Data Collection Basics
In this lesson we will introduce some important terminology related to collecting data. When you are finished you will be able to identify the difference between terms like census and sample. In the following lessons we will rely on your understanding of these terms, so study well!Learning Objectives
- Determine whether a value calculated from a group is a statistic or a parameter
- Identify the difference between a census and a sample
- Identify the population of a study
- Determine whether a measurement is categorical or qualitative
Populations and Samples
Selecting A Focus
Before we begin gathering and analyzing data we need to characterize the population we are studying. If we want to study the amount of money spent on textbooks by a typical first-year college student, our population might be all first-year students at your college. Or it might be:- All first-year community college students in the state of Washington.
- All first-year students at public colleges and universities in the state of Washington.
- All first-year students at all colleges and universities in the state of Washington.
- All first-year students at all colleges and universities in the entire United States.
- And so on.
Population
example
A newspaper website contains a poll asking people their opinion on a recent news article. What is the population?Answer: While the target (intended) population may have been all people, the real population of the survey is readers of the website.
Parameter
Census
Sample
Statistic
example
A researcher wanted to know how citizens of Tacoma felt about a voter initiative. To study this, she goes to the Tacoma Mall and randomly selects 500 shoppers and asks them their opinion. 60% indicate they are supportive of the initiative. What is the sample and population? Is the 60% value a parameter or a statistic?Answer: The sample is the 500 shoppers questioned. The population is less clear. While the intended population of this survey was Tacoma citizens, the effective population was mall shoppers. There is no reason to assume that the 500 shoppers questioned would be representative of all Tacoma citizens. The 60% value was based on the sample, so it is a statistic.
The examples on this page are detailed in the following video. https://youtu.be/NlcDpqnqBKYTry It Now
To determine the average length of trout in a lake, researchers catch 20 fish and measure them. What is the sample and population in this study?Answer: The sample is the 20 fish caught. The population is all fish in the lake. The sample may be somewhat unrepresentative of the population since not all fish may be large enough to catch the bait.
Categorizing Data
Quantitative or Categorical
Once we have gathered data, we might wish to classify it. Roughly speaking, data can be classified as categorical data or quantitative data.Quantitative and categorical data
example
We might conduct a survey to determine the name of the favorite movie that each person in a math class saw in a movie theater. When we conduct such a survey, the responses would look like: Finding Nemo, The Hulk, or Terminator 3: Rise of the Machines. We might count the number of people who give each answer, but the answers themselves do not have any numerical values: we cannot perform computations with an answer like "Finding Nemo." Is this categorical or quantitative data?Answer: This would be categorical data.
Example
A survey could ask the number of movies you have seen in a movie theater in the past 12 months (0, 1, 2, 3, 4, . . .). Is this categorical or quantitative data?Answer: This would be quantitative data.Other examples of quantitative data would be the running time of the movie you saw most recently (104 minutes, 137 minutes, 104 minutes, . . .) or the amount of money you paid for a movie ticket the last time you went to a movie theater ($5.50, $7.75, $9, . . .).
example
Suppose we gather respondents' ZIP codes in a survey to track their geographical location. Is this categorical or quantitative?Answer: ZIP codes are numbers, but we can't do any meaningful mathematical calculations with them (it doesn't make sense to say that 98036 is "twice" 49018 — that's like saying that Lynnwood, WA is "twice" Battle Creek, MI, which doesn't make sense at all), so ZIP codes are really categorical data.
Example
A survey about the movie you most recently attended includes the question "How would you rate the movie you just saw?" with these possible answers: 1 - it was awful 2 - it was just OK 3 - I liked it 4 - it was great 5 - best movie ever! Is this categorical or quantitative?Answer:
Try It Now
Classify each measurement as categorical or quantitative.- Eye color of a group of people
- Daily high temperature of a city over several weeks
- Annual income
Answer: 1. Categorical. 2. Quantitative 3. Quantitative
Licenses & Attributions
CC licensed content, Original
- Introduction and Learning Objectives. Provided by: Lumen Learning License: CC BY: Attribution.
- Revision and Adaptation. Provided by: Lumen Learning License: CC BY: Attribution.
- Screenshot: Portland Zip Codes. Provided by: Lumen Learning License: CC BY: Attribution.
CC licensed content, Shared previously
- Math in Society. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. License: CC BY-SA: Attribution-ShareAlike.
- Populations. Authored by: Nils Dougan. License: CC BY-NC: Attribution-NonCommercial.
- Population and sample. Authored by: OCLPhase2's channel. License: CC BY: Attribution.
- Question ID 6910, 33101. Authored by: David Lippman. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.
- Some cheerful data. Authored by: dirkcuys. Located at: https://www.flickr.com/photos/79237959@N02/12210424505/. License: CC BY-SA: Attribution-ShareAlike.
- Qualitative and Quantitative. Authored by: OCLPhase2's channel. License: CC BY: Attribution.
- Question ID 6743. Authored by: Lippman, David. License: CC BY: Attribution. License terms: IMathAS Community LicenseCC-BY + GPL.