Mathematics Worksheet for 11-Year-Olds: Data Handling & Statistical Inquiry with Predictions

Instructions

Read each question carefully. For the objective questions, circle the best answer or fill in the blank. For the subjective questions, write your answers in full sentences, showing your reasoning where needed.

Part A: Objective Questions

Use the bar chart below, showing the favorite sports of a group of students, to answer questions 1-5.

1. Which sport is the most popular?
2. How many students chose Soccer as their favorite sport?
3. How many more students chose Basketball than Tennis?
4. How many students were surveyed in total?
5. If one more student was surveyed and they chose Soccer, what would be the new total for Soccer?

Use the line graph below, showing the temperature in a city over 6 days, to answer questions 6-10.

6. What was the highest temperature recorded?
7. On which day was the temperature the lowest?
8. What was the difference in temperature between Day 4 and Day 6?
9. The graph shows a general warming trend from Day 1 to Day 5. True or False?
10. Based on the data, what is a reasonable prediction for the temperature on Day 7?
    A) 10°C
    B) 19°C
    C) 30°C

Use the pie chart below, showing how Leo spends his weekly allowance of $20, to answer questions 11-15.

11. What does Leo spend the most money on?
12. How much money does Leo put into Savings each week?
13. What percentage of his money is spent on Comics and Gifts combined?
14. If Leo's allowance doubled to $40 next week and his spending habits stayed the same, how much would he spend on Snacks?
15. Which two categories together make up 75% of his spending?

Use this list of scores from a recent spelling test to answer questions 16-20.
Scores: 9, 10, 7, 8, 9, 6, 9

16. What is the mode of this set of scores? (The number that appears most often)
17. What is the range of the scores? (The difference between the highest and lowest score)
18. What is the median score? (The middle number when the scores are in order)
19. What is the mean score, rounded to the nearest whole number? (The sum of scores divided by the number of scores)
20. If another student scored a 10, would the mode change? (Yes/No)

Part B: Subjective Questions

Answer the following questions in the space provided. Explain your reasoning.

1. You want to find out the most popular book genre (fantasy, sci-fi, mystery, etc.) among students in your year group. Describe the first two steps you would take to start this investigation.


2. A survey asks people leaving a comic book store what their favorite hobby is. Why might the results of this survey be biased or misleading?


3. A café owner tracks the number of hot chocolates sold each month:
   September: 45
   October: 60
   November: 85
   December: 120
   What pattern do you see? Predict how many hot chocolates might be sold in January. Explain why.


4. Look at this data set of daily screen time (in hours) for a student: 3, 2, 4, 3, 7, 2, 3. The "7" on one day is very different from the other numbers. What is this type of data point called, and what might be a reason for it?


5. Two friends are practicing basketball shots.
   Maria's scores (out of 10): 7, 8, 7, 7, 6
   Ben's scores (out of 10): 9, 4, 5, 8, 9
   Based on their scores, who is the more consistent player? Explain your answer using the data.


6. To predict tomorrow's weather, would you look at a line graph of temperatures for the last year or for the last week? Explain your choice.


7. A company claims that "Most people love our new juice!" They surveyed 10 people, and 6 of them liked it. Why is this claim potentially weak or unconvincing?


8. The number of people visiting a local swimming pool is recorded for one week in July:
   Monday: 50, Tuesday: 55, Wednesday: 62, Thursday: 68, Friday: 80
   Predict the number of visitors for Saturday. Justify your prediction.


9. Here are the favorite colors of 12 students:
   Blue, Red, Green, Blue, Yellow, Blue, Red, Blue, Green, Pink, Red, Blue
   Create a simple frequency table (tally chart) to organize this data.


10. Imagine you run a school tuck shop. You have collected data showing that sales of ice cream are highest on Fridays. How would you use this information to make a business decision for the next Friday?

Answer Key

Part A: Objective Questions

1. Basketball
2. 10
3. 6 (13 - 7)
4. 41 (10 + 13 + 7 + 11)
5. 11
6. 20°C (on Day 5)
7. Day 1
8. 1°C (19 - 18)
9. True
10. B) 19°C (It's a reasonable guess that's close to the recent temperatures, unlike the extremes of A and C).
11. Snacks
12. $5 (25% of $20)
13. 25% (15% + 10%)
14. $20 (50% of $40)
15. Snacks and Savings (50% + 25%)
16. 9
17. 4 (10 - 6)
18. 9 (Scores in order: 6, 7, 8, 9, 9, 9, 10)
19. 8 (Sum is 58, 58 / 7 ≈ 8.28)
20. No (There would be three 9s and two 10s, so 9 would still be the mode).

Part B: Subjective Questions

(Note: Student answers may vary slightly but should reflect similar reasoning.)

1. Step 1: Formulate a clear question, like "What is the most popular book genre in Year 6?". Step 2: Decide how to collect the data, such as creating a survey or a tally sheet with a list of genres for classmates to vote on.
2. The results might be biased because the people being surveyed are already at a comic book store, which means they are very likely to enjoy comics. Their favorite hobby is more likely to be related to comics than the general population's.
3. The pattern is that sales are increasing each month as the weather gets colder. A reasonable prediction for January would be a number higher than 120, perhaps around 140-150, because January is typically colder than December, leading to more sales of hot drinks.
4. This data point is called an outlier. A possible reason could be that it was a weekend or a holiday, so the student had much more free time for screens, or they were sick at home.
5. Maria is the more consistent player. Her scores are all close together (range of 2, from 6 to 8). Ben's scores are more spread out (range of 5, from 4 to 9), making him less consistent even though he has higher top scores.
6. You would look at the graph for the last week. Weather patterns change quickly, so recent data is much more useful for predicting the immediate future than data from a year ago.
7. The claim is weak because the sample size (10 people) is very small. A survey of only 10 people is not enough to represent what "most people" in a large population think.
8. A good prediction would be a number higher than 80, likely between 90-100. The trend shows visitor numbers increasing towards the end of the week, and Saturday is part of the weekend when more people are free to go swimming.
9. Favorite Color Tally Chart:
   - Blue: ||||| (5)
   - Red: ||| (3)
   - Green: || (2)
   - Yellow: | (1)
   - Pink: | (1)
10. I would use this information to make sure I have more ice cream in stock on Friday than on other days. I could also consider running a special deal on ice cream on Fridays to maximize sales.