Textbook Question
Why is a sample used more often than a population?
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1. Intro to Stats and Collecting Data
Intro to Stats
2:04 minutesProblem 1.1.17
Textbook Question
Determine whether the data set is a population or a sample. Explain your reasoning.
The number of guests in each room of a hotel
Verified step by step guidance1
Understand the definitions: A population includes all members of a defined group, while a sample is a subset of the population selected for analysis.
Identify the context of the problem: The data set provided is 'the number of guests in each room of a hotel.'
Determine whether the data set includes all rooms in the hotel or just a subset. If it includes all rooms, it represents a population. If it includes only a portion of the rooms, it represents a sample.
Explain the reasoning: If the data set includes every room in the hotel, it is a population because it accounts for the entire group being studied. If it includes only some rooms, it is a sample because it represents a smaller group taken from the population.
Conclude based on the information provided: Since the problem does not specify whether all rooms or only some rooms are included, clarify that the classification depends on whether the data set is complete (population) or partial (sample).
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Population
A population refers to the entire group of individuals or items that share a common characteristic. In statistics, it encompasses all possible observations that could be made. For example, if we consider all the guests in every room of a hotel across all locations, that would represent the population of hotel guests.
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Population Standard Deviation Known
Sample
A sample is a subset of a population, selected to represent the larger group. It is used in statistical analysis to draw conclusions about the population without needing to collect data from every member. For instance, if we only look at the number of guests in a specific hotel or a few selected rooms, we are working with a sample of the overall population of hotel guests.
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Data Set Context
Understanding the context of a data set is crucial for determining whether it represents a population or a sample. In this case, the data set consists of the number of guests in each room of a hotel, which implies that it is a complete count of guests in that specific hotel, thus representing a population rather than a sample.
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