National Figures

New Cars
Table 4 compares the number of new cars to the total each year. All cars are licensed each year.

(Source: Monthly Digest of Statistics)

Table 4 - Cars licensed 1964- 1977 in Great Britain.

Large numbers are often written in thousands in statistical tables like Table 4.

So in 1968 there were about 10 816 000 cars in Britain. Of these, 1 117 000 were new cars.

1. What is the advantage of listing large numbers in terms of thousands?
2. What is a disadvantage of this method?
3. How many cars were there in Britain: in 1964, in 1970, in 1976?
4. In which year was the largest number of new cars licensed?
5. In which year was the percentage of new cars highest?
6. In which year was the percentage of new cars lowest?
7. Draw a graph to show the percentages of new cars each year. (Put 'Years' along the horizontal axis.)

At the end of 1973 there was a shortage of petrol, and prices rose rapidly.

8. What effect do you think this petrol crisis had on the sales of cars?
9. Comment on the general pattern shown by your graph. When was the percentage of new cars falling? When was it rising?

How Old?

(Source: Transport Statistics, Great Britain, 1 966-76)

Table - 5 Ages of cars on January 1, 1977

On January 1, 1977, there were 2 125 000 cars under two years old. Their average age was one year.

Use Table 5 to answer questions a to c about cars on January 1, 1977.

1. How many cars were over six and under eight years old? What was their average age?
2. How many cars were over 10 and under 12 years old? What was their average age?
3. There were 274 000 cars over 16 and under 20 years old. What was their average age? Assume that 274 000 cars were equally spread over the four-year period (so there will be the same number over 16 and under 18, as over 18 and under 20 years old). How many will be over 18 and under 20 years old?
4. Plot the figures of Table 5 in a diagram with 'Age' on the horizontal axis and 'Number of cars' on the vertical axis. For the period over 16 and under 20 years, draw one block, assuming the 274 000 cars are shared equally between the two categories '16 and under 18' and '18 and under 20'.

This diagram is called a HISTOGRAM.

5. Compare the histogram with your bar chart of Section A3. Why are the shapes different? (Hint: how old are the cars at the right-hand end of the axis in the bar chart?)

* There are 2125 thousand cars with an average age of one year. The total of all their ages will be 2125 thousand years. Similarly the total age of the 2763 thousand three-year old cars is 2763 x 3 = 8289 thousand years. We call this the number of car-years.

Some of these figures are given in the last column of Table 5.

6. *Copy and complete the last column of Table 5 and find the total number of car-years.

The MEAN age of the cars can be found by dividing the total number of car-years by the total number of cars.

6. *Find the MEAN age of the cars.

More and More Cars
We can find out how many more cars there are each year by subtraction.

For example: to find the increase in the number of cars on the road from 1969 to 1970, look at Table 4.

The total number of cars in 1970 is:	11 515 000
Subtract the total number of cars in 1969, which is:	11 227 000
So, the increase in number of cars from 1969 to 1970 is:	288 000

1. How many more cars were there:
   in 1972 than in 1971,
   in 1973 than in 1972,
   in 1974 than in 1973,
   in 1975 than in 1974?
2. Which of the years from 1971 to 1975 (inclusive) was worst for the manufacturers?

The proportional increase in 1970 over 1969 is:

Increase from 1969 to 1970 Total number in 1969		288 000 11 227 000
	=

= 0.0257 or 2.57%

3. *Find the proportional increase:
   in 1972 over 1971,
   in 1973 over 1972,
   in 1974 over 1973,
   in 1975 over 1974.

Scrapping Cars
From Table 4 we see there were 1 097 000 new cars registered in 1970. The increase from 1969 to 1970 was only 228 000. Some cars must have been scrapped. We can find this number by subtraction.

The number of new cars in 1970 was: 1097000:	1 097 000
Subtract the increase from 1969 to 1970, which was:	288 000
So, the number of cars scrapped in 1970 was:	809 000

1. Use your answers to Section C3 a to work out how many cars were scrapped: in 1972, in 1973, in 1974 and in 1975.

*The proportion of cars scrapped in 1970 was:

Number of cars scrapped in 1970 Total number of cars In 1969		809 000 11 227 000
	=

= 0.0721 or 7.21%

2. *Find the proportion of cars, scrapped: in 1972, 1973, 1974 and 1975.

Look at your answers to C3b and C4b. Copy and complete the following sentence:

3. *During the years 1964 to 1977, the larger the increase in number of cars from one year to the next, the the number of cars scrapped.

*How Long Do Cars Last?

(Source: Transport Statistics, Great Britain 1 973, 1 975)
¹ This excludes some cars scrapped before they were one year old. This is likely to be a small number (e.g. those involved in serious accidents).

Table 6 - Ages of cars - 1973, 1975 (thousands).

Surveys of car ages were done in 1973 and 1975 (as in Section C1). We can use these to find out how long cars last. Look at the first line of Table 6.

Cars first registered in 1971/72 will be on average one vear old in 1973. In 1975, i.e. two years later, they will
be three years old.

There were 2871 thousand of these cars in 1973, but only 2860 thousand of them in 1975.

The difference (2871 - 2860 = 11 thousand) must have been scrapped. So, between 1973 and 1975, 11 thousand cars were scrapped, with an average age of two years.

1. How many cars were scrapped in each age group?

EITHER

2. Plot the ages of cars scrapped as a histogram.

OR

There were 11 thousand two-year old cars scrapped, so their total age was 2 x 11 thousand = 22 thousand years. This figure is listed in the column headed car-years.

3. Copy and complete Table 6 and find the mean age of cars scrapped between 1973 and 1975. (If you are not sure, look back to C1f.)

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