What is the main difference between population mean and sample mean?
A. Population mean uses a smaller dataset, while sample mean uses a larger dataset.
B. Population mean considers the entire dataset, while sample mean is calculated from a subset of the dataset.
C. Population mean is always larger than the sample mean.
D. Sample mean is calculated only for qualitative data
Answer (1)
Population mean considers the entire dataset.
Sample mean is calculated from a subset of the dataset.
The main difference lies in the scope of data considered.
Therefore, the correct statement is that population mean uses the entire dataset, while sample mean uses a subset.
Explanation
Analyze the options We need to identify the main difference between population mean and sample mean from the given options. Let's analyze each option:
Population mean uses a smaller dataset, while sample mean uses a larger dataset. This is incorrect. The population mean considers the entire population, which is usually a larger dataset than a sample.
Population mean considers the entire dataset, while sample mean is calculated from a subset of the dataset. This is correct. The population mean is calculated using all the data points in the population, while the sample mean is calculated using a smaller, representative subset of the population.
Population mean is always larger than the sample mean. This is incorrect. The population mean can be larger, smaller, or equal to the sample mean, depending on the sample selected and the distribution of the population.
Sample mean is calculated only for qualitative data. This is incorrect. The sample mean is calculated for quantitative data (numerical data), not qualitative data (categorical data).
Identify the correct option Based on the analysis, the main difference between population mean and sample mean is that the population mean considers the entire dataset, while the sample mean is calculated from a subset of the dataset.
State the final answer The correct answer is: Population mean considers the entire dataset, while sample mean is calculated from a subset of the dataset.
Examples
Imagine you want to know the average height of all students in a university (population mean). It's impractical to measure every student, so you measure a smaller group of students (sample mean) to estimate the average height of the entire university population. The sample mean is an estimate, while the population mean is the actual average if you could measure everyone.
