Brief Description

This unit provides a framework and rationale for collecting data from members of the class. Pupils are given the opportunity to collate the collected data into univariate and bivariate tables and display it as pictograms, bar charts and scattergrams. The aim is that pupils should build up a statistical picture of their own class based on distance from and mode of travel to school. This links with some aspects of local geography and gives pupils some insight into the reasons for collecting such data.

Design Time: 4 hours

Aims and Objectives

On the completion of this unit pupils should be able to draw and read one- to-one pictograms, draw and read bar charts using discrete and chssified continuous data, read and make simple inferences from tables, use tally marks and classify data.

They will have practised the preparation and interpretation of tables and used two-way tables to show intuitively the correlation between two variables.

They should be more aware of the inevitable sacrifice of information in order to achieve clarity in the representation of data and of the need and purpose of collecting data and the associated problems of classification.

Prerequisites

Pupils need to be able to draw and label axes and read a map. An optional section requires the ability to plot points on a graph.

Equipment and Planning

A large-scale map (1:25000) or street map of the school neighbourhood is required. It may be safer to use a photocopy. It is necessary to draw concentric circles according to the size of the catchment area and use colour shadings (red, yellow, green, blue, purple in that order). An alternative is to use tracing paper, acetate, glass, perspex or cellophane. Page Rl is available for pupils to complete tables and will be needed for most sections. A metric tape measure, bathroom scales, a calendar, squared and tracing paper are also needed.

Since school catchment areas differ so greatly, some of the tasks suggested in this unit may be impractical. In schools with very localized catchment areas, you may like to consider working with the three variables: distance from home to a grandparent (or aunt, or uncle), method of travel and usual time taken. These data can then be analysed in the same way as the three variables in Sections A and B. Other alternatives are mentioned appropriately in the detailed notes.

The first section may best be taken as a class discussion. It will be necessary to organize the collection of information about the class. The data required for Sections A and B can be collected on a class data sheet:

Pupils will need guidance on the selection of the appropriate colour band and advance warning in order to check the time taken to travel to school.

The data will then need to be reproduced so that each pupil has a copy, or else displayed so that pupils can easily see and make their own copies.

In Section C, similar information is required from each pupil in respect of height, weight, favourite dinner, day of birthday, number of children in family and whether or not a school dinner is taken. The work in this section could be divided out amongst the class and the final results displayed for the whole class to see and discuss.

Detailed Notes

Section A

A1
The opening discussion should stress the idea that the use to be made of the information governs the statistics collected - here, educational and school planning form the rationale. The education authority needs to decide the catchment areas and where to build schools. Here, pupils find out about the catchment area of their own school.

Most of the school statistics mentioned are used in the administration and planning. The pupils study their own class as a part of the school as a whole.

A class data sheet will be required as described under Equipment and Planning. This data could be collected prior to the lesson. It may be necessary to explain the 'usual' method of transport (compare A2a). It may also be worth making the distinction between contract and public service buses. The colour bands on the map correspond to the rainbow: red nearest to school, purple furthest from school. The radii of the circles should be chosen so that a reasonable number of pupils live in each shaded region. Pupils may need help in finding which region they live in. Pupils need to be told in advance to time their journey to school that morning to the nearest minute.

If the colour banding scheme is not appropriate, possible emphasis can be made on areas, bus-routes of specific segments based on geographical features, such as main roads and rivers.

Pupils should be involved with classifications which appear to them to be relevant.

A2
This data can be collected by a show of hands. It is good practice to include an other category on a table to allow for unplanned possibilities. In this case, pupils may wish to make templates for the symbols or use ready-made stencils to draw the pictogram. It is possible to use one symbol for five pupils, though sub-divisions complicate this. It is important that pupils should write statements describing results, as in A2d. They are also encouraged to do this in later sections. Susan's pictogram demonstrates mistakes which are sometimes made: different symbols used, no key, no title and symbols of different size.

A3
Pupils will need to fill in the correct distances on Table 7. Distance is measured in a straight line. Colour bands are used to avoid scale problems, but distance zones may be used directly. Pupils may need help in using tally marks.

f, g These show how information is lost in representation but clarity can be gained.

A4
By assuming no pupil takes zero minutes to reach school, equal size class intervals are facilitated. If the last class interval has to be left open (26 and over rather than 26 to 30), there is a problem of unequal class intervals. There is no need to raise this unless it arises in discussion. With larger or smaller catchment areas it may be necessary to use a different scale on the time axis.

Time has been measured to the nearest minute and then grouped into five- minute intervals to help with the drawing of the bar chart and to ensure that each category includes a multiple of five minutes to catch those who give their time to the nearest five minutes. With brighter pupils you may be able to draw a more accurate graph (a histogram), in which the x-axis and bars of the vertical line are marked as shown, magnified, here. This emphasizes that when time is measured to the nearest minute, the class interval 1 to 5 minutes means ¹/₂ to 5¹/₂ minutes.

It may be worth noting the problems of buses: a pupil may take much longer if he has missed a bus.

Teachers need to know how long pupils take travelling to school when arranging school activities, trips, detentions, or when dealing with late pupils.

If you feel that pupils need more practice, the work in Section A can be supplemented by a bar chart in A2, or pictograms in A3 and A4. More questions can be asked about the data, and the median can be introduced in A3 and A4 (not A2 which is a nominal scale).

Section B

The investigations in this section may prove unproductive for schools with local catchment areas, in which case only B2a and b may be of worth.

It may be possible to consider similar examples, e.g. mode of travel, time taken, distance to visit relatives such as grandparents or mode of travel, time taken, distance to visit the shopping centre. If so desired, consideration of situations such as these might provide additional practice in techniques.

B1
Here pupils compile two-way classifications. Guidance may be necessary to promote understanding of Table 4 and the completion of Table 9. Further questions of the type of B1a and b may prove helpful. Pupils should see the pattern as brought out in B1c, h and i. Pupils living further away may take longer to arrive at school, or they may have quicker means of transport.

B2
This will not work well if there are few different methods of travel. In this case, it may be better for pupils to study the Wombleshire data more closely.

Again, there is a pattern of correlation. Pupils living near school are more likely to walk.

*B3
This is an optional section, intended for pupils who get ahead. Pupils are asked to predict the pattern before constructing a two-way table. In the Wombleshire class pupils who walk. mostly take less than 20 minutes. Pupils coming by bus mostly take more than 10 minutes.

Section C

Each pupil will need a further class data sheet in order to complete this section. The work can be shared between different groups, but preferably combined afterwards as a class display leading to a discussion.

C1
The family sizes can be shown separately by boys and girls: note that each family has at least one child in this sample. The sample cannot be used to work out average family size.

C2
A calendar is necessary for birthdays. The distribution should be approximately uniform. Next year's bar chart would be moved one day, unless it is a leap year, assuming that no-one enters or leaves the class.

C3
Giving children a list of 10 dinners to choose from helps with the analysis. School menus vary for nutritional reasons or to maintain variety.

*C4
An optional section intended to reinforce the interpretation of compiling and reading tables.

*C5
Height and weight introduce an option intended for faster pupils. Further guidance may be required: this section concerns a scattergram. Tall boys tend to be heavier than short boys, etc. Girls aged 11 and 12 are generally heavier and taller than boys of the same age.

Answers

A1	a	See detailed notes.
A2	a	Bus
	e	See detailed notes.
A3	b	Red
	e	Purple
	i	See detailed notes.
A4	f	See detailed notes.
B1	a	5,1
	b	3,1
	c	See detailed notes.
	d	See detailed notes.
	i	See detailed notes.
B2	b	7,3
	c	6,0. See detailed notes.
B3	a	See detailed notes.
C2	d	See detailed notes.
C3	c	See detailed notes.
C5	b	See detailed notes.

Test Questions

1. Girls

   Name	Height (cm)	Weight (kg)
   Jane	147	32
   Elizabeth	154	37
   Carole	159	38
   Ann	163	40
   Barbara	138	33
   Wendy	141	36
   Susan	137	28
   Tracey	157	36
   Karen	140	33
   Mary	168	35

   
   Boys

   Name	Height (cm)	Weight (kg)
   David	144	30
   John	155	35
   Michael	137	26
   Richard	150	33
   Paul	136	26
   Kevin	137	27
   Chris	161	34
   Harold	152	38
   Sean	138	29
   William	143	31

   Table 1 - Class 1Q Heights and weights Girls
   

   1. Copy and complete Table 2 to show the heights of Class 1Q.
   2. Write down one fact from Table 1 which you could not find from Table 2.
   3. Write down one fact which is more easily seen from Table 2 than from Table 1.
2. Draw a bar chart to show the heights of pupils in Class 1Q.
3. Karen drew this pictogram to show the weights of pupils in Class 1Q:
   26 - 30kg + + + + + 0
   31 - 35kg + + + + 0 0 0 0
   36 - 40kg + 0 0 | 0 0 | 0
   Write down one mistake she made.
4. Copy and complete Table 3.
   

   		Weight (kg)			Totals
   		26 - 30	31 - 35	36 - 40
   Height (cm)	131 - 140
   	141 - 150
   	151 - 160
   	161 - 170
   Totals

   Table 3 - Heights and weights of Class 1Q
   
   Use Table 3 to answer the following questions:

5. How many pupils weighed between 26 and 30 kg and were between 131 and 140 cm tall?
6. How may pupils were between 31 and 35 kg in weight?
7. How many pupils over 140 cm high weighed over 35 kg?
8. Write down one sentence to describe the pattern in Table 3.

Answers

1	a	Height (cm) Tally Frequency 131 to 140 7 141 to 150 5 151 to 160 5 161 to 170 3 Table 2 - Heights of Class 1Q
	b	e.g. Mary's height
	c	e.g. The number over 160 cm tall
3		e.g. no key, no title, different symbols
4		Weight (kg) Totals 26 - 30 31 - 35 36 - 40 Height (cm) 131 - 140 5 2   7 141 - 150 1 3 1 5 151 - 160   1 4 5 161 - 170   2 1 3 Totals 6 8 6 20 Table 3 - Heights and weights of Class 1Q
5		5
6		8
7		6
8		e.g. Taller pupils tend to be heavier.

Connections with Other Published Units from the Project

Other Units at the Same Level (Level 1)

Shaking a Six
Being Fair to Ernie
Practice makes Perfect
If at first ...
Tidy Tables
Probability Games
Leisure for Pleasure

Units at Other Levels In the Same or Allied Areas of the Curriculum

Level 3

Pupil Poll

Level 4

Sampling the Census

This unit is particularly relevant to: Humanities, Geography (Local), 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.

Page R1

CLASS SUMMARY SHEET

Usual method of travel	Walk	Cycle	Car	Bus	Other
Number of pupils

Table 6 - How do you come to school?

Table 7 - How far do you live from school?

Table 8 - How long did it take to come to school today?

Table 9 - Distance from school and time taken

Table 10 - Distance from school and method of travel

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