Statistics: Types of Data and Sampling Methods
Classifying data and choosing fair samples
Statistics: Types of Data and Sampling Methods
Classifying data and choosing fair samples
Statistics - Grade 6-8
- 1
A school survey asks students to name their favorite lunch item. Is the data categorical or numerical? Explain your answer.
Categorical data sorts people or objects into groups.
The data is categorical because the answers are names or groups, such as pizza, tacos, or salad, not numbers that are measured or counted. - 2
A coach records the number of laps each runner completes during practice. Is the data categorical or numerical? Explain your answer.
The data is numerical because the number of laps is a quantity that can be counted and compared. - 3
Classify the data as discrete or continuous: the number of pets in each student's home.
Discrete data is counted. Continuous data is measured.
The data is discrete because the number of pets is counted in whole numbers, such as 0, 1, 2, or 3. - 4
Classify the data as discrete or continuous: the height of each plant in a science experiment.
The data is continuous because plant height is measured and can include decimals, such as 12.5 centimeters. - 5
A principal wants to know how all 720 students at a school feel about starting classes later. She surveys 60 students. Identify the population and the sample.
The population is the whole group being studied. The sample is the smaller group that gives data.
The population is all 720 students at the school. The sample is the 60 students who were surveyed. - 6
A teacher puts every student's name in a box, mixes the names, and draws 10 names to answer a survey. What sampling method is being used?
This is a simple random sample because every student has an equal chance of being chosen. - 7
A student asks the first 15 people who enter the cafeteria whether they like the new menu. What sampling method is this, and what is a possible problem with it?
Convenience samples are quick, but they can be biased.
This is a convenience sample because the student chose people who were easy to reach. A possible problem is that the first 15 people may not represent the whole school. - 8
A school has 6th, 7th, and 8th grade students. A researcher randomly selects 20 students from each grade to answer a survey. What sampling method is being used?
This is a stratified random sample because the population is divided into groups by grade, and students are randomly selected from each group. - 9
A researcher has a list of 300 students and surveys every 10th student on the list. What sampling method is being used?
Systematic sampling uses a pattern, such as every 5th or every 10th person.
This is a systematic sample because the researcher selects students at a regular interval from a list. - 10
A city wants to study middle school students' after-school activities. The city randomly chooses 4 middle schools and surveys every student at those schools. What sampling method is being used?
This is a cluster sample because the city randomly chooses whole schools, or clusters, and surveys everyone in those chosen schools. - 11
A website asks visitors to click a button if they want to answer a survey about video games. Is this likely to be a random sample or a voluntary response sample? Explain.
A voluntary response sample depends on people choosing themselves to participate.
This is a voluntary response sample because people choose whether to participate. It may be biased because people with strong opinions are more likely to answer. - 12
A student wants to find the most popular sport at a middle school. Which plan is more likely to give a fair sample: survey only the basketball team, or randomly survey students from all grade levels? Explain your choice.
Randomly surveying students from all grade levels is more likely to give a fair sample because it includes students from different parts of the school. Surveying only the basketball team would likely overrepresent students who like basketball.