Collecting Data

Show your work for each problem.

1.
Which of the following is a method of collecting data?
1. a)Survey
2. b)Addition
3. c)Calculation
4. d)Division
Answer: Survey
A survey is a method of collecting data by asking people questions. Calculation, division, and addition are mathematical operations, not data collection methods.
2.
The entire group you want to learn about is called the:
1. a)Sample
2. b)Survey
3. c)Variable
4. d)Population
Answer: Population
The population is the entire group you want to study. A sample is a smaller subset selected from the population.
3.
A scientist watches birds at a feeder every morning for a week. This is an example of:
1. a)Observation
2. b)Census
3. c)Experiment
4. d)Survey
Answer: Observation
This is an observation because the scientist is watching and recording what happens without intervening. No questions are asked (not a survey) and no conditions are changed (not an experiment).
4.
A school has 800 students. A researcher surveys 80 students. What percentage of the population is in the sample?
Answer: 10
. The sample represents 10% of the total student population.
5.
In a survey, 35 out of 100 people preferred option A. What percentage preferred option A?
Answer: 35
. Since there were exactly 100 people surveyed, 35 people equals 35%.
6.
A student surveys only her friends about their favorite subject. This is an example of:
1. a)Random sampling
2. b)Bias due to convenience sampling
3. c)Observation
4. d)Good experimental design
Answer: Bias due to convenience sampling
Surveying only friends is convenience sampling, which creates bias. Friends often share similar interests, so the results won't represent the whole school population.
7.
Which question is biased?
1. a)Don't you think we need more homework?
2. b)How often do you complete homework on time?
3. c)What is your opinion about homework?
4. d)How many hours do you spend on homework?
Answer: Don't you think we need more homework?
"Don't you think..." is a leading question that pushes respondents toward agreeing. The other questions are neutral and don't suggest a preferred answer.
8.
A company surveys 500 customers. 175 prefer product A, 225 prefer product B, and the rest have no preference. How many customers have no preference?
Answer: 100
customers have no preference.
9.
A researcher surveys 200 people about their favorite season. Spring: 42, Summer: 68, Fall: 54, Winter: 36. What percentage chose summer?
Answer: 34%
1. How many people chose summer? 68
2. What is the total number of people surveyed? 200
3. What fraction chose summer? (as a decimal) 0.34
4. What is this as a percentage? 34
10.
A scientist tests a plant fertilizer. Group A (with fertilizer): average height 24 cm. Group B (no fertilizer): average height 18 cm. How much taller is Group A on average?
Answer: 6 cm
1. What is the average height of Group A? 24
2. What is the average height of Group B? 18
3. What is the difference? 6
11.
Which sampling method would give the LEAST biased results for a school survey?
1. a)Survey the debate club
2. b)Ask students who stay after school
3. c)Randomly select students from the entire school list
4. d)Ask students in the cafeteria at lunch
Answer: Randomly select students from the entire school list
Random selection from the full school list ensures every student has an equal chance of being chosen. The other methods create bias because they only include students with certain behaviors or interests.
12.
In a clinical trial, Group A (treatment, 150 people): 108 improved. Group B (placebo, 150 people): 75 improved. What is the difference in improvement rates between the groups?
Answer: 22%
1. Calculate Group A's improvement rate (108/150 as %) 72
2. Calculate Group B's improvement rate (75/150 as %) 50
3. What is the difference? 22
13.
A town wants to know if residents support a new park. They survey everyone who attends the town hall meeting. What is wrong with this approach?
1. a)Surveys should only be done online
2. b)The sample is too large
3. c)Only people interested in local issues attend, creating selection bias
4. d)Town hall meetings are the best place for surveys
Answer: Only people interested in local issues attend, creating selection bias
Town hall attendees are already engaged in local issues and may have stronger opinions than typical residents. Many people who don't attend (busy workers, elderly, disinterested) are excluded, creating selection bias.
14.
A school with 1200 students wants to survey them about lunch options. They decide to survey 60 students. From each grade (9-12), they randomly select 15 students. What percentage of each grade is in the sample?
Answer: 5%
1. How many grades are there? 4
2. If 1200 students are divided equally among 4 grades, how many per grade? 300
3. How many students from each grade are in the sample? 15
4. What percentage is 15 out of 300? 5
15.
A researcher needs a margin of error of about 5%. The general rule suggests a sample of at least 400 for this. If she has 10000 people in her population, what percentage would she need to sample?
Answer: 4
. She would need to sample 4% of the population. Notice that for large populations, even a small percentage can give reliable results with proper random sampling.
16.
An experiment tests two teaching methods. Method A (25 students): test scores 72, 85, 91, 68, 79, mean = 79. Method B (25 students): test scores 88, 76, 92, 84, 80, mean = 84. By how many points did Method B outperform Method A on average?
Answer: 5
1. What is the mean score for Method A? 79
2. What is the mean score for Method B? 84
3. What is the difference between the means? 5