Brief Description

This unit introduces pupils to statistical tables, explaining how to compose, read and clarify them. Data considered deal with domestic fires, leisure activities, road accidents and employment.

Design time: 4 hours

Aims and Objectives

The aim of this unit is to help pupils understand and read information which is laid out in tabular form, and learn how to simplify data to bring out significant patterns.

On completion of this unit pupils should be able to construct their own single variable frequency tables, two-way classification tables and to read individual figures from published tables. They will have practised drawing simple inferences from both types of table. They will also have practised making tables simpler to read, completing tables from bar charts, sorting out simple data and drawing bar charts. They should be mom aware of sources of data, correct practice in titling and annotating data and the conflict between readability and loss of information.

Prerequisites

Adding of up to six digits, rounding to the nearest ten, hundred or thousand and expressing one number as a fraction of another. Pupils should have had previous experience in drawing up simple bar charts.

Equipment and Planning

Calculators would be useful to aid addition, but they are not essential.

Data from the class, needed in A2 and A6, can be obtained by a show of hands. Since complex issues are raised, especially in Section C, some class discussion is desirable. The arrangement of the unit is that Section A deals with the construction of tables, Section 8 looks at annotations and titling and Section C deals with some methods of simplifying and interpreting tabulated data.

The following reference may be of value for Section C3: Data Reduction by A.S.C. Ehrenburg (Wiley, 1975), Chapter 1.

Detailed Notes

Copies of all tables are included in the R pages for easy reference. The journal Social Trends is a useful source for further data.

Many of the tables have been adapted (e.g. by changing percentages to frequencies) from the source to make them easier to work with.

Section A

A1
Table 1 is given in the text to provide a useful discussion point to start the unit. It is also reproduced as Table 8 on page R1 for ease of reference later. The questions remind pupils that not all tables are statistical, but all convey information.

A2
The unit deals only with discrete data, not with the compilation of class intervals. All data come initially in an unsorted form and have to be sorted before they are of much use.

If e is done, it will be necessary to collate the selections from the pupils. This can conveniently be done using the bhckboard. It is important to make sure that pupils do not use too many categories of sweets. One way of doing this is to nominate a few general categories from which they must choose. Remind them to include the total frequency in their table. An alternative survey would be favourite drinks.

A3
This takes the sorting one stage further, to bar charts, and indicates how some questions then become easier to answer.

A4
In this section we proceed the other way round. Data given in the form of a bar chart are written in tabular form. It is not practical to collect class data here as then it would be necessary to draw the table first. This secbon includes the first introduction to reading tables.

*A5
An optional exercise for reinforcement provides a check on the basic work before continuing to two-way tables.

A6
This again starts with given data so that pupils practise reading the table. Then they can collect their own data and draw up the table for them. This collection of class data needs organizing.

A suggestion for single-sex classes is instead of using Boys and Girls to use Oldest in the family and Not oldest in the family. Single children count as Oldest.

Pupils should notice that the sum of the row totals should equal the sum of the column totals. This is the number of pupils in the class.

A7
This returns to Table 1 (reproduced as Table 8 on page Rl) and is an exercise in reading a harder table. Questions f and g start to draw simple comparisons and lead towards inference, e.g. Where should the fire brigade concentrate its fire prevention advertising?

With pupils of lower ability, further reinforcement may be necessary at this stage. This can be done either by using collected data (e.g. a vehicle survey), or using further tables from sources such as Social Trends.

Section B

This section brings out the importance of four things: a clear title, the data, use of footnotes and quoting the source. B1-4 take each of these in turn, using Table 1 as the main example.

Bl
Titles often show the incompatible demands of accuracy of description and brevity for ease of reading. They should indicate clearly what the data are about.

B2
Since many data, particularly sociological and economic data, change rapidly, it is important to indicate the date to which they apply.

B3
The source should be given in sufficient detail to allow others to trace it and find out further details of meaning, background, method of collection, and so on.

B4
Footnotes are often used to help clear up problems of definition and nomenclature, explain changes in method of collection and give further details that cannot be included in a row or column heading.

B5
An exercise on leisure activities using Table 9 on page R2 to bring together the work of 81 to 84. (Note the distinction between United Kingdom and Great Britain; the former includes Northern Ireland.) Question g shows that tables should be consistent and can often be checked in this way.

B6
A rather harder exercise on accidents uses the two-way Table 10 on page R2. In the discussion on questions d and e comparisons can be made for Fatal and Serious or for Slight injuries. Comparisons may also be made in relative terms (using proportions) or in absolute terms (using differences). The age range 5-9 shows the greatest sex differences.

The difference between numbers of slight injuries to 15 and 16 year old boys and girls are too small to be significant. It appears that carefulness on the road by boys and girls at these ages is about the same. The large differences at the younger age, with young boys being far more prone to accident than young girls, may reflect different games played, attitudes to life, and so on.

It may be desirable with some groups to omit one or other of these last two sections.

Section C

This section is concerned with reading difficult tables and making them easier to read. Two techniques of simplifying the tables are introduced;

1. Reduce the number of digits printed in the table. Although this means that accuracy is lost, it makes the individual items much easier to identify, and in many cases this accuracy may be sufficient to give a general impression.
2. Put the columns in decreasing order of total, or average, from the left. It is then easier to pick out anomalies and simple relationships. A more able group could perhaps go on to convert actual figures to percentages, as is often done to make a table clearer.

Before attempting this section pupils must be able to round figures to the nearest ten, hundred or thousand.

C1
Table 9 on page R2 is rewritten as Table 11 with figures rounded to the nearest hundred. If pupils find this task difficult, it may be preferable to begin with a class discussion. The pupils' text does contain an instruction to ask for help if necessary. It also tells pupils to show the teacher their table for checking. This may be more easily done by a self-checking system. It should be obvious that the general picture is made clearer but accuracy has been lost.

C2
This is a parallel exercise to C1 and can be used as reinforcement. In both C1 and C2 rounding may result in the columns not adding to the rounded total.

C3
This is definitely a harder section. Class discussion on the value of changing the order of columns is probably useful, otherwise the way it shows up exceptions to the pattern may not be seen. A new table is introduced because it shows more clearly the advantages of the method than the other tables in the unit. Tables 8 and 9 can also be re-ordered in this way (numbers to the nearest hundred) and yield some interesting information. Table 10 shows no exceptions to the general pattern when rewritten in this way, and it is the exceptions that are interesting.

Answers

A1	a	Bus or train timetable
	b	Multiplication table or ready reckoner
	c	Lesson timetable
A2	a	5
	b	Guitar
	c	Guitar 4; drums 1; accordion 1; tin whistle 2
	d	4/11
A3	a	6p
	b	12p
	c	The bar chart is the most obvious way. However, in a distribution of this kind, the table is easy to read.
A4	a	4
	b	Brown 9, blond 3, red 1, black 2
	d	10
	e	9
	f	9/10
A5	b	5 + 10 + 15 + 25 + 30 + 20 + 15 + 10 = 130
	c	4
	d	15, 30
A6	a	8
	b	4
	c	14
	d	10
	e	28
	f	8/18 or 4/9
	g	6/10 or 3/5
	h	Girls - a larger proportion owned bicycles
A7	a	50900
	b	7848
	c	3300
	d	1547
	e	255
	f	kitchen
	g	Cooking
B	a	Table 1 conforms to the rules.
	b	Table 2 does not have a title, date or source. Table 3 does not have a title, date or source.
B1	a	Domestic fires in the United Kingdom, by cause and room of origin.
	c	United Kingdom (England, Wales, Scotland, Northern Ireland)
	d	In homes
B2	a	1976
	b	1 year, 1st January to 31st December, 1976
	c	The data are meaningless without a date as the incidence of fires varies considerably from year to year.
B3	a	Social Trends
	b	See detailed notes.
B4	a	Bed-sitting rooms have been counted as bedrooms.
	b	Hall
	c	'Elsewhere or not known'
B5	a	'Frequency of selected leisure activities reported by 16 year olds, 1974'
	c	1974
	d	Social Trends
	e	11070
	f	England, Scotland, Wales (Great Britain)
	g	Because 11 070 pupils replied to each category of activities
B6	a	0-16 years
	b	Between 1st Jan. 1975 and 31st Dec. 1975
	c	Age 15 - slight; age 16 - slight
	d	Age 5 to 9. See detailed notes.
	e	See detailed notes.
C1	a	Table 11 becomes: (numbers in hundreds)   Often Sometimes Never or hardly ever Like to, but no chance Reading 30 51 27 3 Outdoor games 42 39 27 3 Swimming 23 49 30 9 Indoor games 28 36 36 11 TV 72 32 6 1 Parties 21 53 29 8 Dances 44 34 27 6 Voluntary work 8 33 52 18
	c	The numbers are easier to find and simpler to read.
	d	There is a loss of accuracy. Answer may be given as, e.g. 30 instead of 30 hundred.
	e	49 hundred
	f	52 hundred
	g	28 hundred
C2	a	Table 10 becomes: (numbers in hundreds)     Age 0-4 5-9 10-14 15 16 Males Fatal and Serious 10 27 15 2 2 Slight 24 68 41 4 5 Females Fatal and Serious 6 13 11 1 2 Slight 15 39 34 5 5
C3	a	Table 13 becomes: (numbers in thousands)   SE GL EA SW WM EM Y+H NW N W SC NI Males   0-2 12 12 3 6 7 5 7 10 6 4 10 - 2-4 10 10 2 5 6 4 6 9 5 4 9 - 4-8 14 13 3 8 8 6 8 13 6 5 15 - 8+ 94 92 21 64 72 43 65 117 61 47 94 - Total 130 127 29 83 92 57 85 149 77 59 127 39 Females   0-2 5 4 1 2 3 2 3 4 2 2 5 - 2-4 4 3 1 2 3 1 2 4 2 2 4 - 4-8 6 5 1 3 4 2 3 6 3 3 7 - 8+ 28 23 6 20 25 13 20 37 21 16 37 - Total 43 35 8 28 34 19 28 50 29 22 53 17
	b	Table 14 becomes: (numbers in thousands)   NW SC SE GL WM Y+H SW N W EM NI EA Male   0-2 10 10 12 12 7 7 6 6 4 5 - 3 2-4 9 9 10 10 6 6 5 5 4 4 - 2 4-8 13 15 14 13 8 8 8 6 5 6 - 3 8+ 117 94 94 92 72 65 64 64 47 43 - 21 Total 149 127 130 127 92 85 83 77 59 57 39 29 Female   0-2 4 5 5 4 3 3 2 2 2 2 - 1 2-4 4 4 4 3 3 2 2 2 2 1 - 1 4-8 6 7 6 5 4 3 3 3 3 2 - 1 8+ 37 37 28 23 25 20 20 21 16 13 - 6 Total 50 53 43 35 34 28 28 29 22 19 17 8

Test Questions

1. Name a kind of TABLE which has numbers in it. Give an example of DATA you could find in a table.
2. On July 4, 1977, 25 pupils from Class lu in the Mandonham Comprehensive School took a swimming test. The numbers of widths swum without touching down were:
   5, 4, 1, 0, 5, 6, 4, 7, 3, 4, 3, 2, 5, 5, 4, I, 0, 3, 4, 6, 8, 4, 3, 5, 9
   1. Show the data in a frequency table.
   2. One of the pieces of information below can only be read from the data list above. Which is it? (All the others are easier to read from the table.)
      1. The number of pupils who swam five widths
      2. The number of widths swum by the sixth pupil
      3. The number of widths with the highest frequency
      4. The highest frequency
3. In question 2, the first 10 figures were the girls' results. Complete this two-way table:
   

   	Number of widths
   	Less than 4	4 or more
   Girls
   Boys
   Total

    

4. Every statistical table should have a TITLE
   Write down a title for the table in Question 3.
   Name two other things a statistical table should have.
   Write down one of these for the table in Question 3.
5.  
   1. The table below mentions 2486 casualties altogether. Over what period of time did these happen?
   2. How many more people were slightly injured than seriously injured?
   3. On which classes of road were the largest number of people killed?
   4. On which class of road was the smallest number killed?
   5. On motorways there were fewer slight injuries than there were serious injuries. For which other type of road is this true? Give a possible reason.
      

      Class of road	Fatal (killed)	Serious injuries	Slight injuries	Total (all casualties)
      Motorway	4	88	78	170
      Trunk roads	25	290	321	636
      A roads	25	311	296	632
      B roads	1	85	86	172
      C roads	12	242	252	506
      Unclassified roads	6	173	191	370
      Total (all roads)	73	1189	1224	2486

      Casualties in road accidents. Northamptonshire, 1974
      (Source: Northamptonshire Transport Policies and Progremme, 1976-1977)

6.  
   1. Re-write the table from Question 5, adding together fatal and serious injuries and writing the answer in one column.
   2. Simplify the table in one other way. (Hint: either think about the numbers or the order of the columns.) Give one advantage and one disadvantage of your table.

Answers

1		Any suitable examples of tables and data are acceptable.
2	a	Number of widths Pupils 0 2 1 2 2 1 3 4 4 6 5 5 6 2 7 1 8 1 9 1   25
	b	ii
3		Under 4 4 and over Total Girls 3 7 10 Boys 6 9 15 Totals 9 16 25
4		Any appropriate title A statistical table should also have: A date and a source (for secondary data) For the table in Question 3 the date is July 4, 1977.
5	a	One year - January 1 to December 31 1974
	b	35 (1224-1189)
	c	Trunk roads and A roads
	d	B roads
	e	Because traffic is faster moving so any injury is more likely to be severe.
6	a	Class of road Fatal and serious Slight All accidents M 92 78 170 T 315 321 636 A 336 296 632 B 86 86 172 C 254 252 506 U 179 191 370 All roads 1262 1224 2486
	b	Either alter the row order to T A C U B M or round numbers to nearest hundred (or nearest ten). Advantage: Table is easier to read (or equivalent) Disadvantage: Loss of information, or deaths too few to show, or loss of distinction between numbers of serious and slight

Connections with Other Published Units from the Project

Other Units at the Same Level (Level 1)

Shaking a Six
Being Fair to Ernie
Probability Games
Practice makes Perfect
Leisure for Pleasure.
Wheels and Meals
If at first...

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

Level 3

Car Careers

Level 4

Figuring the Future
Sampling the Census
Smoking and Health
Equal Pay

This unit is particularly relevant to: Mathematics, Social Sciences

Interconnections between Concepts and Techniques Ueed 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

Type of sweet	Frequency
Total

Table 5 - Favourite sweets in out class

Table 6 - Colour of hair of 10 pupils

Table 7 - Number of peas in a pod

¹ Includes bed-sitting rooms
² Includes stairs and corridors
³ Includes fires which started outside and spread to the building
⁴ Totals have been rounded to the nearest thousand
Table 8 - Domestic fires in the United Kingdom: by cause and room of origin, 1976
(Source: Social Trends, No. 8, 1977, page 197)

Page R2

Activity	Often	Sometimes	Never or hardly ever	Like to, but no chance
Reading books (apart from school work/homework)	2989	5092	2657	332
Playing outdoor games/sports	4207	3874	2657	332
Swimming	2325	4871	2989	885
Playing indoor games/sports	2806	3572	3572	1120
Watching TV	7195	3210	554	111
Going to parties	2103	5314	2878	775
Dancing at discos, etc.	4427	3432	2657	554
Voluntary work to help others	775	3321	5203	1771

Total sample size = 11070 persons
Figures are for Great Britain
Table 9 - Frequency of selected leisure activities reported by 16 year olds, 1974
(Source: Social Trends, No. 8, 1977, page 184)

Table 10 - Pedestrian casualties, 1975: severity. sex and age
(Source: RoadAccidents, Great Britain, 1975 (HMSO). From Tables 26 and 27.)

Table 11 - Frequency of selected leisure activities reportedby 16 year olds, 1974 (Hundreds)

Page R3

	South-east except GLC	Greater London	East Anglia	South West	West Midlands	East Midlands	Yorkshire and Humberside	North West	North	Wales	Scotland	Northern Ireland
Length of time on register
Males
up to 2 weeks	12124	11845	2814	5799	6700	4498	6946	9657	5567	3858	9547	-
over 2 and up to 4 weeks	9786	10018	2320	5242	5877	3671	5768	9024	4744	3757	8644	-
over 4 and up to 8 weeks	14226	13465	3185	7875	7746	5541	7778	13318	6236	5210	14840	-
over 8 weeks	93938	91989	20785	64299	71836	43116	64997	116676	60657	46581	93518	-
Total	130074	127317	29104	83215	92159	56826	85489	148675	77204	59406	126549	39521
Females
up to 2 weeks	5091	4182	817	2305	2670	1593	2561	4080	2203	1709	4468	-
over 2 and up to 4 weeks	4207	3460	763	2200	2582	1417	2200	3903	1912	1730	4328	-
over 4 and up to 8 weeks	5797	4559	1068	3319	3801	2395	3415	5726	3117	2578	7494	-
over 8 weeks	27908	23123	5600	20153	24761	13415	19857	36641	21431	15868	36733	-
Total	43003	35324	8248	27977	33814	18820	28033	50350	28663	21885	53023	17139

Table 12 - Regional analysis of unemployment: February 10, 1977
(Figures for Northern Ireland showing the length of time on the register are available only quarterly in respect of March, June, September and December.
(Source: Departement of Employment Gazette, March 1977, page 278)

Table 13 - Regional Analysis of Unemployment: February 10, 1977 (Numbers in thousands)
(Source: Department of Employment Gazette, March 1977, page 278)

Table 14 As Table 13 but with the columns reordered (Numbers in thousands)
(Source: Department ofEmployment Gazette, March 1977, page 278)

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