Car Careers Statistics In Your World 
Student Notes
Teachers Notes
How Many N-Cars?
 
R-Cars
 
Different Samples
 
Cars and Caravans
 

Estimating Answers

How Many N-Cars?
You can use your results to estimate the number of cars of a particular age in Britain, e.g. N-registered.

  1. How many cars did you count altogether? The Rochdale sample counted 200.
  2. How many N-registered cars were there? The Rochdale sample had 17.
  3. What is the fraction of N-registered cars? The fraction in the Rochdale sample was 17/200 or 0.085.

The licensing office at Swansea knows how many cars are licensed each year. The numbers are published in the Monthy Digest of Statistics. At present there are about 15 000 000 cars on the road.

You have estimated the fraction of N-registered cars in your sample. If you multiply this fraction by 15 000 000, you get an estimate of the number of N-registered cars altogether.

The Rochdale sample estimates 0.085 x 15 000 000 cars = 1 275 000 N-registered cars.

  1. Estimate the number of N-registered cars using your results.
  2. Compare your results with those of other class members. Why are they different?
  3. Do any of the estimates give the correct answer?
    Give a reason for your answer.

 

R-Cars

  1. Work out the fraction of R-registered cars in your sample.
  2. Use this to estimate the number of R-registered cars in Britain.

The Rochdale fraction is 28/200 = 0.14.

The Rochdale estimate for R-registered cars is: 0.14 x 15 000 000 = 2 100 000.

In fact there were about 1 270 000 R-registered cars produced altogether. The Rochdale estimate is too high. The Rochdale sample does not fairly represent the cars on the road in Britain. The sample is unfair or biased.

  1. Was your sample biased? Write down one reason why it might be biased.

 

Different Samples
How would the results of your sample have been different if you had carried it out:

  1. at 8 am.,
  2. on an early closing day,
  3. in a town car park,
  4. outside a secondhand car sales centre,
  5. in a part of town with a lot of expensive houses,
  6. in an industrial estate,
  7. on a Sunday,
  8. on a motorway?
  9. Now write down reasons why your sample is probably biased.
  10. How could you get a less biased sample?

 

*Cars and Caravans
A survey of the end registration letter of 200 cars towing caravans was done on the M62 on August 25, 1978. The results are given in Table 3.

Registration letter Number of cars
E or earlier 8
F 6
G 2
H 6
J 17
K 14
L 32
M 20
N 20
P 17
R 26
S 27
T 5
Total 200

Table 3 - Table of results of survey of cars towing caravans.

There were about 320 000 touring caravans in Britain in 1978.

For August 1978 estimate:

  1. the number of caravans towed by L-registered cars.
  2. the number of caravans towed by cars that are E-registered or earlier.
  3. the number of caravans towed by cars that are P-, R- or S-registered.
  4. Draw a bar chart to show the distribution of the end registration letter of cars in this sample.
  5. Write two sentences to describe this distribution.
  6. Is this sample likely to be biased?

 

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