📈 Maths: Tables, Charts and Data Interpretation

1. A train timetable is described as a table. The rows are stations (Leeds, York, Hull) and the columns are three departure times. The cell where the row 'York' meets the second time column shows 09:42. Reading this table, at what time does a train leave York in the second column?

1. 09:42
2. 09:24
3. 10:42
4. 09:40

Reading a value from a table means finding where the correct row (York) and the correct column (second time) meet, which gives 09:42. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 'Handling information and data', GOV.UK)

2. A table lists the price of three jacket sizes (Small, Medium, Large) at two shops (Shop A, Shop B). The cell where row 'Medium' meets column 'Shop B' shows £38. What is the price of a Medium jacket at Shop B?

1. £38
2. £83
3. £48
4. £36

The required value is found at the intersection of the 'Medium' row and the 'Shop B' column, which reads £38. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 'Handling information and data', GOV.UK)

3. A two-way table records 100 staff by department (Sales, Admin) and whether they cycle to work. The Sales row shows 30 who cycle and 25 who do not; the Admin row shows 18 who cycle and 27 who do not. How many Admin staff cycle to work?

1. 18
2. 27
3. 30
4. 45

A two-way table cross-tabulates two categories, so the figure is read where the 'Admin' row meets the 'cycle' column, giving 18. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 statement 26, GOV.UK)

4. A two-way table records 100 staff by department and whether they cycle to work. The Sales row shows 30 who cycle and 25 who do not. The Admin row shows 18 who cycle and 27 who do not. How many staff are in the Sales department altogether?

1. 55
2. 48
3. 52
4. 45

The Sales total is the sum across the Sales row: 30 + 25 = 55. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 statement 26, GOV.UK)

5. A two-way table records 100 staff. The Sales row shows 30 who cycle and 25 who do not; the Admin row shows 18 who cycle and 27 who do not. How many staff in total cycle to work?

1. 48
2. 52
3. 55
4. 45

The number who cycle is the column total: 30 (Sales) + 18 (Admin) = 48. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 statement 26, GOV.UK)

6. A two-way table records 100 staff. The Sales row shows 30 who cycle and 25 who do not; the Admin row shows 18 who cycle and 27 who do not. If one member of staff is chosen at random, what is the probability they are an Admin worker who does NOT cycle?

1. 27/100
2. 18/100
3. 45/100
4. 27/45

The Admin/does-not-cycle cell shows 27 out of 100 staff, so the probability is 27/100. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 statements 26 and 27, GOV.UK)

7. A table shows monthly rainfall in millimetres for one town: January 84, February 61, March 55, April 49. Reading the table, which month had the most rainfall?

1. January
2. February
3. March
4. April

Comparing the values in the table, 84 mm is the largest, so January had the most rainfall. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 'Handling information and data', GOV.UK)

8. A table shows monthly rainfall in millimetres: January 84, February 61, March 55, April 49. What is the range of the rainfall figures?

1. 35 mm
2. 133 mm
3. 84 mm
4. 49 mm

The range is the largest value minus the smallest: 84 − 49 = 35 mm. (Pass Functional Skills, 'Mean, Median, Mode and Range' (Functional Skills Maths Level 2 revision guidance))

9. A table shows the number of goals scored by a team in five matches: 2, 3, 1, 4, 0. Using the values in the table, what is the mean number of goals per match?

1. 2
2. 3
3. 10
4. 4

The mean is the total divided by the number of values: (2 + 3 + 1 + 4 + 0) ÷ 5 = 10 ÷ 5 = 2. (Pass Functional Skills, 'Mean, Median, Mode and Range' (Functional Skills Maths Level 2 revision guidance))

10. A table lists six house prices in thousands of pounds, already in ascending order: 85, 91, 98, 110, 114, 123. What is the median price?

1. £104,000
2. £98,000
3. £110,000
4. £103,500

With an even number of values the median is the mean of the two middle values: (98 + 110) ÷ 2 = 104, i.e. £104,000. (Pass Functional Skills, 'Mean, Median, Mode and Range' (Functional Skills Maths Level 2 revision guidance))

11. A table records shoe sizes sold in one day: 6, 7, 7, 8, 7, 9, 8. Reading the table, what is the mode of the shoe sizes?

1. 7
2. 8
3. 6
4. 9

The mode is the value that appears most often; size 7 appears three times, more than any other size. (Pass Functional Skills, 'Mean, Median, Mode and Range' (Functional Skills Maths Level 2 revision guidance))

12. A grouped frequency table gives ages of club members using midpoints: midpoint 25 with frequency 4, midpoint 35 with frequency 6, midpoint 45 with frequency 10. Using the midpoints, what is the estimated mean age?

1. 38
2. 35
3. 40
4. 37

Estimate the mean using (midpoint × frequency) totals: (25×4 + 35×6 + 45×10) ÷ 20 = (100 + 210 + 450) ÷ 20 = 760 ÷ 20 = 38. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 statement 24, GOV.UK)

13. A table shows a worker's hours: Monday 7, Tuesday 6, Wednesday 8, Thursday 5, Friday 7. How many hours were worked on Monday and Wednesday together?

1. 15
2. 13
3. 14
4. 16

Read the two cells and add them: Monday 7 + Wednesday 8 = 15 hours. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 'Handling information and data', GOV.UK)

14. A survey of 120 students is shown two ways. A table states that 30 students chose football. A pie chart of the same data shows the football sector as a 90 degree angle. Do the two forms agree?

1. Yes, because (90 ÷ 360) × 120 = 30
2. No, the pie chart shows 45 students
3. No, the pie chart shows 60 students
4. Yes, because 90 degrees always means 30 people

The sector frequency is (sector angle ÷ 360) × total = (90 ÷ 360) × 120 = 30, which matches the table. (Pearson Edexcel Functional Skills teaching resources (pie charts), Functional Skills Maths Level 2)

15. A table shows that 20 of 80 customers chose tea. If this data is redrawn as a pie chart, what angle should the 'tea' sector be?

1. 90 degrees
2. 20 degrees
3. 72 degrees
4. 45 degrees

The sector angle is (frequency ÷ total) × 360 = (20 ÷ 80) × 360 = 90 degrees. (Pearson Edexcel Functional Skills teaching resources (pie charts); Level2Maths Charts guidance)

16. A pie chart shows that 25% of 200 survey responses chose 'bus'. A table claims 60 people chose the bus. Which statement correctly compares the two forms?

1. They disagree: 25% of 200 is 50, not 60
2. They agree, because 25% always equals 60
3. They disagree: 25% of 200 is 75
4. They agree, because 200 ÷ 4 is 60

25% of 200 is 200 × 0.25 = 50, so the pie chart represents 50 people, not the 60 stated in the table. (Pearson Edexcel Functional Skills teaching resources (pie charts); DfE subject content Level 2, GOV.UK)

17. A bar chart is described: the bar for 'Saturday' reaches 45 and the bar for 'Sunday' reaches 30. A separate table states Saturday was 45 and Sunday was 35. Which value disagrees between the two forms?

1. Sunday
2. Saturday
3. Both values
4. Neither value

Saturday matches at 45 in both forms, but Sunday is 30 on the bar chart and 35 in the table, so Sunday disagrees. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 'Handling information and data', GOV.UK)

18. Two delivery firms are compared. A table gives Firm A a mean delivery time of 48 minutes with a range of 12 minutes. A chart shows Firm B has a mean of 48 minutes and a range of 30 minutes. Which firm is more consistent, and why?

1. Firm A, because its smaller range shows less spread
2. Firm B, because its larger range shows more reliability
3. Neither, because the means are equal
4. Firm B, because a larger range is always better

When means are equal, the smaller range indicates less spread and greater consistency, so Firm A is more consistent. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 statement 25, GOV.UK)

19. A scatter diagram plots hours of revision against test scores. The description says that as revision hours increase, test scores also increase. What type of correlation does this show?

1. Positive correlation
2. Negative correlation
3. No correlation
4. Zero range

When both variables increase together, the scatter diagram shows positive correlation. (Pass Functional Skills, 'Scatter Graphs' (Functional Skills Maths Level 2 revision guidance); DfE subject content Level 2 statement 28)

20. A scatter diagram plots the outside temperature against the number of hot drinks sold. The description says that as the temperature rises, the number of hot drinks sold falls. What type of correlation is this?

1. Negative correlation
2. Positive correlation
3. No correlation
4. Equal correlation

When one variable increases as the other decreases, the scatter diagram shows negative correlation. (Pass Functional Skills, 'Scatter Graphs' (Functional Skills Maths Level 2 revision guidance); DfE subject content Level 2 statement 28)

21. A scatter diagram of revision hours against test scores has a line of best fit. A learner wants to estimate the likely score for a student who revised for 5 hours. What should they do?

1. Read up from 5 hours to the line of best fit, then across to the score axis
2. Pick the single nearest plotted point and use only that
3. Calculate the range of all the scores
4. Find the mode of the revision hours

A line of best fit is used to predict an unknown value by reading up to the line from the known value and across to the other axis. (Pass Functional Skills, 'Scatter Graphs' (Functional Skills Maths Level 2 revision guidance))

22. A table shows that 1/4 of 80 members are juniors. A pie chart of the same data labels the junior sector as 25%. How many juniors does each form represent?

1. 20 in both forms
2. 25 in both forms
3. 20 from the table but 25 from the chart
4. 40 in both forms

Both 1/4 and 25% of 80 give the same figure: 80 ÷ 4 = 20, so both forms represent 20 juniors. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 statement 27, GOV.UK)

23. Class X marks are listed in a table: 4, 6, 6, 8, 6. Class Y marks are shown on a bar chart as 5, 5, 7, 9, 4. Using the mode of each class to compare them, which statement is correct?

1. Class X has a mode of 6 and Class Y has a mode of 5
2. Both classes have a mode of 6
3. Class X has a mode of 8 and Class Y has a mode of 9
4. Neither class has a mode

The mode is the most frequent value: in Class X, 6 occurs three times; in Class Y, 5 occurs twice, more than any other Y value. (DfE 'Subject content functional skills: mathematics' (DFE-00046-2018), Level 2 statements 23 and 25, GOV.UK)

24. A pie chart is used to display data. What does the complete circle of a pie chart represent?

1. The whole data set, equal to 360 degrees and 100%
2. Only the largest category in the data
3. The average of all the categories
4. Half of the total data, equal to 180 degrees

A pie chart represents proportions of a whole, where the full circle equals 360 degrees and 100% of the data. (Pearson Edexcel Functional Skills teaching resources (pie charts); Level2Maths Charts guidance)

25. A survey of 120 students is shown on a pie chart. The sector for 'cycle to school' has an angle of 90 degrees. How many students cycle to school?

1. 30 students
2. 45 students
3. 60 students
4. 90 students

The frequency is (sector angle / 360) x total = (90 / 360) x 120 = 30 students. (Pearson Edexcel Functional Skills teaching resources (pie charts), Functional Skills Maths Level 2)

26. A pie chart shows how 200 people travel to work. The sector for 'bus' has an angle of 72 degrees. How many people travel to work by bus?

1. 40 people
2. 36 people
3. 72 people
4. 20 people

Frequency = (72 / 360) x 200 = 0.2 x 200 = 40 people. (Pearson Edexcel Functional Skills teaching resources (pie charts), Functional Skills Maths Level 2)

27. A class of 30 pupils is shown on a pie chart by favourite sport. If 10 pupils chose football, what angle should the football sector have?

1. 120 degrees
2. 90 degrees
3. 100 degrees
4. 60 degrees

Sector angle = (frequency / total) x 360 = (10 / 30) x 360 = 120 degrees. (Pearson Edexcel Functional Skills teaching resources (pie charts); Level2Maths Charts guidance)

28. A pie chart of 360 customers shows that exactly half of the circle is shaded for 'satisfied'. How many customers were satisfied?

1. 180 customers
2. 90 customers
3. 240 customers
4. 120 customers

Half the circle is 180 degrees, which is half the total: half of 360 customers is 180 customers. (Pearson Edexcel Functional Skills teaching resources (pie charts); Level2Maths Charts guidance)

29. A pie chart and a bar chart both show the same survey of favourite drinks. Which statement about reading them is correct?

1. A pie chart best shows each drink as a proportion of the whole, while a bar chart best shows the actual frequency of each drink
2. A bar chart can only show two categories at a time
3. A pie chart always shows exact frequencies on its sectors
4. Neither chart can be used to compare categories

A pie chart emphasises each category's share of the whole, whereas a bar chart shows the actual frequency (count) for each category along an axis. (Pearson Edexcel Functional Skills teaching resources (charts); Level2Maths Charts guidance)

30. A bar chart shows monthly sales: January 40, February 55, March 30 and April 75. Which month had the highest sales?

1. April
2. February
3. January
4. March

Reading the bar heights, April (75) is the tallest bar and therefore the highest sales. (Level2Maths Charts guidance, Functional Skills Maths Level 2)

31. A bar chart shows the number of books read: Alice 12, Ben 8, Carla 15 and Dev 5. How many more books did Carla read than Dev?

1. 10 books
2. 20 books
3. 3 books
4. 7 books

Carla read 15 and Dev read 5, so the difference is 15 - 5 = 10 books. (Level2Maths Charts guidance, Functional Skills Maths Level 2)

32. A bar chart shows daily takings: Monday 200, Tuesday 200, Wednesday 350 and Thursday 250. Which two days had equal takings?

1. Monday and Tuesday
2. Wednesday and Thursday
3. Tuesday and Thursday
4. Monday and Thursday

Monday and Tuesday both show takings of 200, so their bars are the same height. (Level2Maths Charts guidance, Functional Skills Maths Level 2)

33. A pie chart of 240 pupils shows: walk 90 degrees, bus 120 degrees, car 60 degrees and cycle 90 degrees. How many pupils travel by bus?

1. 80 pupils
2. 60 pupils
3. 90 pupils
4. 120 pupils

The angles total 360 degrees (90 + 120 + 60 + 90 = 360). For the bus sector, frequency = (120 / 360) x 240 = 80 pupils. (Pearson Edexcel Functional Skills teaching resources (pie charts), Functional Skills Maths Level 2)

34. A pie chart shows the holidays of 90 people: beach 160 degrees, city 80 degrees, mountains 120 degrees. How many people chose a city holiday?

1. 20 people
2. 40 people
3. 30 people
4. 80 people

The angles total 360 degrees (160 + 80 + 120). City = (80 / 360) x 90 = 20 people. (Pearson Edexcel Functional Skills teaching resources (pie charts), Functional Skills Maths Level 2)

35. In a pie chart of 50 households, the 'no car' sector is 36 degrees. What percentage of households have no car?

1. 10%
2. 36%
3. 5%
4. 18%

36 degrees out of 360 is 36 / 360 = 0.1, which is 10%. (Pearson Edexcel Functional Skills teaching resources (pie charts); Level2Maths Charts guidance)