# Sample statistics vs population statistics

• 939
In summary, the conversation discusses the difference between sample statistics and population statistics and the reasons for these differences. The speaker mentions the concepts taught in class, such as the Central Limit Theorem, and acknowledges that the distribution being non-normal can affect the validity of the empirical rule. They also mention the possibility of their data-based values for mean and standard deviation being inaccurate due to only having one sample. However, they question if there are any other concepts that could explain the differences.
939

## Homework Statement

My task is to explain why the sample statistics I have obtained differ from the population statistics I have obtained from some data - using "concepts taught in class, if they exist". I have calculated x̄ and s, as well as σ and µ.

## Homework Equations

First of all, the distribution is not normal, thus the emperical rule is invalid.

## The Attempt at a Solution

Part of me thinks it's a trick question because there are very few "concepts" I can think of. The only thing I can come up with is that the mean differs because it is merely one sample, and according to the Central Limit Theorum, if I had a bigger sample space, the mean would be similar. Similarly, the standard deviation differs because it is merely one sample. Is this all there is to it or am I missing something?

Sample statistics are obtained by sampling from a population. The idea is that the statistical properties of a population can (usually) be only estimated. In this respect, I slightly doubt about your data-based $\mu, \sigma^2$ :-)

## What is the difference between sample statistics and population statistics?

Sample statistics refers to data collected from a smaller subset, or sample, of a larger population. Population statistics, on the other hand, refers to data collected from the entire population.

## Why is it important to understand the difference between sample statistics and population statistics?

Understanding the difference between sample statistics and population statistics is crucial in order to make accurate and meaningful conclusions about a population as a whole. It also helps in determining the reliability and generalizability of the data.

## How are sample statistics and population statistics related?

Sample statistics are used to estimate population statistics. By collecting data from a representative sample, we can make inferences about the entire population.

## What are some common examples of sample statistics and population statistics?

Examples of sample statistics include the mean, median, and standard deviation of a sample. Examples of population statistics include the true mean, median, and standard deviation of the entire population.

## How can the results of sample statistics and population statistics differ?

The results of sample statistics and population statistics may differ due to sampling error. This is the difference between the true value of a population statistic and the estimated value based on a sample. The larger the sample size, the smaller the sampling error and the closer the results will be to the population statistics.

Replies
5
Views
2K
Replies
12
Views
2K
Replies
1
Views
2K
Replies
2
Views
2K
Replies
1
Views
2K
Replies
8
Views
3K
Replies
5
Views
2K
Replies
2
Views
1K
Replies
4
Views
2K
Replies
1
Views
1K