Mean, Mode, Median, Range

  1. For the following lists of numbers, find the (i) mode if applicable (ii) the median, (iii) the mean, and (iv) the range.
  2. 2, 4, 5, 5
  3. 1.3, 4.6, 5.8, 6.3
  4. 1, 1, 1, 1, 2, 12
  5. I record the height of three boys. Two of them are 1.5m and 1.7m. The average of the three boys’ heights is 1.7m. What is the height of the third boy?
  6. There are four numbers written on cards. Three of the numbers are 2, 3 and 4. The mean of the four numbers is 5. What is the fourth number?
  7. The range of two numbers is 10. One of the numbers is 5. What are the possible means of the two numbers?
  8. The mode of 4 numbers is 10, the median is 7.5 and the mean is 6.875. What are the four numbers?
  9. Three numbers are , and . Their average is 10. Determine .
  10. The mean average mark of 30 students doing an exam is 63%. However, there was one further student who was absent that day (he was singing in the Hobbit soundtrack). What mark would he require to bring the class average up to 64%?
  11. The mean mark of students in a test was 50%. A new boy joined the class the day after, and taking the same test, achieved an impressive 100%. The class average rose to 52%. What is ?
  12. [Source: JMC] Nicky has to choose 7 different positive whole numbers whose mean is 7. What is the largest possible such number she could choose?
    A 7B 28C 34D 43E 49
  13. [Source: IMC] What is the maximum possible value of the median number of cups of coffee bought per customer on a day when Sundollars Coffee Shop sells 477 cups of coffee to 190 customers, and every customer buys at least one cup of coffee?
    A 1.5B 2C 2.5D 3E 3.5

Mean of Frequency Tables

  1. At a party, thirty people have an age of 30, forty have an age of 40 and fifty an age of fifty. What is their average age?
  2. In a hardware shop, there are 30 spanners costing £6, 55 hacksaws costings £9 and 10 soldering irons costings £20. What is the average cost per item?
  3. Using this frequency table, find the average height of a turnip.

Height (to nearest cm) / 6cm / 7cm / 8cm / 9cm / 10cm
Frequency / 3 / 8 / 12 / 4 / 1
  1. Sam collects the weights of 50 squirrels and puts them into weight ranges. His data is presented below. Estimate the mean weight of a squirrel.

Weight / 10-16kg / 16-20kg / 20-30kg / 30kg-32kg
Frequency / 7 / 3 / 4 / 1
  1. Miss Clarke values a number of pieces of artwork in the Tiffin School Vault. The price ranges are summarised below. Estimate the average value of a piece of art in school.

Value / £0-£1000 / £1 000-5 000 / £5 000-£20 000 / £20 000-£100 000
Frequency / 10 / 25 / 6 / 1
  1. I record the times of 50 runners in a 10km race. Their times are summarised below. Determine their mean time in minutes.

Time (minutes) / 35-40 / 40-42 / 42-48 / 48-60
Frequency / 5 / 15 / 20 / 10

Mean, Mode, Median, Range

  1. For the following lists of numbers, find the (i) mode if applicable (ii) the median, (iii) the mean, and (iv) the range.
  2. 2, 4, 5, 5
  3. 1.3, 4.6, 5.8, 6.3
  4. 1, 1, 1, 1, 2, 12
  5. I record the height of three boys. Two of them are 1.5m and 1.7m. The average of the three boys’ heights is 1.7m. What is the height of the third boy?
  6. There are four numbers written on cards. Three of the numbers are 2, 3 and 4. The mean of the four numbers is 5. What is the fourth number?
  7. The range of two numbers is 10. One of the numbers is 5. What are the possible means of the two numbers?
  8. The mode of 4 numbers is 10, the median is 7.5 and the mean is 6.875. What are the four numbers?
  9. Three numbers are , and . Their average is 10. Determine .
  10. The mean average mark of 30 students doing an exam is 63%. However, there was one further student who was absent that day (he was singing in the Hobbit soundtrack). What mark would he require to bring the class average up to 64%?
  11. The mean mark of students in a test was 50%. A new boy joined the class the day after, and taking the same test, achieved an impressive 100%. The class average rose to 52%. What is ?
  12. [Source: JMC] Nicky has to choose 7 different positive whole numbers whose mean is 7. What is the largest possible such number she could choose?
    A 7B 28C 34D 43E 49
  13. [Source: IMC] What is the maximum possible value of the median number of cups of coffee bought per customer on a day when Sundollars Coffee Shop sells 477 cups of coffee to 190 customers, and every customer buys at least one cup of coffee?
    A 1.5B 2C 2.5D 3E 3.5

Mean of Frequency Tables

  1. At a party, thirty people have an age of 30, forty have an age of 40 and fifty an age of fifty. What is their average age?
  2. In a hardware shop, there are 30 spanners costing £6, 55 hacksaws costings £9 and 10 soldering irons costings £20. What is the average cost per item?
  3. Using this frequency table, find the average height of a turnip.

Height (to nearest cm) / 6cm / 7cm / 8cm / 9cm / 10cm
Frequency / 3 / 8 / 12 / 4 / 1
  1. Sam collects the weights of 50 squirrels and puts them into weight ranges. His data is presented below. Estimate the mean weight of a squirrel.

Weight / 10-16kg / 16-20kg / 20-30kg / 30kg-32kg
Frequency / 7 / 3 / 4 / 1
  1. Miss Clarke values a number of pieces of artwork in the Tiffin School Vault. The price ranges are summarised below. Estimate the average value of a piece of art in school.

Value / £0-£1000 / £1 000-5 000 / £5 000-£20 000 / £20 000-£100 000
Frequency / 10 / 25 / 6 / 1
  1. I record the times of 50 runners in a 10km race. Their times are summarised below. Determine their mean time in minutes.

Time (minutes) / 35-40 / 40-42 / 42-48 / 48-60
Frequency / 5 / 15 / 20 / 10

Answers

  1. –
  2. Mode = 5, Range = 3, Median = 4.5, Mean = 4
  3. No mode. Range = 5, Median = 5.2, Mean = 4.5
  4. Mode = 1, Range = 11, Median = 1, Mean = 3
  5. 1.9m
  6. 11
  7. 0 or 10
  8. 2.5, 5, 10, 10
  9. . Therefore .
  10. . The first 94 customers could have had 1 cup of coffee to maximise the first of the pair of items in the middle. That leaves 383 cups of coffee left to distribute. 95 goes into 383 four times leaving a remainder of 3. Thus let the 95 customers who drank most coffee each had 4 cups of coffee (this maximises the items in the middle). And with the remainder of 3, we set the first of the two items in the middle to be 3. Thus the two middle values are 3 and 4, and thus the maximum median is 3.5.

Answers to frequency tables

  1. 41.7
  2. £9.21
  3. 5.68cm
  4. 18.4kg
  5. £5119.04
  6. 44.85 minutes (or 44 minutes and 51 seconds)