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Sampling and Data: Key Terms
Summary: This module introduces a number of key terms related to statistical sampling and data.
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In statistics, we generally want to study a population. You can think of a population as an entire collection of persons, things, or objects under study. To study the larger population, we select a sample. The idea of sampling is to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population.
Because it takes a lot of time and money to examine an entire population, sampling is a very practical technique. If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. The data collected from the sample would be the students' grade point averages. In presidential elections, opinion poll samples of 1,000 to 2,000 people are taken. The opinion poll is supposed to represent the views of the people in the entire country. Manufacturers of canned carbonated drinks take samples to determine if a 16 ounce can contains 16 ounces of carbonated drink.
From the sample data, we can calculate a statistic. A statistic is a number that is a property of the sample. For example, if we consider one math class to be a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. The statistic is an estimate of a population parameter. A parameter is a number that is a property of the population. Since we considered all math classes to be the population, then the average number of points earned per student over all the math classes is an example of a parameter.
One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. The accuracy really depends on how well the sample represents the population. The sample must contain the characteristics of the population in order to be a representative sample. We are interested in both the sample statistic and the population parameter in inferential statistics. In a later chapter, we will use the sample statistic to test the validity of the established population parameter.
A variable, notated by capital letters like
Data are the actual values of the variable. They may be numbers or they may be words. Datum is a single value.
Two words that come up often in statistics are average and proportion. If you were to take three exams in your math classes and obtained scores of 86, 75, and 92, you calculate your average score by adding the three exam scores and dividing by three (your average score would be 84.3 to one decimal place). If, in your math class, there are 40 students and 22 are men and 18 are women, then the proportion of men students is
Example 1
Problem 1
Define the key terms from the following study: We want to know the average amount of money first year college students spend at ABC College on school supplies that do not include books. We randomly survey 100 first year students at the college. Three of those students spent $150, $200, and $225, respectively.
Solution
The population is all first year students attending ABC College this term.
The sample could be all students enrolled in one section of a beginning statistics course at ABC College (although this sample may not represent the entire population).
The parameter is the average amount of money spent (excluding books) by first year college students at ABC College this term.
The statistic is the average amount of money spent (excluding books) by first year college students in the sample.
The variable could be the amount of money spent (excluding books) by one first year student. Let
The data are the dollar amounts spent by the first year students. Examples of the data are $150, $200, and $225.
Optional Collaborative Classroom Exercise
Do the following exercise collaboratively with up to four people per group. Find a population, a sample, the parameter, the statistic, a variable, and data for the following study: You want to determine the average number of glasses of milk college students drink per day. Suppose yesterday, in your English class, you asked five students how many glasses of milk they drank the day before. The answers were 1, 0, 1, 3, and 4 glasses of milk.
Glossary
- Average:
- A number that describes the central tendency of the data. There are a number of specialized averages, including the arithmetic mean, weighted mean, median, mode, and geometric mean.
- Data:
- A set of observations (a set of possible outcomes). Most data can be put into two groups: qualitative (hair color, ethnic groups and other attributes of the population) and quantitative (distance traveled to college, number of children in a family, etc.). Quantitative data can be separated into two subgroups: discrete and continuous. Data is discrete if it is the result of counting (the number of students of a given ethnic group in a class, the number of books on a shelf, etc.). Data is continuous if it is the result of measuring (distance traveled, weight of luggage, etc.)
- Proportion:
- As a number: A proportion is the number of successes divided by the total number in the sample.
- As a probability distribution: Given a binomial random variable (RV),
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This work is licensed by Maxfield Foundation under a Creative Commons Attribution License (CC-BY 2.0), and is an Open Educational Resource.
Last edited by Susan Dean on Feb 18, 2009 9:27 pm US/Central.
"Collaborative Statistics was written by two faculty members at De Anza College in Cupertino, California. This book is intended for introductory statistics courses being taken by students at two- […]"