitious data for a class of 36 (or 30 or 24) pupils.

Taking 360/n to the nearest whole number for the usual class size makes very little difference to the final appearance of the pie chart if the sectors are dra wn in increasing order of size. The error is shown in the following table.

When the pie chart is drawn as described, the overall error gets included in the largest sector. It is least noticeable here, and this should be pointed out to pupils.

More able pupils may find it more satisfying to work the angle per pupil to one decimal place; the final check of adding the sector angles to see if you get 360^o is then more accurate. Visually, the pie charts differ little. Pupils need to be told how accurately they are to calculate their angles. More accurate figures for Creektown School pie chart are as follows:

³⁶⁰/₃₂ = 11.3 (to one decimal place)

Table 3 (more accurately)

The first pie chart drawn by the class is probably best done as a class activity. The teacher's (and later the pupils') judgement is needed for the pie chart radius. Although the largest sector is approximate, a rough measurement of it can be made bearing in mind the overall error (see table). Some classes may benefit from being told that pie charts do not necessarily have to be drawn in increasing order of sector size. Some children like to shade or colour the pie chart.

There may be a wide choice of favourite television programmes. A restricted list from which the pupils may choose their favourites might help, for example, Match of the Day, Bionic W'oman, Batman, Dr Who, Starsky and Hutch and Blue Peter.

g and i are most easily answered from the bar chart.
h and j are most easily answered from the pie chart.

B3
This section shows 'numbers of viewers out of a known population', whereas Bl shows proportions, and shows that some pupils like several television programmes. The frequencies obtained here can be much higher than those obtained for 'Favourite programmes'. The modal column is a good indicator of popularity, and relates to viewing audience figures. There may be a wide choice of programmes watched regularly. As in B2, a restricted list from which pupils can choose may help. This could perhaps be the same as their list of 'Favourite programmes'.

1. The data are nominal, so ideally the bars should be separate.
2. For more able pupils. The set of frequencies is not mutually exclusive, and the pie chart can be misleading.

*B4 - B8
These options give the possibility of getting different pupils to do different bar/pie charts and to build up a wider view of the class leisure activities by displaying the charts. It is suggested that pupils do one of B4 and B5, followed by one of B6, B7 and B8. More than this can be done if reinforcement is needed. The instruction 'Write two sentences ......' is to encourage the pupils to interpret their pictorial representation of statistics.

B9
The class intervals have been carefully chosen to make the histogram easy to draw. Note that 'exactly 2 hours' goes into the '2 but less than 4 hours' category. Encourage pupils to complete their diary as accurately as possible (not rounding to the nearest ¹/₄ or ¹/₂ hour) to minimize this boundary problem. Since all class intervals are equal, this representation can be considered as both a bar chart and histogram. Strictly speaking, in a histogram it is the area of the rectangle that represents the frequency; in a bar chart it is the height that represents the frequency. Hence the distinction is unimportant when the class intervals are all equal and none is open-ended. It may be necessary to choose different limits for your class intervals if the distribution of time spent reading is not like the one illustrated.

Section C

This covers simple interpretation and comparison of statistics, particularly the comparison between class data and national aggregates. It can be done as an individual, group or class activity, depending on the number of Radio Times, TV Tirnes or newspapers available.

C1
This bar chart is similar to that in B9. If you calculate the class mean viewing time from the original figures to compare with the published figures, pupils may find this interesting but difficult. A discussion on 'average' is possible. Pupils may need help with the class intervals for C1a. C1d requires an arrow to show the national mean on the class distribution. This gives a quick visual comparison of the class and national figures.

The national figures quoted came from surveys carried out for the BBC.

C2
The programmes from 4.00 to 10.00 p.m. can easily be put on a pie chart, since this is 360 minutes. The problem of programmes running from, for example, 9.30 to 10.30 pm may arise when 4.00 to 10.00 pm is being considered. The problems of definition have to be faced squarely here. Magic Roundabout could be considered under 'Comedy' or 'Children's programmes'. It does not matter what decisions are made, but they must be consistent and clearly explained in any comment on the figures. Usually programmes from 4.00 pm to the early evening would be 'Children's programmes'.

It may be interesting to compare BBC1 with ITV. Different groups of children could do each. It is left to the teacher to tell the children which channel to choose. It may be best to use BBC1 and ITV only for C2a to C2d; BBC2 programmes often do not begin until later in the evening.

When comparing the whole of the weekday with the whole of Saturday, different groups could look at ITV and BBC. Different total hours of broadcasting on the various days and channels mean that simple pie charts are inappropriate.

*C3
For more able pupils. The pie charts show the proportion of different newspapers taken and NOT the proportion of families. This means there is no 'None' category, allowance is made for families who take more than one paper, and there is direct comparability with national figures. A true national comparison with the national daily papers taken can only be made by ignoring local and evening papers.

National sales are given in the unusual unit 'hundreds of thousands' to help computation. Social Trends gives the figures in thousands, and it is usual to quote the figures as multiples of 10³ⁿ. The comparison in e should have some mention of the class not being a representative sample of the newspaper-buying public. The differences show the ways in which it is not representative.

Different groups of children could do C3a, c, e or C3b, d, e.

Answers

See detailed notes.

Numerical answers depend on the answers to the questionnaire.

Test Questions

1. Here is how John spent the 12 hours from 6.00am to 6.00 pm on a certain day.
   Sleeping 2 hours
   Eating 1 hour
   School 5 hours
   Play 3 hours
   Other 1 hour
   Draw a pie chart to show this information.
2. The 32 pupils in Class 1b at Park House Middle School gave the following information

   Musical instrument played
   Piano
   Recorder
   Trumpet
   Clarinet
   Violin
   Guitar
   None

   Favourite colour
   Red
   Blue
   Green
   Yellow
   Orange

   1. Draw a bar chart to show the musical instruments played.
   2. Why is the total greater than 32?
   3. *Why would it be misleading to draw a pie chart for these data?
   4. Draw a pie chart to show favourite colours. (360 / 32 = 11¹/₄)
   5. Which colours are the favourite of more than a quarter of the class?
3. The same 32 pupils measured the time spent watching television last week. Here are their answers in hours.
   6¹/₂ 12 15¹/₂ 18 21 0 3 7 10 14 2 23 9 8 14 17
   16 12 3 0 4 5 12 15 18 3 4¹/₂ 7 9 11 22 1
   1. Draw up a tally chart using the categories 'less than 5 hours', '5 but less than 10 hours', etc.
   2. Plot your results as a histogram.
   3. Use the histogram to write two sentences about these pupils' television viewing.
4. Class 1c at Newtown School decided to find out which were their favourite animals. They filled in a questionnaire and recorded their results in a frequency table:
   

   Animal	Number
   Cat	3
   Dog	10
   Lion	4
   Elephant	3
   Rabbit	5
   Horse	6
   Gerbil	2
   Other	3
   Total	36

   1. Draw a bar chart to show their favourite animals.
   2. Draw a pie chart to show their favourite animals.

   Use your bar chart and pie chart to answer these questions:

   3. How many pupils liked rabbits best?
   4. Which animal was the favourite of more than a quarter of the class?
   5. What fraction of the class voted for the most popular animal?
   6. What is your favourite animal? If you had been an extra member of class 1c, how would your answer have altered:
      1. your original bar chart
      2. your original pie chart

Answers

2	b	Some pupils play more than one musical instrument.
	*c	The fractions on the pie chart would not be fractions of the number of pupils in the class.
	e	Red, green
4	c	5
	d	Dog
	e	10/36 or 5/18

Connections with Other Published Units from the Project

Other Units at the Same Level (Level 1)

Shaking a Six
Being Fair to Ernie
Wheels and Meals
Probability Games
Practice makes Perfect
If at first ...
Tidy Tables

Units at Other Levels In the Same or Allled Areas of the Currlculum

Level 2

On the Ball
Opinion Matters
Fair Play

Level 3

Car Careers
Cutting it Fine
Pupil Poll
Multiplying People
Phoney Figures

Level 4

Figuring the Future
Sampling the Census
Equal Pay
Retail Price Index
Smoking and Health

This unit is particularly relevant to: Humanities, Social Sciences, Mathematics.

Interconnections between Concepts and Techniques Used In these Units

These are detailed in the following table. The code number in the left-hand column refers to the items spelled out in more detail in Chapter 5 of Teaching Statistics 11-16.

An item mentioned under Statistical Prerequisites needs to be covered before this unit is taught. Units which introduce this idea or technique are listed alongside.

An item mentioned under Idea or Technique Used is not specifically introduced or necessarily pointed out as such in the unit. There may be one or more specific examples of a more general concept. No previous experience is necessary with these items before teaching the unit, but more practice can be obtained before or afterwards by using the other units listed in the two columns alongside.

An item mentioned under Idea or Technique Introduced occurs specifically in the unit and, if a technique, there will be specific detailed instruction for carrying it out. Further practice and reinforcement can be carried out by using the other units listed alongside.

My Diary

	Sun	Mon	Tue	Wed	Thurs	Fri	Sat	Total
Time reading (hours and minutes; not schoolwork)
Tme watching TV (hours and minutes)

Questionnaire

What is your favourite television programme?
Which programmes do you watch regularly?
Which sport do you most enjoy playing?
Which sport do you most enjoy watching?
Which musical instrument (if any) do you play?
Which club or young people's organisation do you belong to (if any)?
What are your other hobbies?
How many hours did you spend reading last week?
How many hours did you spend watching television last week?
Which national daily newspaper(s) is taken by your family?
Which Sunday newspaper(s) is taken by your family?

Section A2

Pie Chart

Results Of Questionnaire

Title	Tally	Number

Table 8 - Favourite television programme

Table 9 - Favourite television programme in order of popularity

Table 10 - Television programmes watched regularly

Table 11 - Favourite sports to play

Table 12 - Favourite sports to watch

Table 13 - Musical instrument(s) played

Table 14 - Clubs belonged to

Table 15 - Hobbies

Table 16 - Time spent reading

Table 17 - Time spent watching television

Table 18 - National daily newspapers taken

Table 19 - Sunday newspapers taken

Section C Television Programmes

Type of programme	Tonight 4.00-10.00 pm (minutes)
News and current affairs
Comedy and variety
Plays and films
Sport
Children's programmes
Regular series
Other

Table 20 - Channel:

Table 21 - Channel:

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