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Samples and Surveys

Last updated about 3 years ago
9 questions
When collecting data to examine a problem, you need to make sure that your methods are fair and that you accurately represent the results. Previously we looked at determining which measure of center, mean, median, or mode, you should use when analyzing one or comparing two data sets. In this assignment, we are going to learn about
  • types of data,
  • populations versus samples,
  • sample size
  • bias
Data can be collected based on measurements or qualities.
  • Quantitative data measure quantities. All quantitative data is numeric, such as height and distance.
  • Qualitative data is described using qualities or categories such as color or region.
For the most part, qualitative data is not numerical. However, there are a few categories, such as zip and area codes, that use numbers to represent a category.
2

Is each data set qualitative or quantitative?

  • number of students taking Spanish in 7th grade
  • the time it takes for each student to run a mile
  • postal code
  • Jersey numbers for all NHL members
  • favorite movie
  • qualitative
  • quantitative
The kind of data you are working with determines the type of graph you use to display the data. A set of data that uses only one variable is univariate. A set of data that uses two variables is bivariate.

Examples: Identifying Types of Data
  1. A research team is conducting a study of 200 men and women. The study looks about how many times a day each person walks more than a mile. Every week the team collects data on the participants' weight and waist circumference. This is an example of bivariate data because two variables are being measured 1) weight and 2) waist circumference.
  2. Marena is writing a project for ELA on Internet costs. She records her findings for the cost of Internet service from different providers in a table. This is an example of univariate data, the variable being measured is cost.
2

Is each data set univarite or bivariate?

  • the edge lengths and volumes of triangular prisms
  • average number of YouTube videos your classmates watch per day
  • circumference and radii of pizzas
  • the atomic mass of the elements in the periodic table
  • lengths and weights of reptiles
  • univariate
  • bivariate
Researchers and statisticians collect information about specific groups of objects or people. The entire group that you want information about is called a population. When a population is too large to survey, they survey a part of it to find characteristics of the whole. The part that is surveyed is called a sample.

Three possible sampling methods are random, systematic, and stratified. When designing a survey, you should choose a sample that reflects the population.

Examples: Choosing a Sample
  1. You want to find out how many Netflix shows or movies your classmates stream every week. You interview every 10th teenager you see at three different basketball games. What sampling method are you using? Is this a good method to use? Since you are interviewing every 10th teenager, you are using a systematic method. However, each game may have teenagers that do not attend Renaissance Academy.
  2. You revise your plan and interview all students leaving a school assembly who are wearing green or purple school lanyards. This time you are using a stratified sampling method. First, you divided the population into people with or without lanyards. Then you used a random characteristic, lanyard color, to determine whom to interview.

2

Determine whether each sampling method is random, systematic, or stratified.

  • You survey every seventh student who enters the cafeteria.
  • You draw student ID numbers out of a hat and survey those students.
  • You survey two students ata random from each class.
  • A factory tests the quality of every 40th cell phone made.
  • A pollster randomly selects 100 people from each town in a certain canidate's district to see if they support the canidate.
  • random
  • systematic
  • stratefied
A survey question has a bias when it contains assumptions that may or may not be true. Bias can influence opinion and can make one answer seem better than another. Survey questions must be carefully worded to avoid bias.

Example: Determining Bias in a Survey Question
A reporter wants to find out what kinds of movies are most popular with local residents. The reporter asks, "Do you prefer exciting action movies or boring documentaries?" The question is biased because the adjectives exciting and boring are the reporter's assumptions about each type of film. The question could be worded, "Do you prefer exciting action movies or boring documentaries?" Or the reporter could ask, "What types of movies do you prefer to watch?"

Adjectives are a key feature to be on the lookout for in surveys. The use of adjectives often creates a biased question.

3

Determine whether the question is biased. Explain your answer.
Do you prefer shopping alone online or the excitement of going to stores with friends?

Samples can also be biased. For example, all voluntary-response samples are biased because you cannot be sure that the people who choose to respond are representative of teh population. The location where a survey is conducted can also cause a sample to be biased.

Example: Determining Bias in a Sample
You want to determine what percentage of teens between the ages of 14 and 18 watch wrestling on TV. At a high school wrestling match, you ask every third teenager whether he or she watches wrestling on TV. The sample chosen is not representative of the population. Since you are attending a wrestling match, there is a high likelihood that the teenagers attending like wrestling. This means the population is more likely to watch TV than your average teenager.

A sample is less likely to be biased if:
  • it is determined randomly
  • every member of the population is equally likely to be picked and represented
3

A classic radio station posts an online poll asking their listeners to vote for the best band of all time. After 2 weeks, the radio station analyzes the results and determines 54% of its viewers voted for the same band. The station releases an article announcing the band as the best band of all time. Is the conclusion valid? Explain.

HINT: A valid conclusion is affected by bias.

Practice Problems

3

Classify the data as qualitative or quantitative, and as univariate or bivariate.

  • hours of daylight per day in Anchorage, Alaska
  • the batting averages and RBIs for members of a baseball team over 5 seasons
  • the color of your classmate's livingroom
  • qualitative
  • quantitative
  • univariate
  • bivariate
1

Determine whether the sampling method is random, systematic, or stratefied.

  • Every student whose driver's license ends in an odd number is asked to complete a survey on safe driving habits
  • You ask 15 of the residents on your street whether they support the local bond issue to build a community center across town
  • A bottle manufacturer checks the quality of every third bottle it makes
  • random
  • systematic
  • stratefied
2

Pick one of the sampling methods from question 7. Identify the method and:
  • Determine whether the method will produce a good sample.
  • Explain your answer.

5

You want to find out how much time people in your town spend doing volunteer work. You call 100 homes in the community during between 10 am and 3 pm on Mondays and Wednesdays. Of those surveyed, 85% are over the age of 60.
  • How might this create bias in your survey results?
  • Describe a survey method that could reduce bias.