# Sample mean and sample covariance

• EnglsihLearner
In summary, the conversation discusses the concept of sample mean and sample covariance, and the difficulty in understanding a specific part of the concept as explained in a Wikipedia article. The solution is to search for a tutorial or more concrete explanation of the concept using keywords.
EnglsihLearner
Let xij be the ith independently drawn observation (i=1,...,N) on the jth random variable (j=1,...,K). These observations can be arranged into N column vectors, each with K entries, with the K ×1 column vector giving the ith observations of all variables being denoted xi (i=1,...,N).

http://en.wikipedia.org/wiki/Empirical_mean
to learn the Sample mean and sample covariance. But I am failing to understand the above part. Could someone please explain it to me in a easiest way?

When a Wikipedia article is too schematic or abstract ... just do a search using the key words plus tutorial.
Then look over the articles found to find one that is more concrete such as this one:
https://online.stat.psu.edu/~ajw13/stat505/fa06/07_propmean/04_propmean_summary.htm

## 1. What is the sample mean and how is it calculated?

The sample mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding all the values in the sample and dividing by the number of values in the sample.

## 2. How does the sample mean differ from the population mean?

The sample mean is calculated based on a subset of the entire population, while the population mean is calculated based on all members of the population. The sample mean is used to estimate the population mean, but it may not be exactly the same.

## 3. What is the significance of the sample mean in statistical analysis?

The sample mean is an important statistic in statistical analysis because it provides information about the central tendency of a data set. It can be used to make inferences about the population mean and to compare different data sets.

## 4. How is sample covariance calculated and what does it represent?

Sample covariance is a measure of the relationship between two variables in a sample. It is calculated by multiplying the differences between each pair of values for the two variables and then dividing by the sample size. A positive covariance indicates a positive relationship, while a negative covariance indicates a negative relationship.

## 5. What is the difference between sample covariance and sample correlation?

Sample covariance and sample correlation are both measures of the relationship between two variables, but they differ in terms of scale. Sample covariance is measured in units of the variables, while sample correlation is a unitless measure that ranges from -1 to 1. Sample correlation is a standardized version of sample covariance, making it easier to compare relationships between different data sets.

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