Handling Data and Statistics

What is the mean of these numbers: 2, 4, 6, 8?

• A5✓
• B6
• C6.5
• D8

Answer: Mean = (2 + 4 + 6 + 8) ÷ 4 = 20 ÷ 4 = 5.

What is the median of these numbers: 3, 5, 7, 9, 11?

• A5
• B7✓
• C9
• D11

Answer: The median is the middle value when in order. 3, 5, 7, 9, 11. The middle value is 7.

What is the mode of these numbers: 2, 3, 3, 5, 7, 3, 8?

• A2
• B3✓
• C5
• D8

Answer: The mode is the value that appears most often. 3 appears three times, so the mode is 3.

What is the range of these numbers: 2, 5, 8, 9, 15?

• A7
• B9
• C13✓
• D15

Answer: Range = highest value - lowest value = 15 - 2 = 13.

A data set has values: 10, 20, 30, 40, 50. What is the mean?

• A20
• B30✓
• C35
• D40

Answer: Mean = (10 + 20 + 30 + 40 + 50) ÷ 5 = 150 ÷ 5 = 30.

What is the median of: 1, 3, 5, 7?

• A3
• B4✓
• C5
• D6

Answer: With an even number of values, the median is the mean of the two middle values: (3 + 5) ÷ 2 = 4.

What is the range of: 100, 150, 200, 250, 300?

• A50
• B100
• C150
• D200✓

Answer: Range = 300 - 100 = 200.

A survey asks 20 people their age. The mean age is 35. What is the total of all ages?

• A35
• B55
• C700✓
• D7,000

Answer: Total = mean × number of values = 35 × 20 = 700.

What is the mode of: 5, 5, 5, 10, 10, 15?

• ANo mode
• B15
• C10
• D5✓

Answer: 5 appears three times, which is more than any other value, so the mode is 5.

The mean of 4 numbers is 10. The numbers are 8, 10, 12, and X. What is X?

• A8
• B10✓
• C12
• D14

Answer: Mean = (8 + 10 + 12 + X) ÷ 4 = 10. So (30 + X) = 40. X = 10.

A pie chart shows 25% of people prefer tea. If 100 people were surveyed, how many prefer tea?

• A10
• B20
• C25✓
• D50

Answer: 25% of 100 = 0.25 × 100 = 25 people.

What is the median of: 2, 4, 6, 8, 10?

• A4
• B6✓
• C8
• D10

Answer: The median is the middle value. 2, 4, 6, 8, 10. The middle value is 6.

The mean of 5 numbers is 20. The numbers are 15, 20, 25, 30, and X. What is X?

• A10✓
• B15
• C20
• D30

Answer: Mean = (15 + 20 + 25 + 30 + X) ÷ 5 = 20. So (90 + X) = 100. X = 10.

What is the mode of: 1, 1, 2, 2, 2, 3, 3, 4?

• A1
• B2✓
• C3
• D4

Answer: 2 appears three times, which is more than any other value, so the mode is 2.

A bar chart shows: Monday 5 sales, Tuesday 8 sales, Wednesday 11 sales, Thursday 12 sales. What is the mean number of sales?

• A8
• B8.5
• C9✓
• D10

Answer: Mean = (5 + 8 + 11 + 12) ÷ 4 = 36 ÷ 4 = 9.

What is the mean of: 12, 15, 18?

• A13
• B14
• C15✓
• D16

Answer: Mean = (12 + 15 + 18) ÷ 3 = 45 ÷ 3 = 15.

A dataset has a range of 20 and a minimum value of 10. What is the maximum value?

• A10
• B20
• C30✓
• D40

Answer: Range = maximum - minimum. 20 = maximum - 10. Maximum = 30.

What is the median of: 10, 20, 30, 40?

• A20
• B25✓
• C30
• D35

Answer: With an even number of values, median = (20 + 30) ÷ 2 = 50 ÷ 2 = 25.

In a survey, 40% of 50 people said yes. How many said yes?

• A10
• B20✓
• C25
• D40

Answer: 40% of 50 = 0.4 × 50 = 20.

What is the range of: 5, 10, 15, 20, 25?

• A10
• B15
• C20✓
• D25

Answer: Range = 25 - 5 = 20.

A bar chart shows frequencies: 2, 5, 8, 10, 5. What is the total frequency?

• A10
• B20
• C25
• D30✓

Answer: Total = 2 + 5 + 8 + 10 + 5 = 30.

If the median of 5 numbers is 15, which statement is true?

• AThe mean of the five numbers must also be 15
• BEvery one of the five numbers must be 15 or more
• CThe range of the five numbers must be 15
• DIn order, the third of the five numbers is 15✓

Answer: The median is the middle value once the numbers are in order. With five numbers, that is the third one, so it must be 15. The mean, the range and the other values can be anything.

What is the mode of: 7, 7, 7, 8, 9?

• ANo mode
• B7✓
• C9
• D8

Answer: 7 appears three times, which is more than any other value, so the mode is 7.

A dataset has values: 100, 200, 300, 400, 500. What is the median?

• A200
• B300✓
• C350
• D400

Answer: With 5 values, the median is the 3rd value: 300.

In a class of 30 students, 60% passed the test. How many passed?

• A10
• B15
• C18✓
• D20

Answer: 60% of 30 = 0.6 × 30 = 18.

A works social club sells 250 raffle tickets and Jodie buys 10 of them. What is the probability that Jodie holds the winning ticket?

• A0.4
• B0.04✓
• C0.1
• D0.025

Answer: Jodie holds 10 of the 250 tickets, and 10 ÷ 250 = 0.04.

A machine produces 3 faulty items in every 200 made. What is the probability that an item taken at random is not faulty?

• A0.015
• B0.97
• C0.15
• D0.985✓

Answer: 197 of every 200 items are free of faults, and 197 ÷ 200 = 0.985.

The probability that a particular bus is late is 0.15. Out of 60 journeys, how many would you expect to be late?

• A9✓
• B51
• C15
• D0.9

Answer: The expected number is the probability multiplied by the number of journeys: 0.15 × 60 = 9 journeys.

A quality check shows that 4% of light bulbs fail. In a delivery of 1,500 bulbs, how many would you expect to fail?

• A600
• B6
• C60✓
• D375

Answer: 4% of 1,500 is 0.04 × 1,500 = 60 bulbs.

In a prize draw the probability of winning a meal voucher is 0.1 and the probability of winning a cinema ticket is 0.05. One ticket cannot win both prizes. What is the probability of winning one of these two prizes?

• A0.005
• B0.85
• C0.5
• D0.15✓

Answer: The two outcomes cannot both happen, so the probabilities are added: 0.1 + 0.05 = 0.15.

A vending machine gives a cold drink with a probability of 0.4 and a hot drink with a probability of 0.35. The only other thing it gives is a snack. What is the probability of getting a snack?

• A0.75
• B0.05
• C0.25✓
• D0.14

Answer: All the probabilities must add up to 1, so the snack probability is 1 − 0.4 − 0.35 = 0.25.

A shift survey covers 80 staff. Of the 45 who work nights, 24 drive to work. Of the 35 who work days, 16 drive to work. What is the probability that a member of staff chosen at random both works nights and drives to work?

• A0.533
• B0.6
• C0.3✓
• D0.5

Answer: 24 of the 80 staff surveyed both work nights and drive, and 24 ÷ 80 = 0.3.

A college has 200 learners. 120 study maths, of whom 90 passed. The other 80 study English, of whom 60 passed. What is the probability that a learner chosen at random passed?

• A0.75✓
• B0.6
• C0.45
• D0.25

Answer: Altogether 90 + 60 = 150 learners passed out of 200, and 150 ÷ 200 = 0.75.

A café runs a promotion. A customer tosses a coin and rolls a fair six-sided dice, and wins a free drink only if they get a head and a six. What is the probability that a customer wins?

• A1/12✓
• B1/8
• C1/6
• D7/12

Answer: The two results do not affect each other, so the probabilities are multiplied: 1/2 × 1/6 = 1/12.

The probability that a delivery van breaks down on any given day is 0.1, and the days do not affect each other. What is the probability that it breaks down on two particular days in a row?

• A0.2
• B0.02
• C0.01✓
• D0.05

Answer: For both days to happen the probabilities are multiplied: 0.1 × 0.1 = 0.01.

A supermarket records what 60 customers spend. £0 up to £10: 8 customers. £10 up to £20: 21 customers. £20 up to £30: 19 customers. £30 up to £40: 12 customers. Which is the modal class?

• A£20 up to £30
• B£30 up to £40
• C£0 up to £10
• D£10 up to £20✓

Answer: The modal class is the class with the highest frequency, and the largest frequency here is 21 customers, in the class £10 up to £20.

Twenty staff record how long they take to get to work. 0 up to 10 minutes: 4 staff. 10 up to 20 minutes: 6 staff. 20 up to 30 minutes: 7 staff. 30 up to 40 minutes: 3 staff. Estimate the mean travel time.

• A14.5 minutes
• B19.5 minutes✓
• C24.5 minutes
• D97.5 minutes

Answer: Each class is represented by its midpoint: (4 × 5) + (6 × 15) + (7 × 25) + (3 × 35) = 390, and 390 ÷ 20 staff = 19.5 minutes.

Fifty households record their weekly shopping bill. £20 up to £40: 9 households. £40 up to £60: 16 households. £60 up to £80: 15 households. £80 up to £100: 10 households. Estimate the mean weekly bill.

• A£50.40
• B£60.40✓
• C£70.40
• D£755.00

Answer: Using the midpoint of each class: (9 × £30) + (16 × £50) + (15 × £70) + (10 × £90) = £3,020, and £3,020 ÷ 50 households = £60.40.

A manager records how long her staff take to travel to work in a grouped frequency table. To estimate the mean journey time, which value should she use to stand for the class '30 up to 40 minutes'?

• A35 minutes✓
• B30 minutes
• C40 minutes
• D70 minutes

Answer: Each class is represented by its midpoint, and halfway between 30 and 40 is 35 minutes.

A delivery firm works out a mean delivery time from a grouped frequency table. Why can that mean only ever be an estimate?

• AThe frequencies in a grouped table are rounded to the nearest ten before they are used
• BThe individual values are not recorded, so the midpoint of each class stands in for them✓
• CA grouped frequency table always leaves out the highest and the lowest values collected
• DThe classes in a grouped frequency table are always of different widths

Answer: A grouped table shows only how many values fall in each class, not the values themselves, so the midpoint has to stand in for them and the mean that results is an estimate.