11+ Maths: Data Interpretation

Data Interpretation is the process of examining, analysing, and drawing conclusions from numerical data presented in various forms such as tables, charts, graphs, and diagrams. This skill is essential for the 11+ exam, as it enables students to interpret information accurately and make informed decisions based on quantitative data.

Key Concepts in Data Interpretation

1. Types of Data Representation

• Tables: Organised rows and columns that display data clearly for easy comparison.
• Bar Graphs: Visual representations of data using rectangular bars to compare quantities.
• Line Graphs: Graphs that show trends over time, using points connected by straight lines.
• Pie Charts: Circular charts divided into slices to illustrate numerical proportions.
• Histograms: Similar to bar graphs but used for continuous data, showing frequency distribution.

2. Reading and Understanding Data

To interpret data correctly, it is important to:

• Identify the variables and their units of measurement.
• Understand the scale used in graphs and charts.
• Compare different data points to identify trends, patterns, or anomalies.

3. Basic Calculations

• Averages: Calculate the mean, median, and mode of data sets.
• Percentages: Determine what percentage a particular value represents out of the total.
• Ratios: Compare two quantities in relation to each other.

4. Drawing Conclusions

After analysing data, students should be able to:

• Summarise the main findings.
• Make predictions based on trends observed.
• Justify their conclusions with reference to the data.

Practice Questions on Data Interpretation

Easy Level

1. If a pie chart shows that 25% of students like maths, what fraction of the students like maths?
2. A bar graph shows that 10 students like football, 5 like basketball, and 15 like cricket. How many students like cricket?
3. If there are 20 students in a class and 8 are girls, what percentage of the class are girls?
4. A table shows that 30% of fruits are apples. If there are 100 fruits, how many are apples?
5. In a line graph, if the value increases from 10 to 15, what is the increase?
6. A pie chart shows that 50% of a pizza is eaten. How much pizza remains?
7. If a histogram shows that 5 people are aged 10-15, 8 people are aged 16-20, and 7 people are aged 21-25, how many people are surveyed?
8. If 60% of students passed a test and there are 30 students, how many students passed?
9. A bar graph indicates that 12 students prefer chocolate ice cream. How many students were surveyed if the total number of preferences is 60?
10. If a class consists of 12 boys and 18 girls, what is the ratio of boys to girls?
11. If a pie chart shows that 1/4 of the circle represents sports, what percentage does this represent?
12. A line graph starts at 5 and ends at 20. What is the total change in value?
13. If there are 40 candies and 10 are red, what percentage of the candies are red?
14. A table shows the number of pets: 5 cats, 10 dogs, and 2 birds. What is the total number of pets?
15. In a survey, 20% of 50 respondents preferred tea. How many preferred tea?
16. If a line graph rises from 30 to 50, what is the change in value?
17. A bar graph indicates that 10 students like reading. What is the total number of students if 25% of them like reading?
18. If 15% of 200 is 30, what is 85% of 200?
19. A pie chart indicates that 30% of the chart represents oranges. How much does this represent if the total is 200?
20. If a table shows that there are 40 males and 60 females, what is the ratio of males to females?

Medium Level

1. A pie chart represents the distribution of books in a library: 30% fiction, 20% non-fiction, and 50% reference. If there are 200 books, how many are fiction?
2. A bar graph shows that 15 students prefer apples, 25 prefer bananas, and 10 prefer grapes. What percentage of students prefer bananas?
3. If a line graph shows a rise from 40 to 100 over 5 days, what is the average daily increase?
4. A table shows that 50% of employees work in sales. If there are 80 employees, how many work in sales?
5. If a histogram indicates that 20 people are aged 20-25, 30 people are aged 26-30, and 50 people are aged 31-35, what is the total number of people?
6. If 40% of 250 is 100, what is the remaining percentage of the total?
7. A bar graph indicates that 15 students like pizza, while 10 like pasta. What is the ratio of students who like pizza to those who like pasta?
8. If a line graph represents sales increasing from £200 to £500 over three months, what is the total increase in sales?
9. A pie chart shows that 60% of the surveyed people prefer tea. If 180 people were surveyed, how many prefer tea?
10. If a table shows the number of pets: 10 cats, 5 dogs, and 3 birds, what percentage of the pets are dogs?
11. A survey reveals that 70% of students enjoy sports. If there are 150 students, how many enjoy sports?
12. If a pie chart indicates that 20% of a cake is left, how much is left if the cake originally weighed 1 kg?
13. A bar graph shows the number of votes for three candidates: A: 40, B: 50, C: 10. What percentage of the total votes did Candidate B receive?
14. If a line graph shows the value of a stock increasing from £150 to £300, what is the percentage increase?
15. A table shows that 30% of a group of 60 people are children. How many adults are in the group?
16. If a histogram indicates that 50 students scored between 60-70, 30 scored between 70-80, and 20 scored above 80, how many students were surveyed?
17. If 75% of a total of 160 is represented as a bar graph, how many does it represent?
18. A pie chart shows that 15% of people prefer chocolate. If there are 200 people surveyed, how many prefer chocolate?
19. If a class has 30 students and 40% are boys, how many boys are there?
20. A table shows sales figures: January: £2000, February: £3000, March: £4000. What is the total sales for these three months?

Hard Level

1. A survey shows that 30% of participants are from London. If there are 500 participants, how many are from London?
2. If a pie chart shows 25% of a company’s expenses are on salaries, what is the amount spent on salaries if the total expenses are £400,000?
3. A bar graph represents the distribution of scores: 60, 75, 90, 100. What is the average score?
4. If a line graph shows a decrease from 200 to 50 over 6 months, what is the average monthly decrease?
5. A survey shows that 12% of people prefer tea. If there are 800 respondents, how many prefer tea?
6. If a table shows that 45% of students are girls and there are 180 students, how many are boys?
7. A pie chart represents the distribution of fruit: 40% apples, 30% oranges, 30% bananas. If there are 300 fruits, how many are oranges?
8. If a histogram indicates that 60% of people are satisfied with a service and there are 1,200 people surveyed, how many are satisfied?
9. A line graph shows sales increasing from £1,000 to £5,000 over 4 years. What is the average annual increase?
10. If a bar graph shows that 35% of a total of 500 votes were for Candidate A, how many votes did Candidate A receive?
11. A survey shows that 60% of people prefer action movies. If 240 people were surveyed, how many prefer action movies?
12. A pie chart indicates that 10% of a budget is allocated for marketing. If the total budget is £1,000,000, how much is allocated for marketing?
13. If a table shows the number of books read: 5, 10, 15, what is the mean number of books read?
14. A line graph shows a decrease in temperature from 30°C to 15°C. What is the total decrease in temperature?
15. If 80% of a total of 250 is represented as a bar graph, how much does it represent?
16. A pie chart shows that 35% of people prefer dogs. If there are 500 people surveyed, how many prefer dogs?
17. A table shows that 15% of students received an A grade. If there are 200 students, how many received an A grade?
18. A survey reveals that 70% of people are happy with their jobs. If there are 400 people surveyed, how many are happy with their jobs?
19. If a pie chart shows that 5% of a cake is left, what is left if the cake originally weighed 2 kg?
20. A line graph shows monthly expenses rising from £500 to £800 over three months. What is the total increase in expenses?

Answers and Explanations

Easy Level

1. $$\frac{1}{4}$$
2. $$15$$
3. $$40\%$$
4. $$30$$
5. $$1$$
6. $$50\%$$
7. $$60 \text{ students}$$
8. $$18 \text{ students}$$
9. $$12 \text{ students}$$
10. $$\frac{2}{3}$$
11. $$25\%$$
12. $$75\%$$
13. $$30 \text{ students}$$
14. $$40 \text{ cm}$$
15. $$70\%$$
16. $$100 \text{ grams}$$
17. $$10 \text{ grams}$$
18. $$0.25$$
19. $$40\%$$
20. $$25 \text{ grams}$$

Medium Level

1. $$60 \text{ books}$$
2. $$30\% = 0.3 \times 200 = 60 \text{ books}$$
3. $$2 \text{ cups}$$
4. $$30\% = 60 \text{ cups}$$
5. $$25 \text{ grams}$$
6. $$50 \text{ grams}$$
7. $$15 \text{ grams}$$
8. $$60\% = 300 \text{ books}$$
9. $$5 \text{ hours}$$
10. $$80\% = 40 \text{ books}$$
11. $$70\% = 500 \text{ books}$$
12. $$75\% = 75 \text{ books}$$
13. $$70\% = 60 \text{ books}$$
14. $$80\% = 150 \text{ books}$$
15. $$90\% = 600 \text{ books}$$
16. $$70\% = 80 \text{ books}$$
17. $$200 \text{ books}$$
18. $$75\% = 30 \text{ books}$$
19. $$80\% = 200 \text{ books}$$
20. $$100 \text{ books}$$

Hard Level

1. $$150 \text{ participants}$$
2. $$£100,000$$
3. $$30 \text{ books}$$
4. $$50 \text{ kg}$$
5. $$240 \text{ kg}$$
6. $$70 \text{ books}$$
7. $$60 \text{ kg}$$
8. $$100 \text{ books}$$
9. $$75\% = 15 \text{ books}$$
10. $$25 \text{ books}$$
11. $$240 \text{ books}$$
12. $$£100,000$$
13. $$70 \text{ books}$$
14. $$80 \text{ books}$$
15. $$60 \text{ kg}$$
16. $$100 \text{ kg}$$
17. $$80 \text{ books}$$
18. $$150 \text{ books}$$
19. $$25 \text{ kg}$$
20. $$20 \text{ grams}$$

This set of questions and answers provides a comprehensive overview of data interpretation relevant to the 11+ exam, covering various difficulty levels and encouraging students to develop their understanding and problem-solving skills.