## Using the data from Problem 1.6:(a) Calculate the mean, median

Using the data from Problem 1.6:

(a) Calculate the mean, median and mode of the distribution. Why do they differ?

(b) Calculate the inter-quartile range, variance, standard deviation and coefficient of variation of the data.

(c) Calculate the coefficient of skewness of the distribution.

Problem 1.6

The data below show the number of manufacturing plants in the UK in 1991/92 arranged according to employment:

Number of employees ………………….. Number of firms
1– 95 ………………………………………………….. 409
10– ………………………………………………….. 15 961
20– ………………………………………………….. 16 688
50– ………………………………………………….. 7 229
100– ………………………………………………….. 4 504
200– ………………………………………………….. 2 949
500– ………………………………………………….. 790
1000– ………………………………………………….. 332

## Using the data from Problem 1.5:(a) Calculate the mean, median

Using the data from Problem 1.5:

(a) Calculate the mean, median and mode of the distribution. Why do they differ?

(b) Calculate the inter-quartile range, variance, standard deviation and coefficient of variation of the data.

(c) Calculate the skewness of the distribution.

(d) From what you have calculated, and the data in the chapter, can you draw any conclusions about the degree of inequality in wealth holdings, and how this has changed?

(e) What would be the effect upon the mean of assuming the final class width to be £10m? What would be the effects upon the median and mode?

Problem 1.5

The distribution of marketable wealth in 1979 in the UK is shown in the table below (taken from Inland Revenue Statistics 1981, p. 105):

## Using the data from Problem 1.1:(a) Which education category has

Using the data from Problem 1.1:

(a) Which education category has the highest proportion of people in work? What is the proportion?

(b) Which category of employment status has the highest proportion of people with a degree? What is the proportion?

Problem 1.1

The following data show the education and employment status of women aged 20–29 (from the 1991 General Household Survey):

Figure 1.1

Figure 1.3

Figure 1.4

Figure 1.5

## Using the data from Problem 1.2:(a) What is the premium,

Using the data from Problem 1.2:

(a) What is the premium, in terms of median earnings, of a degree over A levels? Does this differ between men and women?

(b) Would you expect mean earnings to show a similar picture? What differences, if any, might you expect?

Problem 1.2

The data below show the median weekly earnings (in £s) of those in full time employment in Great Britain in 1992, by category of education.

(a) In what fundamental way do the data in this table differ from those in Problem 1.1?

(b) Construct a bar chart showing male and female earnings by education category. What does it show?

(c) Why would it be inappropriate to construct a stacked bar chart of the data? How should one graphically present the combined data for males and females? What extra information is necessary for you to do this?

Problem 1.1

## The following data show the education and employment status of

The following data show the education and employment status of women aged 20–29 (from the 1991 General Household Survey):

(a) Draw a bar chart of the numbers in work in each education category. Can this be easily compared with the similar diagram for 2003 (Figure 1.1)?

(b) Draw a stacked bar chart using all the employment states, similar to Figure 1.3. Comment upon any similarities and differences from the diagram in the text.

(c) Convert the table into (column) percentages and produce a stacked bar chart similar to Figure 1.4. Comment upon any similarities and differences.

(d) Draw a pie chart showing the distribution of educational qualifications of those in work and compare it to Figure 1.5 in the text.

Figure 1.1

Figure 1.3

Figure 1.4

Figure 1.5

## The data below show the median weekly earnings (in £s)

The data below show the median weekly earnings (in £s) of those in full time employment in Great Britain in 1992, by category of education.

(a) In what fundamental way do the data in this table differ from those in Problem 1.1?

(b) Construct a bar chart showing male and female earnings by education category. What does it show?

(c) Why would it be inappropriate to construct a stacked bar chart of the data? How should one graphically present the combined data for males and females? What extra information is necessary for you to do this?

Problem 1.1

## An important numerical calculation on a spacecraft is carried out

An important numerical calculation on a spacecraft is carried out independently by three computers. If all arrive at the same answer it is deemed correct. If one disagrees it is overruled. If there is no agreement then a fourth computer does the calculation and, if its answer agrees with any of the others, it is deemed correct. The probability of an individual computer getting the answer right is 99%. Use a tree diagram to find:

(a) The probability that the first three computers get the right answer;

(b) The probability of getting the right answer;

(c) The probability of getting no answer;

(d) The probability of getting the wrong answer.

## The following data give duration of unemployment by age, in

The following data give duration of unemployment by age, in July 1986.

The ‘economically active’ column gives the total of employed (not shown) plus unemployed in each age category.

(a) In what sense may these figures be regarded as probabilities? What does the figure 27.2 (top-left cell) mean following this interpretation?

(b) Assuming the validity of the probability interpretation, which of the following statements are true?

(i) The probability of an economically active adult aged 25–34, drawn at random, being unemployed is 531.4/3600.

(ii) If someone who has been unemployed for over one year is drawn at random, the probability that they are aged 16–19 is 19%.

(iii) For those aged 35–49 who became unemployed before July 1985, the probability of their still being unemployed is 56.2%.

(iv) If someone aged 50–59 is drawn at random from the economically active population, the probability of their being unemployed for eight weeks or less is 8.9%.

(v) The probability of someone aged 35–49 drawn at random from the economically active population being unemployed for between 8 and 26 weeks is 0.166 × 521.2/4900.

(c) A person is drawn at random from the population and found to have been unemployed
for over one year. What is the probability that they are aged between 16 and 19?

## ‘Odds’ in horserace betting are defined as follows: 3/1 (three-to-one

‘Odds’ in horserace betting are defined as follows: 3/1 (three-to-one against) means a horse is expected to win once for every three times it loses; 3/2 means two wins out of five races; 4/5 (five to four on) means five wins for every four defeats, etc.

(a) Translate the above odds into ‘probabilities’ of victory.

(b) In a three-horse race, the odds quoted are 2/1, 6/4, and 1/1. What makes the odds different from probabilities? Why are they different?

(c) Discuss how much the bookmaker would expect to win in the long run at such odds, assuming each horse is backed equally.

## Is the employment and unemployment experience of the UK economy

Is the employment and unemployment experience of the UK economy worse than that of its competitors? Write a report on this topic in a similar manner to the project above. You might consider rates of unemployment in the UK and other countries; trends in unemployment in each of the countries; the growth in employment in each country; the structure of employment (e.g. full-time/part-time) and unemployment (e.g. long-term/short-term). You might use data for a number of countries, or concentrate on two in more depth. Suitable data sources are: OECD Main Economic Indicators; European Economy (published by the European Commission); Employment Gazette.