Math 7 · Unit 6: Collecting data · Cambridge Lower Secondary Maths Stage 7

Questions

1. 1. Kimsant is investigating the heights of 13-year-old boys. He finds the heights of a **sample** of five boys. What average could Kimsant work out from these five boys, and how?

   • The range: the tallest height minus 5.
   • The mean: add the five heights and divide by 13.
   • The mean: add the five heights and divide by 5.
   • The mode: the tallest boy's height.
   Check

2. 2. Kimsant finds the heights of a **sample** of five 13-year-old boys. Why is five not a good **sample size**?

   • It is too many boys to measure.
   • Five boys may not be typical of all 13-year-old boys.
   • Five is an odd number.
   • Heights cannot be averaged.
   Check

3. 3. Kimsant is investigating the heights of 13-year-old boys. Would 1000 boys be a good sample size?

   • Yes
   • No
   Check

4. 4. A questionnaire is given to people who have stayed at a hotel. Here is one question: Was the hotel good value for money? Circle one number. Why is the question asked with numbers to circle?

   • The answers are easy to collect and compare.
   • Because numbers are categorical.
   • So that people can write their opinions.
   • So that everybody gives 10.
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5. 5. A hotel questionnaire asks people to score the hotel from 1 (very bad value) to 10 (excellent value). Here is a summary of the results. What is the sample size?

   • 100
   • 55
   • 10
   • 4.07
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6. 6. A hotel questionnaire asks people to score the hotel from 1 (very bad value) to 10 (excellent value). Here is a summary of the results. Is there evidence that the hotel is good value for money?

   • Yes
   • No
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7. 7. A hotel questionnaire asks people to score the hotel from 1 (very bad value) to 10 (excellent value). Here is a summary of the results. What is the median score?

   • 5
   • 3
   • 4
   • 5.5
   Check

8. 8. A website that sells shoes asks customers to fill in an online questionnaire after they receive their shoes. What is one advantage of sending a questionnaire in this way?

   • Everybody will fill it in.
   • It is quick and cheap to reach many customers.
   • It does not need any questions.
   • Only happy customers can answer.
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9. 9. A website that sells shoes asks customers to fill in an online questionnaire after they receive their shoes. Which is a prediction the questionnaire could test?

   • Most customers are happy with their shoes.
   • Shoes cost less in shops than online.
   • It will rain tomorrow.
   • Everybody in the country wears size 7.
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10. 10. A website that sells shoes asks customers to fill in an online questionnaire after they receive their shoes. Is asking the customers who choose to reply a good way to choose a sample?

    • It is a good way, because it is cheap and easy to send to many customers, but the customers who choose to reply may not be representative of all customers.
    • Yes: every customer is certain to reply, so the sample is representative.
    • No: it is too expensive and slow, because every customer must be visited.
    • No: an online questionnaire cannot give any useful data.
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11. 11. Students at a large college are aged 17 to 22. Zara predicts that older students are likely to study more subjects. She collects data from a sample of 20 students. Why is a sample size of 20 not large enough?

    • Students cannot be sampled.
    • 20 students is too many to ask.
    • With six different ages, there would only be about 3 students of each age.
    • Zara needs exactly 22 students.
    Check

12. 12. Rosario is investigating adults who use a library. He predicts that older adults use the library more often than younger adults. Which is a good way for Rosario to choose a sample to test his prediction?

    • Ask only his friends.
    • Ask only the first adult he sees.
    • Choose names at random from the library's membership list.
    • Ask only the adults over 50.
    Check

13. 13. Rosario collects data about visits to the library and presents it in this table. What is the sample size?

    • 12
    • 9
    • 28
    • 3
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14. 14. Rosario predicts that older adults use the library more often than younger adults. His table shows the number of visits in a 3-month period. Is there evidence that Rosario's prediction is correct?

    • Yes
    • No
    Check

15. 15. Rosario predicts that older adults use the library more often than younger adults. His table shows the number of visits in a 3-month period. Do you think the sample is large enough?

    • Yes
    • No
    Check

16. 16. A large company has over 2000 employees. The manager wants to question a sample of employees about the staff restaurant. What is a suitable sample size?

    • About 100 employees
    • 2 employees
    • All 2000 employees
    • 10 employees
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17. 17. A large company has over 2000 employees. The manager wants to question a sample of employees about the food in the staff restaurant. How can the manager choose the sample?

    • Ask only the manager's friends.
    • Ask only people who like the food.
    • Choose employees at random, from different departments and times.
    • Ask only people who eat at 12 o'clock.
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18. 18. A large company has over 2000 employees. The manager wants to question a sample of employees about the food in the staff restaurant. Which is a good way to collect the data?

    • An online questionnaire sent by email to the employees chosen.
    • Count the employees in the car park.
    • Ask the chef what he thinks.
    • Look at what the manager had for lunch.
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19. 19. A company employs 265 people. The table shows the ages of a sample of 30 employees. What can you say about the ages of the employees in the company?

    • Every employee is 39 years old.
    • They are mostly between 25 and 55; about half are under 40.
    • They are all under 30.
    • They are all over 50.
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20. 20. There are 150 learners of your age at your school. You choose a sample of 30 learners to ask about mathematics. Why would it NOT be a good idea just to choose 30 of your friends?

    • Your friends may have similar views, so they may not represent everyone.
    • Your friends are not learners.
    • 30 is too many people.
    • Friends always give the same answer.
    Check