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Data Sheet
Life is a risky business. Whatever you are doing, whether you are at work, at home or somewhere
else, there is always the risk that you will have an accident of some sort. People have even been
known to hurt themselves doing something as simple as getting out of bed or putting on their socks!
But obviously some activities and places are more dangerous than others.
Accidents and Activities
The Consumer Safety Unit of the Department of Trade and Industry collects data relating to home and
leisure accidents from a sample of hospitals. The data in the table below are their national estimates of
the annual number of accidents requiring hospital treatment that occurred whilst doing home or leisure
activities. The table does not include accidents that happened at work.
Activity Number of Accidents
Household Activity 5 286
DIY/Maintenance 15 236
Shopping 71 514
Education/Training 172 895
Sport (excluding education) 784 220
Leisure/Hobby 574 745
Travelling/Touring 415 238
Basic Needs 222 608
Other/Unspecified 805 016
Total 3 066 758
Source: www.dti.gov.uk
Accidents at Work
The following table gives government figures for the number of people employed in each of the major
industrial sectors and the number of accidents that occurred in each sector during the course of a year.
The accidents are divided into 3 categories: fatal accidents, major accidents that were not fatal and
more minor accidents that caused the worker to be off work for 3 or more days. Very minor accidents
that did not cause three or more days absence are not included.
Number of Accidents Number Employed
Industry Type Fatal Major Over 3 Days (thousands)
Agriculture, Forestry & Inland Fishing 36 726 1 456 314
Energy & Water Supply & Mining 7 506 2 511 189
Manufacturing 41 8 038 39 460 3 950
Construction 81 4 749 10 504 1 177
Service 55 15 296 82 182 19 707
Total 220 29 315 136 113 25 337
Sources: www.hse.gov.uk , www.statistics.gov.uk
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Accidents at Home
The information in the table below was collected by the Consumer Safety Unit of the Department of Trade and Industry. It gives the number of different
types of home accidents that needed hospital treatment during a year from a sample of hospitals. The sample of hospitals dealt with roughly 5% of the
country’s casualties from home injuries. The Consumer Safety Unit finds national estimates for each type of injury and location by multiplying the figures
given in the table by 18.29
For example, the national estimate for the total number of people who had a fall indoors at home that required hospital treatment during one year is:
32 494 18.29 594 315 = 594 000 to the nearest thousand
Fall Struck Cut Bite/Sting Poisoning Thermal Electric Other Total
Kitchen 3714 2228 4507 231 315 1944 24 1604 14567
Bathroom/Toilet 2468 901 506 20 85 214 3 809 5006
Living/Dining Room 6653 5042 1135 541 165 523 26 3159 17244
Stairs/Hall 12275 2263 371 95 26 27 3 882 15942
Porch/Conservatory 1448 418 213 79 4 7 1 706 2876
Bedroom 5630 3317 766 165 211 191 20 1937 12237
Other Indoor 306 166 67 9 11 24 3 125 711
Total Indoor 32494 14335 7565 1140 817 2930 80 9222 68583
Garage 306 450 384 9 6 12 9 364 1540
Driveway/Path/Patio 3682 1235 446 85 16 62 17 1100 6643
Greenhouse/Shed 106 120 205 9 5 3 1 90 539
Garden 8258 4017 2568 841 87 183 63 2434 18451
Other Outdoor 1382 404 119 27 3 22 11 991 2959
Total Outdoor 13734 6226 3722 971 117 282 101 4979 30132
Total 46228 20561 11287 2111 934 3212 181 14201 98715
Source: www.dti.gov.uk
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Worksheet
Use Accidents and Activities from the Data Sheet.
Relative frequencies can be used to compare the proportions of hospital casualties from home or
leisure accidents that occurred during these activities.
Number of accidentsthat occurredwhilst doing the activity
Relative frequency =
Totalnumber of home or leisure accidents
71 514
eg Relative frequency of accidents occurring during shopping = = 0.023 (to 3 dp).
3 066 758
Relative frequencies can be given as fractions, decimals or percentages. When the values in the
numerator and denominator of the fraction are large and difficult (as they are here), the decimal
version is more convenient. To find the corresponding percentage, multiply by 100.
1. Complete the rest of the table below.
Activity Number of Accidents Relative Frequency %
Household Activity 5 286
DIY/Maintenance 15 236
Shopping 71 514 0.023 2.3
Education/Training 172 895
Sport (excluding education) 784 220
Leisure/Hobby 574 745
Travelling/Touring 415 238
Basic Needs 222 608
Other/Unspecified 805 016
Total 3 066 758
Each relative frequency gives an estimate of the probability that a hospital casualty who had a home
or leisure accident was taking part in that particular activity when the accident occurred.
2. Use the relative frequencies to put the activities in order of the likelihood that a hospital casualty
was involved in the activity when the accident occurred.
……………………………………………………………………………………………………….
……………………………………………………………………………………………………….
……………………………………………………………………………………………………….
……………………………………………………………………………………………………….
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Use Accidents at Work from the Data Sheet.
The probability of a worker having an accident during a year that was not major but caused him/her to
be off work for over 3 days can be estimated by using relative frequency where:
Number of workers who had an accidentcausing3 or more daysoff work
Relative Frequency =
Totalnumber of workers
136 113
The probability of a worker having such an accident during a year = = 0.0054 (to 2 sf)
25 337 000
This overall probability can be compared with the probabilities for particular types of industry.
For example, the probability of a construction worker having an accident during a year that is not
10 504
major but results in more than 3 days off work = = 0.0089 (to 2 sf).
1 177 000
This suggests that a construction worker is much more likely to have such an accident than the
‘average’ worker.
Note that these probabilities are rough estimates, rather than accurate values. They assume that none
of the workers had more than one accident during the year. Also because the number of accidents
varies from one year to the next, another year’s results would give different probabilities.
3. Complete the rest of this table:
Probability of worker having accident during year
Industry Type Fatal Major Over 3 Days
Agriculture, Forestry & Inland Fishing
Energy & Water Supply & Mining
Manufacturing
Construction 0.0089
Service
All included industries 0.0054
Use the table to answer these questions:
4. In which industry is a worker most likely to have:
a a fatal accident? …………………………………
b a major but non-fatal accident? ….…………………………….
c an accident that is not major but results in an absence of 3 days or more? .…………………….
5. In which industry is a worker least likely to have:
a a fatal accident? …………………………………
b a major but non-fatal accident? ...…………………………….
c an accident that is not major but results in an absence of 3 days or more? …………………….
6. Overall which type of industry do you think is a the least dangerous? ………………………
b the most dangerous? ……………...………
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Use Accidents at Home from the Data Sheet.
You can see from the values given in the table which types of accident are most likely at home and
where they are likely to happen. For example, the most likely place for having a fall that requires
hospital treatment is in the stairway and hall since more casualties had falls there than anywhere else.
The totals can also give useful information. For example, the total number of accidents indoors is
68 583 whereas the total number of accidents outdoors is 30 132. This means that an accident at home
that requires hospital treatment is more than twice as likely to be indoors as outdoors.
Use the data from Accidents at Home to answer the following questions about accidents needing
hospital treatment.
7. Which of these types of accident is a most likely to happen at home?……………………………
b least likely to happen at home? ……………………………
8. In which room in your house are you most likely to be a cut?………………………………….
b struck by something? ……………….
c burnt (thermal accident)?…………..
9. What type of accident are you most likely to have: a in the kitchen?……………………………
b in the garden? ……………………………
c in the greenhouse or shed? ………………
10. Overall, what type of accident is most likely to happen a indoors at home? ………………………
b outdoors at home? ……………………
National estimates can be found for each type of injury and location by multiplying the figures given
in the table on the Data Sheet by 18.29
For example, the national estimate for the total number of people who had a fall indoors at home that
required hospital treatment during one year is:
32 494 18.29 594 315 = 594 000 to the nearest thousand
This has been entered into the table below.
11. a Complete the rest of the table, giving answers to the nearest thousand.
National Estimate Fall Struck Cut Bite/Sting Poisoning Thermal Electric Other Total
Indoor Accidents 594 000
Outdoor Accidents
Total at Home
b The total population of the country when this data was collected was approximately 59 756 000.
Use this information to estimate the probability that in one year a person has an accident at
home that requires hospital treatment.
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Estimates of the probabilities of particular types of accidents in particular locations can be found using
relative frequencies.
For example, if a person has an accident at home that requires hospital treatment, then the probability
11 287
that it was a cut is = 0.11 (to 2 sf).
98 715
This probability is shown on the probability line below. A probability line stretches from 0 (which
represents the probability of something that is impossible) to 1 (which represents the probability of
something that is certain to happen).
Probabilities that accidents at home (needing hospital treatment) are of particular types
P(cut)
0 0.5 1
Note that this is an overall probability. In practice the probability will vary widely from one person to
another – can you explain why?
12. If a person has an accident at home that requires hospital treatment, find the probability it was:
a a fall …..………………………………………………………………………………………..
b because of being struck by something ………………………………………………………..
c bite or sting …………………………………………………………………………………….
Show these probabilities on the probability line above.
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Probabilities can also be shown on a bar chart.
If, for example, a person has a fall indoors at home, the probability that it was in the kitchen is:
3714
= 0.114 (to 3 sf)
32 494
This is shown on the bar chart below.
13. a Complete the bar chart.
Falls indoors at home needing hospital treatment
0.4
0.3
Probability
0.2
0.1
0.0
Bedroom
Stairs/Hall
Living/Dining
Other Indoor
Kitchen
Porch/Conservatory
Bathroom/Toilet
Room
Location
b If a person has a fall indoors at home, where is it most likely to be? ……………………………
14. a Draw a similar bar chart on graph paper for falls that happen outdoors.
b If a person has a fall outdoors at home, where is it most likely to be? …………………………
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Teacher Notes
Unit Intermediate Level, Handling and interpreting data
Notes
The Data Sheet gives simplified versions of the official statistics for the year 2000. The data is also
supplied on a spreadsheet. If you wish to use the original or more recent data, search for HASS (Home
Accident Surveillance System) or LASS (Leisure Accident Surveillance System) on the DTI website and
Labour Market Trends or the Monthly Digest of Statistics on the National Statistics website.
Students need to be aware that real data such as these give only rough estimates of probabilities. It is
recommended that you spend time discussing the methods and results to point out their limitations. Some
of the most important discussion points are given with the answers below.
Answers and Suggestions for Discussion
Accidents and Activities
1.
Activity Number of Accidents Relative Frequency %
Household Activity 5286 0.002 0.2
DIY/Maintenance 15236 0.005 0.5
Shopping 71514 0.023 2.3
Education/Training 172895 0.056 5.6
Sport (excluding education) 784220 0.256 25.6
Leisure/Hobby 574745 0.187 18.7
Travelling/Touring 415238 0.135 13.5
Basic Needs 222608 0.073 7.3
Other/Unspecified 805016 0.262 26.2
Total 3066758 1.000 100.0
2. Other/Unspecified Activities, Sport, Leisure/Hobby, Travelling/Touring, Basic Needs,
Education/Training, Shopping, DIY/Maintenance, Household Activity.
Discussion Points:
What could be included in Basic Needs?
This category includes things like eating and drinking.
What could be included in the Other/Unspecified Activities?
This category includes more accidents from the other categories as well as activities that are not
covered by the other categories.
DIY is often seen as a dangerous activity. Why is it so far down the list?
Far fewer people may be involved in DIY than in the other activities further up the list, so DIY may be
more dangerous than some of these activities but still less likely to be responsible for a hospital
casualty.
How could you use relative frequencies to reflect how dangerous an activity is?
A discussion about this could bring up a number of valuable points. One suggestion might be to
estimate how many people are involved in each activity during a year and give the number of resulting
casualties as a fraction or % of this number. However this does not allow for different people
spending different times on the activity - this could lead to further discussion about methods that could
be used that take into account the time spent on the activity. For a particular person, the probability of
having an accident would also depend on how careful they are, how much experience they have etc.
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Accidents at Work
3.
Probability of worker having accident during year
Industry Type Fatal Major Over 3 Days
Agriculture, Forestry & Inland Fishing 0.000115 0.0023 0.0046
Energy & Water Supply & Mining 0.000037 0.0027 0.0133
Manufacturing 0.000010 0.0020 0.0100
Construction 0.000069 0.0040 0.0089
Service 0.000003 0.0008 0.0042
All included industries 0.000009 0.0012 0.0054
4. a Agriculture, Forestry & Inland Fishing b Construction
c Energy & Water Supply & Mining
5. a Service b Service c Service
6. a Service
b Opinions could vary about this with Agriculture, Forestry & Inland Fishing the most likely choice
because of the much higher probability of a fatal accident.
Discussion Points:
The worksheet mentions that ‘these probabilities are rough estimates, rather than accurate values.
They assume that none of the workers had more than one accident during the year. Also because
the number of accidents varies from one year to the next, another year’s results would give
different probabilities.’
These important points could be explained and discussed further.
Students could be asked to use the probabilities to estimate the number of accidents that would
occur in a particular workplace with a given number of employees.
Discussion about this should include the fact that the results may not be very accurate as the work
done in a particular workplace might be more or less dangerous than the norm and the workers
may be more or less safety-conscious.
You could ask students to suggest ways of estimating the probability that a particular worker
doing a particular job in a particular workplace has a minor, major or fatal accident during his/her
whole career?
Suggestions might include using records of accidents that have occurred in the past for that
particular job and workplace, but there are many reasons why it would be difficult to arrive at an
accurate estimate. For example, there may have been very few accidents, especially in the major
or fatal categories. Some workers may have stayed in the job for a long time, whilst others moved
on to another job after a short time. Some workers will have been more careless than others, and
may have had more than one accident. Considering the past record of the particular worker in
question may give useful information about the rate of minor accidents, but this will not allow for
his/her increasing experience of the job. There are so many variables that it would only be
possible to give a very rough estimate.
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Accidents at Home
7. a Fall b Electric
8. a Kitchen b Living/Dining Room c Kitchen
9. a Cut b Fall c Cut
10. a Fall b Fall
11.
National Estimates Fall Struck Cut Bite/Sting Poisoning Thermal Electric Other Total
Indoor Accidents 594 000 262 000 138 000 21 000 15 000 54 000 1 000 169 000 1 254 000
Outdoor Accidents 251 000 114 000 68 000 18 000 2 000 5 000 2 000 91 000 551 000
Total at Home 846 000 376 000 206 000 39 000 17 000 59 000 3 000 260 000 1 805 000
12. a 0.47 (2 dp) b 0.21 (2 dp) c 0.02 (2 dp)
Probabilities that accidents at home are of particular types
P(bite/sting)
P(cut) P(struck) P(fall)
0 0.5 1
13. a
Falls indoors at home needing hospital treatment
0.4
0.3
Probability
0.2
0.1
0.0
Bedroom
Stairs/Hall
Living/Dining
Other Indoor
Kitchen
Porch/Conservatory
Bathroom/Toilet
Room
Location
b Stairs and hall
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14 a
Falls outdoors at home needing hospital treatment
0.7
0.6
0.5
0.4
Probability
b Garden
0.3
0.2
0.1
0.0
Other Outdoor
Greenhouse/Shed
Driveway/Path/Patio
Garage
Garden
Location
Discussion Points:
How accurate are the national estimates and probabilities found?
Discussion should include the importance of using a representative sample and what this means.
In fact in this case the sample of hospitals used is not very representative and so the national estimates
(and probabilities) calculated can only be taken as very rough guides.
Is it possible to use the data to find a good estimate of the probability that a particular person will have
a particular type of accident in a particular room in their house?
Students need to realise that the data just give overall probabilities that home accidents requiring
hospital treatment were of particular types in particular locations. The probability of a particular type
of accident in a particular location will vary widely from one person to another depending on how
long the person spends in each location, what they do there, how careful they are, and so on.
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