Mathematics Worksheet for 11-Year-Olds: Data Handling, Statistical Inquiry & Graphs

Instructions

Read each question carefully. For Part 1, circle the best answer. For Part 2, write your answers in the space provided, showing your work where necessary. Good luck!

Part 1: Objective Questions

Instructions: For each question, choose the best answer.

1. Which of the following is a good question for a statistical investigation in your classroom?
• A. What is my teacher's name?
• B. What is the most common shoe size in the class?
• C. How many windows are in the school?
2. If you roll a standard six-sided die 60 times, you would predict the number '4' will appear about how many times?
• A. 6 times
• B. 10 times
• C. 60 times
3. To find out the favourite type of movie for students in your school, the best method would be to:
• A. Ask only the students in the film club.
• B. Ask your 5 best friends.
• C. Ask a random sample of students from each year group.
4. Use the frequency table below for questions 4 and 5.

4. How many students took part in the survey?
• A. 10
• B. 20
• C. 22
5. Which colour was the second most popular?
• A. Blue
• B. Red
• C. Green
6. A pie chart shows the results of a survey of 40 students about their favourite pets. The "Dog" section takes up exactly half of the chart (50%). How many students chose Dog?
• A. 40
• B. 50
• C. 20
7. In the same pet survey, the "Cat" section is a quarter of the chart (25%). How many students chose Cat?
• A. 10
• B. 15
• C. 25
8. A pie chart is most useful for showing:
• A. How data changes over many years.
• B. The proportion or percentage of each category from a total.
• C. The exact number of people who chose each item.
9. Use the following data set for questions 9, 10, and 11:   9, 4, 11, 5, 4
10. What is the mode of the data set?
• A. 9
• B. 4
• C. 5
11. What is the range of the data set?
• A. 11
• B. 7
• C. 4
12. What is the median of the data set?
• A. 11
• B. 4
• C. 5
13. What is the mean of the numbers 5, 10, and 15?
• A. 10
• B. 15
• C. 30
14. A scatter graph shows that as the temperature outside increases, the number of ice creams sold also increases. This is an example of a:
• A. Negative Correlation
• B. No Correlation
• C. Positive Correlation
15. On a scatter graph, a data point that is very far from the other data points is called an:
• A. Outlier
• B. Average
• C. Median
16. To find the range of a data set, you:
• A. Add all the numbers and divide by how many numbers there are.
• B. Find the number that appears most often.
• C. Subtract the smallest value from the largest value.
17. Look at this pattern: 5, 10, 15, 20, ___. What is the next number?
• A. 21
• B. 30
• C. 25
18. A graph shows that a plant's height increases by 2 cm each week. After 5 weeks, how tall would you predict the plant to be if it started at 0 cm?
• A. 7 cm
• B. 10 cm
• C. 5 cm
19. The middle value in an ordered list of data is called the:
• A. Mean
• B. Mode
• C. Median
20. A frequency chart most often uses _______ to record data as it is being collected.
• A. Pie slices
• B. Tally marks
• C. Lines
21. A scatter graph is used to show:
• A. The relationship between two different sets of numerical data.
• B. What fraction of a whole each category represents.
• C. The average of one set of data.

Part 2: Subjective Questions

Instructions: Write your full answer in the space provided. Show your work for calculations.

1. You want to investigate the most popular lunchtime activity (e.g., playing football, talking, reading) for students in your year group. Briefly explain the steps you would take to collect this data fairly.
2. The scores on a science quiz out of 10 are: 7, 9, 8, 6, 9, 10, 9, 8, 7, 8. Create a frequency chart (with tallies) to organize this data.
3. Would a bar chart or a pie chart be better to display the science quiz data from question 2? Explain your choice.
4. Using the science quiz scores from question 2 (7, 9, 8, 6, 9, 10, 9, 8, 7, 8), calculate the following. Show your work.
   a. Mean:
   b. Median:
   c. Mode:
   d. Range:
5. A basketball player scores the following points in five games: 15, 22, 18, 15, 20. What is his mean score per game?
6. What is the range of his scores?
7. Imagine you are plotting a scatter graph with "Age of a car" on the x-axis and "Value of the car" on the y-axis. What kind of pattern or correlation would you expect to see? Explain why.
8. Look at this data set of daily temperatures (°C) for a week: 14, 16, 15, 14, 35, 13. Identify the outlier. How will this outlier affect the mean temperature?
9. The data below shows the number of visitors to a library during one day.
   
   • Morning (9am-12pm): 65 people
   • Afternoon (12pm-4pm): 110 people
   • Evening (4pm-7pm): 40 people
   Describe the pattern you see and suggest a reason for it.
10. A survey of 60 students found that 15 of them chose Reading as their favourite hobby. If you were making a pie chart, what angle in degrees would represent the Reading section? (Remember, a full circle is 360°). Show your calculation.

Answer Key

Part 1: Objective Questions

1. B. What is the most common shoe size in the class?
2. B. 10 times
3. C. Ask a random sample of students from each year group.
4. C. 22
5. B. Red
6. C. 20
7. A. 10
8. B. The proportion or percentage of each category from a total.
9. B. 4
10. B. 7 (Calculation: 11 - 4)
11. C. 5 (Ordered set: 4, 4, 5, 9, 11)
12. A. 10 (Calculation: (5 + 10 + 15) / 3)
13. C. Positive Correlation
14. A. Outlier
15. C. Subtract the smallest value from the largest value.
16. C. 25
17. B. 10 cm (Calculation: 2 cm * 5 weeks)
18. C. Median
19. B. Tally marks
20. A. The relationship between two different sets of numerical data.

Part 2: Subjective Questions

1. Answer: (Answers will vary). A good answer should include:
   • Deciding on the categories (e.g., football, reading, talking, etc.).
   • Creating a survey or tally sheet.
   • Asking a fair sample of students, not just one friend group. For example, asking 5 random students from each class in the year group.
   • Counting the results accurately.
2. Answer:

   Score	Tally	Frequency
   6	I	1
   7	II	2
   8	III	3
   9	III	3
   10	I	1

3. Answer: A bar chart would be better.
   Explanation: A bar chart is better for comparing the exact number of students who got each distinct score. A pie chart is better for showing parts of a whole, which is less helpful here as we want to see which scores were most common.
4. Answer:
   a. Mean: (7 + 9 + 8 + 6 + 9 + 10 + 9 + 8 + 7 + 8) / 10 = 81 / 10 = 8.1
   b. Median: Ordered set: 6, 7, 7, 8, 8, 8, 9, 9, 9, 10. The middle two numbers are 8 and 8. The median is 8.
   c. Mode: The numbers 8 and 9 both appear 3 times. So the modes are 8 and 9.
   d. Range: 10 (highest) - 6 (lowest) = 4.
5. Answer: Mean = (15 + 22 + 18 + 15 + 20) / 5 = 90 / 5 = 18.
6. Answer: Range = 22 (highest) - 15 (lowest) = 7.
7. Answer: You would expect to see a negative correlation.
   Explanation: As the age of a car increases, its value or price generally decreases. The points on the scatter graph would tend to go downwards from left to right.
8. Answer: The outlier is 35.
   Explanation: It will make the mean temperature higher than it would be otherwise, because it is a much larger number than the rest of the data. It will pull the average up.
9. Answer: (Answers will vary).
   Pattern: The library is busiest in the afternoon and quietest in the evening.
   Conclusion: This might be because students and adults visit during their lunch breaks or after school/work has finished for the afternoon, and fewer people visit in the evening when they are home for dinner.
10. Answer:
    Calculation: First find the fraction of students: 15 / 60 = 1/4.
    Then find that fraction of 360°: (1/4) * 360 = 90°.