Question A

Categorise the following data types into Nominal, Ordinal, Interval or Ratio data:

  1. Floor area
  2. Memory card capacity
  3. Premier league positions
  4. Shapes
  5. Latitude
  6. Pay grades
  7. Salary
  8. Playing cards
  9. Longitude
  10. Olympic medals (gold, silver, bronze)
  11. Vegetables
  12. Date
  13. Foot size
  14. Musical notes
  15. Horsepower

Question B

  1. Give an example of a data set with 6 values that has the same mean, median, and mode.
  2. Give an example of a data set with 5 values that has different values of mean, median, and mode.

Question C

For each of the following determine the most appropriate data visualisation and draw it:

Company End of Year Profit
Apple $12 million
Tesco $3 million
Microsoft $10 million
Swatch $2 million
McDonalds $7 million


Height (cm) 131 142 130 127 138 149 131 135 143 145
Weight (kg) 70 74 70 71 78 82 72 75 78 80


Ages of patients in a ward: {57, 64, 69, 69, 69, 74, 75, 76, 76, 77, 78, 79, 80, 81, 81, 84, 86, 87, 87, 88, 89, 89, 92, 98}

Question D

Look at the data visualisation below:

  1. Give the range, median, Q1, Q3, and IQR for the weigths of dogs, cats and rats.
  2. Can we select a dog that is heavier than a cat?
  3. Can we select a cat that is heavier than a dog?
  4. Can we select a rat that is heavier than a dog?
  5. Can we select a cat that is lighter than a rat?
  6. A dog is selected at random, what is the probability that there exists a cat heavier than it?
  7. Look at the data visualisation below:

Give a data set with 11 values that would correspond to this.

Question E

In one day, the total amount of money spent at 2 shops by customers are shown below:

  • Shop 1: {£3.00, £2.50, £7.80, £10.11, £0.99, £1.20, £3.00, £2.99, £2.40, £0.50, £5.00, £3.35, £2.40, £2.40, £5.10, £1.20, £3.00, £3.00}
  • Shop 2: {£50.10, £48.30, £41.99, £50.30, £61.00, £48.20, £51.50, £39.00, £60.00, £42.12, £39.00, £55.00, £59.99, £47.80, £39.00}
  1. Calculate the mean and median of each data set.
  2. Calculate the variance and standard deviations of each data set.
  3. Which data set has the largest relative variance?
  4. Draw box and whisker plots for both data sets on different axes and comment on their shape.

Question F

  1. Put the following in order of skew:

  2. Put the following in order of kurtosis: