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Chapter 1: Problem 33

Indicate whether each of the following constitutes data collected from a population or a sample. a. A group of 25 patients selected to test a new drug b. Total items produced on a machine for each year from 1995 to 2012 c. Yearly expenditures on clothes for 50 persons d. Number of houses sold by each of the 10 employees of a real estate agency during 2012

Short Answer

Expert verified
a. Sample, b. Population, c. Sample, d. Population

Step by step solution

01

Identify Data Collection Types for a: A group of 25 patients selected to test a new drug

This data was taken from a subset (25 patients) of a larger group (all potential patients) thus it is a sample.
02

Identify Data Collection Types for b: total items produced on a machine for each year from 1995 to 2012

Here, the data covers all items produced over a specified time period (1995-2012). So this is regarded as population data, as it includes all units of interest.
03

Identify Data Collection Types for c: Yearly expenditures on clothes for 50 persons

This scenario mentions data from a specific number of individuals (50 persons), which does not represent all possible individuals who expend on clothes yearly. This is therefore a sample.
04

Identify Data Collection Types for d: Number of houses sold by each of the 10 employees of a real estate agency during 2012

Data collected is concerning all 10 employees from a real estate agency during a specific year (2012). This represents all potential contributors (the employees of the agency), therefore it is a population data.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Data Collection
Data collection is a crucial step in any statistical analysis process. It involves gathering information to derive insights, make predictions, and inform decision-making.
In the context of population vs. sample, understanding data collection helps in determining whether you are dealing with all members of a particular group (population) or just a subset (sample).
Let's look into a few points:
  • **Purpose**: The objective of data collection can vary from exploring medical outcomes, as in testing a new drug, to analyzing yearly spending habits.
  • **Methods**: Common methods include surveys, experiments, or existing records.
  • **Scope**: The scope of data collection can dictate if you'll have a complete representation (population) or a selective one (sample).
Effective data collection requires clear objectives and careful consideration of what constitutes a population or a sample, guiding the subsequent steps of research and analysis.
Statistical Analysis
Statistical analysis is the process of interpreting data to discover patterns or trends. It's an essential part of transforming raw data into meaningful insights.
When dealing with data, here are key aspects to consider:
  • **Descriptive Statistics**: Summarizes features of collected data such as the average number of houses sold by employees.
  • **Inferential Statistics**: Draws conclusions about a population based on sample data, like testing a drug on a subset of patients and making general predictions.
  • **Tools**: Various tools like graphs, mean, median, and mode help in understanding data patterns.
Choosing the right type of statistical analysis depends on the dataset, understanding whether your data collection was from a sample or a whole population. Accuracy in analysis leads to more credible results and decision-making.
Population Data
Population data encompasses every member of a specified group, offering a comprehensive view with no sampling errors.
Situations where population data is gathered can often be rare due to logistical challenges. Nonetheless, it's invaluable in providing complete data sets.
Considerations include:
  • **Complete Coverage**: Every individual in the defined group is studied, like all items produced over specific years.
  • **Accuracy**: The absence of sampling errors means population data is highly reliable for making population-wide decisions.
  • **Cost and Time**: Although thorough, gathering and analyzing population data can be resource-intensive.
When population data is available, such as employee performance in a small firm, it provides a clear snapshot of the whole group鈥檚 dynamics, unlike sample data which may infer but not accurately reflect the entire group.

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Most popular questions from this chapter

Classify the following as cross-section or time-series data. a. Average prices of houses in 100 cities b. Salaries of 50 employees c. Number of cars sold each year by General Motors from 1980 to 2012 d. Number of employees employed by a company each year from 1985 to 2012

Explain whether each of the following constitutes data collected from a population or a sample. a. The number of pizzas ordered on Fridays during 2012 at all of the pizza parlors in your town. b. The dollar values of auto insurance claims filed in 2012 for 200 randomly selected policies. c. The opening price of each of the 500 stocks in the S\&P 500 stock index on January 3, 2012 . d. The total home attendance for each of the 18 teams in Major League Soccer during the 2012 season. e. The living areas of 35 houses listed for sale on March 7,2012 in Chicago, Illinois.

Explain the meaning of the following terms. a. Quantitative variable b. Qualitative variable \(\underline{\text { c. }}\) Discrete variable d. Continuous variable e. Quantitative data f. Qualitative data

The number of pizzas delivered to a college campus on six randomly selected nights is \(48,103,95\), 188,286, and 136, respectively. Let \(x\) denote the number of pizzas delivered to this college campus on any given night. Find: a. \(\Sigma x\) b. \((\Sigma x)^{2} \quad\) c. \(\Sigma x^{2}\)

A car was filled with 16 gallons of gas on seven occasions. The number of miles that the car was able to travel on each tankful was \(387,414,404,396,410,422\), and 414 . Let \(x\) denote the distance traveled on 16 gallons of gas. Find: a. \(\Sigma x\) b. \((\Sigma x)^{2}\) c. \(\Sigma x^{2}\)
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