1. Compile a grouped frequency distribution for these figures.
2. Construct a histogram to portray the distribution.

1. Find the mode, median and mean for this set of data. Compare your results.
2. Plot a simple bar chart to portray the data.

1. Find the median and quartiles for this set of data.
2. Determine the semi-interquartile range.
3. Calculate the mean and standard deviation for this set of data.

Calculate the mean and standard deviation for each set of times and use them to compare the travel times for the two commuters.

Construct a boxplot to represent this set of data.

1. Determine values for the mean and median of the distributions.
2. Find an approximate value for the standard deviation of each distribution.
3. Use the figures you obtain for (a) and (b) to compare the two distributions.

1. Portray the data on a scatter diagram with Balance as the dependent variable.
2. Calculate the correlation coefficient and comment on its value.

1. Portray the data on a scatter diagram.
2. Calculate the slope and intercept of the line of best fit using simple linear regression analysis.
3. Plot the line of best fit and use it to estimate the time that a journey of 9 miles would take.

1. Present these figures in the form of a scatter diagram.
2. Find the least squares line of best fit and plot it on your scatter diagram.
3. Predict the price of a car of this type that has travelled 25 000 miles.

The values of the Retail Price Index (RPI) for this period were:

Use the RPI values to deflate the turnover figures so that they are all expressed in 2014 pounds.
(Source of RPI figures: ‘Retail Price Index’, Office for National Statistics. Contains public sector information licensed under the Open Government Licence v3.0.)

In 2017 the company purchased 2500 metres of lining fabric, 400 metres of interfacing fabric, and 2750 metres of outer fabric. In 2018 these quantities were 2800, 500, and 3200 respectively. In 2009 they were 3000, 500, and 5000 respectively.

1. lot the series and calculate five-point moving averages.
2. Estimate daily components for the series.
3. Produce estimates for the values of the trend in week 4 using regression analysis.
4. Compile forecasts for the number of absence the company should expect each day in week 4.

1. they do not purchase goods on-line?
2. they do purchase goods on-line?

1. It is a postal account?
2. It is an Internet account?
3. It is either branch-based or postal?

What is the probability that:

1. An injury to a pedestrian proves fatal?
2. An accident involved a sports car?
3. An accident involved a 4×4 car or resulted in a non-serious injury?
4. An accident resulted in serious injury and involved an ‘other’ type of car?
5. An accident that involved a 4×4 car resulted in a fatal injury? Compare this figure and your answer to (a), and comment on whether the type of car and degree of injury are independent.

1. What is the probability that none of the rooms you get is en suite?
2. What is the probability that one of the rooms you get is en suite?
3. What is the probability that two or more of the rooms you get are en suite?

1. None of the tins contain asparagus?
2. All three tins contain soup?
3. One tin contains raspberries?
4. Two tins contain carrots?
5. The contents of the three tins are different?

1. A team consists entirely of males?
2. There are three females in a team?
3. There are three or fewer females in a team?
4. The majority of a team are female?

1. None of the eggs contain harmful bacteria?
2. More than two eggs contain harmful bacteria?
3. Half the eggs contain harmful bacteria?
4. Less than two eggs contain harmful bacteria?

1. He receives no e-mails in an hour?
2. He receives one e-mail in an hour?
3. He receives two or fewer e-mails in an hour?
4. He receives more than four e-mails in an hour?

1. Construct a decision tree and use it to advise the arable farmer.
2. An expert puts the probability that there will be contamination of the crops of the neighbouring farmer at 60%. Should the arable farmer change her strategy in the light of this information?

1. Above 12?
2. Above 11.3?
3. Below 11.6?
4. Below 11.1?
5. Between 11.2 and 11.4?
6. Between 11.5 and 11.9?

1. Less than 5 minutes?
2. More than 10 minutes?
3. Less than 15 minutes?
4. Between 3 and 7 minutes?
5. Between 10 and 14 minutes?
6. Between 8 and 12 minutes?

1. What proportion of applications would be expected to score over 70 points?
2. What proportion of applications would be expected to score under 40 points
3. What proportion of applications would be expected to score between 50 and 65 points?
4. What score is exceeded by 20% of applicants?
5. What is the highest score achieved by the 5% of applicants who do least well in the test?

1. More than 25,000 miles?
2. More than 22,000 miles?
3. Less than 24,000 miles?
4. Less than 23,000 miles?
5. Between 22,500 and 24,500 miles?
6. Between 23,400 and 24,200 miles?

1. More than 12 minutes?
2. More than 10 minutes?
3. Less than 8 minutes?
4. Less than 11 minutes?
5. Between 9 minutes and 10.5 minutes?
6. Between 11.5 and 12.5 minutes?
7. Between 9.5 and 14 minutes?

1. What mean weight of bags in multipacks will be exceeded by 10% of packs?
2. What mean weight of bags in multipacks will be exceeded by 5% of packs?
3. What mean weight of bags in multipacks will be exceeded by 1% of packs?

1. A 90% confidence interval for the mean burning time of the candles.
2. A 99% confidence interval for the mean burning time of the candles.

1. Construct a 90% interval estimate of the mean rent of two-bedroom flats in the area
2. The population standard deviation turns out to be £59. In the light of this new information, determine the size of sample necessary to enable the mean rent to be estimated to within £10, in other words for the error to be £10, with a 90% level of confidence.

1. Produce a 95% confidence interval for the weight of ‘one pound’ bags of pears.
2. Produce a 99% confidence interval for the weight of ‘one pound’ bags of pears.

1. Produce a 95% confidence interval for the proportion of women in the UK who consider that having children held back their career prospects.
2. Produce a 95% confidence interval for the proportion of women in Denmark who consider that having children held back their career prospects.
3. How do the two confidence intervals compare?

1. Test the claim made for the product using a 5% level of significance.
2. What assumption must be made for the test to be valid?

1. Test the bus company’s claim at the 5% level of significance and comment on the result.
2. It appears that for nine of these journeys the regular driver was absent from work through illness and relief drivers, who were unfamiliar with the route, had to be used. The mean journey time for the remaining journeys was 55 minutes with a standard deviation of 3.1 minutes. Test the bus company’s claim again at the 5% level of significance using these figures and comment on the result.
3. What do you need to assume about the population of journey times for the results from the second test to be valid?

Test the hypothesis that there is no association between mode of travel and opinion on parking places:

1. At the 5% level of significance.
2. At the 1% level of significance.

1. Using a 1% level of significance test for association between type of pet and type of household.
2. Examine the components of the test statistic and comment on the patterns they reveal.

1. Find the regression equation and test the hypothesis that the population slope is zero at the 5% level of significance.
2. Produce a 95% confidence interval for the mean profit from auctions that attract 300 people.
3. Produce a 95% prediction interval for the profit that can be expected from a single auction that attracts 300 people.