Sample Mean vs. Population Mean: What's the Difference?

Edited by Aimie Carlson || By Harlon Moss || Published on November 22, 2023
The sample mean is the average of a subset of a population, while the population mean is the average of all members in the entire population.

Key Differences

The sample mean is calculated from a subset of a population and used as an estimate of the population mean. The population mean, however, is the exact average of all individuals in a whole population.
Sample mean is commonly used in statistical analyses when it's impractical or impossible to measure the entire population. Population mean is used when the entire population data is available and can be measured.
The sample mean represents an approximation and can vary depending on the sample chosen. While, the population mean is a precise measure and does not vary, representing the true average of the entire population.
Sample mean is subject to sampling error and variability. In contrast, the population mean, being a measure of the entire population, is not influenced by sampling variability.
The sample mean is often used for inferential statistics to draw conclusions about the population. The population mean is used in descriptive statistics to provide an exact description of the population.

Comparison Chart

Definition

Average of a subset of the population
Average of the entire population

Use

Estimation and inferential statistics
Precise measurement and descriptive statistics

Accuracy

Approximate, varies with sample
Precise and constant

Influenced by

Sampling error and variability
No sampling variability

Calculation

Based on a selected portion
Based on all population data

Sample Mean and Population Mean Definitions

Sample Mean

A statistical measure used to estimate a population parameter.
We calculated the sample mean to understand the general trend.

Population Mean

A precise measure reflecting the entire population.
They used the population mean to set the national policy.

Sample Mean

The average of a selected group from a larger population.
The sample mean of the students' test scores was 75.

Population Mean

A descriptive statistic that provides an exact average.
The population mean was crucial for the demographic study.

Sample Mean

A representative value of a subset of a population.
The sample mean helped in predicting the election results.

Population Mean

The sum of all population values divided by the total population size.
The population mean of the test scores was higher than expected.

Sample Mean

The sum of sampled values divided by the number of samples.
The sample mean was used to gauge customer satisfaction.

Population Mean

The average of all values in an entire population.
The population mean income of the country was calculated.

Sample Mean

An approximate measure reflecting a part of the population.
The sample mean of the survey indicated a positive response.

Population Mean

The true average used in comprehensive data analysis.
Understanding the population mean helped in addressing health issues.

FAQs

How is the sample mean calculated?

By summing up the values of the sample and dividing by the number of samples.

Why use a sample mean instead of a population mean?

When it's impractical or impossible to collect data from the entire population.

Can the sample mean be equal to the population mean?

It can be close but is not always exactly equal due to sampling variability.

What is a sample mean?

It's the average of a subset of a population used in statistical analysis.

What is a population mean?

The population mean is the average of all members of a whole population.

Is the sample mean always accurate?

It's an approximation and can vary depending on the sample selected.

How do you calculate the population mean?

By adding all values in the population and dividing by the total number of population members.

Is the population mean influenced by sample size?

No, as it involves the entire population, not a subset.

Can the sample mean be used to predict the population mean?

Yes, it's often used to estimate the population mean.

How accurate is the population mean?

It's precise and represents the true average of the population.

What is the importance of the sample mean in research?

It's crucial for making inferences about a population in statistical studies.

In what scenarios is the population mean used?

When the entire population data is available and can be measured.

Does the sample mean vary with different samples?

Yes, it can vary based on the characteristics of the sample.

How does sample size affect the sample mean?

Larger sample sizes generally yield a more accurate sample mean.

Why is the population mean considered stable?

Because it is not subject to sampling variability.

What happens to the sample mean as sample size increases?

It tends to get closer to the population mean.

Is the sample mean sufficient for small populations?

In small populations, the sample mean can be a good representation of the population mean.

How do outliers affect the sample mean?

Outliers can skew the sample mean, making it less representative of the population.

What role does variability play in sample mean?

Variability in the sample can lead to differences between the sample mean and the population mean.

Are sample mean and population mean always numerical?

Yes, both are numerical measures of average.