Data and Statistics

What is the range of these numbers: 3, 7, 5, 9, 4?

• A5
• B6✓
• C7
• D9

Answer: Range = highest - lowest = 9 - 3 = 6.

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

• A2✓
• B5
• C6
• D8

Answer: Mode is the number that appears most often. 2 appears three times.

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

• A5
• B7✓
• C9
• D11

Answer: Median is the middle value. In order: 3, 5, 7, 9, 11. The middle is 7.

What is the mean (average) of these numbers: 4, 6, 8, 10?

• A6
• B7✓
• C8
• D9

Answer: Mean = (4 + 6 + 8 + 10) ÷ 4 = 28 ÷ 4 = 7.

If a survey of 10 people shows 6 prefer tea and 4 prefer coffee, what fraction prefer tea?

• A4/5
• B2/5
• C1/2
• D3/5✓

Answer: 6 out of 10 prefer tea = 6/10 = 3/5.

What is the mode of: 10, 15, 10, 20, 10, 25?

• A10✓
• B15
• C20
• D25

Answer: Mode is the most frequent number. 10 appears 3 times.

A bar chart shows 20 people in 2020 and 30 people in 2021. What is the increase?

• A10✓
• B15
• C25
• D50

Answer: Increase = 30 - 20 = 10 people.

If 80 out of 100 people pass a test, what percentage pass?

• A80%✓
• B20%
• C40%
• D60%

Answer: Percentage = (80 ÷ 100) × 100% = 80%.

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

• A4
• B5✓
• C6
• D8

Answer: With 4 numbers, median = average of 2nd and 3rd = (4 + 6) ÷ 2 = 5.

What is the mean of 10, 20, 30?

• A15
• B20✓
• C25
• D30

Answer: Mean = (10 + 20 + 30) ÷ 3 = 60 ÷ 3 = 20.

In a pie chart, if one section is 90 degrees, what fraction is it?

• A1/4✓
• B1/3
• C1/2
• D1/5

Answer: 90 out of 360 degrees = 90/360 = 1/4.

A box contains 5 red, 3 blue, and 2 yellow balls. What is the total?

• A8
• B10✓
• C12
• D15

Answer: Total = 5 + 3 + 2 = 10 balls.

A box contains 5 red, 3 blue, and 2 yellow balls. What is the probability of picking a red ball?

• A5/10✓
• B3/10
• C2/10
• D1/10

Answer: Probability = 5 red balls out of 10 total = 5/10.

A survey shows sales: Jan £100, Feb £120, Mar £150. What is the total?

• A£270
• B£450
• C£250
• D£370✓

Answer: Total = £100 + £120 + £150 = £370.

If sales increase from £200 to £250, what is the percentage increase?

• A30%
• B50%
• C20%
• D25%✓

Answer: Increase = £250 - £200 = £50. Percentage increase = (50 ÷ 200) × 100% = 25%.

What is the range of: 15, 22, 18, 30, 25?

• A12
• B13
• C15✓
• D22

Answer: Range = highest - lowest = 30 - 15 = 15.

In a class of 40 students, 25 passed. What percentage passed?

• A62.5%✓
• B50%
• C60%
• D40%

Answer: Percentage = (25 ÷ 40) × 100% = 62.5%.

What is the mean of 5, 10, 15, 20, 25?

• A12
• B15✓
• C18
• D20

Answer: Mean = (5 + 10 + 15 + 20 + 25) ÷ 5 = 75 ÷ 5 = 15.

A pie chart divides data into 4 equal sections. What is each section in degrees?

• A45
• B60
• C90✓
• D120

Answer: 360 ÷ 4 = 90 degrees per section.

In a survey, 3 out of 5 people prefer Option A. What percentage is this?

• A60%✓
• B40%
• C50%
• D75%

Answer: Percentage = (3 ÷ 5) × 100% = 60%.

What is the median of: 7, 3, 9, 5, 1?

• A3
• B5✓
• C7
• D9

Answer: In order: 1, 3, 5, 7, 9. The middle value is 5.

A spinner has 8 equal sections, 2 are red. What is the probability of spinning red?

• A1/4✓
• B1/8
• C3/4
• D1/2

Answer: Probability = 2 red sections out of 8 = 2/8 = 1/4.

Monthly sales are £500, £600, £700. What is the mean?

• A£650
• B£700
• C£600✓
• D£550

Answer: Mean = (£500 + £600 + £700) ÷ 3 = £1800 ÷ 3 = £600.

If 45 out of 90 items are defective, what percentage are defective?

• A60%
• B25%
• C40%
• D50%✓

Answer: Percentage = (45 ÷ 90) × 100% = 50%.

A frequency table shows: Value 2 appears 3 times, Value 4 appears 5 times, Value 6 appears 2 times. What is the mode?

• A2
• B3
• C4✓
• D5

Answer: Mode is the value with the highest frequency. Value 4 appears 5 times (most frequent).

A bar chart shows a shop's sales: Monday 5, Tuesday 8, Wednesday 11 and Thursday 12. What is the mean number of sales per day?

• A10
• B8
• C9✓
• D8.5

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

A café sells 45, 52, 38, 61 and 54 lunches on five days. What is the mean number of lunches sold per day?

• A50✓
• B250
• C23
• D52

Answer: Add the five values: 45 + 52 + 38 + 61 + 54 = 250. Divide by the number of days: 250 ÷ 5 = 50. The total, 250, is not the mean.

The ages of five people in a team are 23, 17, 31, 19 and 26. What is the range of their ages?

• A14✓
• B8
• C31
• D12

Answer: The range is the highest value minus the lowest value: 31 − 17 = 14.

A bag holds 3 red, 5 blue and 2 green counters. One counter is taken out without looking. What is the probability that it is blue?

• A5/8
• B1/5
• C1/2✓
• D3/10

Answer: There are 3 + 5 + 2 = 10 counters and 5 of them are blue. The probability is 5 out of 10, which simplifies to 1/2.

A weather forecast gives a 30% chance of rain tomorrow. What is the chance that it does not rain?

• A100%
• B30%
• C60%
• D70%✓

Answer: Either it rains or it does not, so the two chances add up to 100%. 100% − 30% = 70%.

In a survey of 120 people, a quarter say tea is their favourite drink. On a pie chart of the results, what angle shows tea?

• A90°✓
• B30°
• C120°
• D25°

Answer: A full pie chart is 360°. A quarter of the people means a quarter of the circle: 360° ÷ 4 = 90°.

A table shows the ages of a gym's members: 16 to 25, 14 members; 26 to 35, 22 members; 36 to 45, 9 members; 46 and over, 5 members. How many members are aged 26 or over?

• A31
• B36✓
• C50
• D22

Answer: Add the three groups that are 26 or over: 22 + 9 + 5 = 36. The total for all four groups is 50.

A line graph shows the temperature rising steadily from 14°C at 9 am to 23°C at 3 pm. How much does it rise each hour, on average?

• A2.5°C
• B1.5°C✓
• C9°C
• D6°C

Answer: The rise is 23 − 14 = 9°C. From 9 am to 3 pm is 6 hours. 9 ÷ 6 = 1.5°C each hour.

Over four weeks a shop's takings are £3,200, £2,950, £3,480 and £3,010. What is the mean weekly takings?

• A£530
• B£3,105
• C£3,160✓
• D£12,640

Answer: Add the four weeks: £3,200 + £2,950 + £3,480 + £3,010 = £12,640. Divide by 4: £12,640 ÷ 4 = £3,160.