What is x bar?

Here's some information about <a href="https://www.wikiwhat.page/kavramlar/x%20bar">x bar</a> (often written as x̄ or x̅):

• What it represents: x̄ is the symbol used to denote the sample mean. In statistics, the sample mean is the average of a set of observed values drawn from a larger population. It's a key <a href="https://www.wikiwhat.page/kavramlar/descriptive%20statistic">descriptive statistic</a>.

• Calculation: It's calculated by summing all the individual values in the sample and then dividing by the number of values in the sample. Mathematically: x̄ = (Σxᵢ) / n, where xᵢ represents each individual value in the sample, and n is the <a href="https://www.wikiwhat.page/kavramlar/sample%20size">sample size</a>.

• Relationship to population mean (μ): x̄ is an estimator of the population mean (μ). The <a href="https://www.wikiwhat.page/kavramlar/law%20of%20large%20numbers">Law of Large Numbers</a> states that as the sample size increases, the sample mean (x̄) tends to get closer to the population mean (μ).

• Sampling Distribution: The distribution of sample means (taken from multiple samples of the same population) is called the <a href="https://www.wikiwhat.page/kavramlar/sampling%20distribution%20of%20the%20mean">sampling distribution of the mean</a>. This distribution is important in inferential statistics. The <a href="https://www.wikiwhat.page/kavramlar/central%20limit%20theorem">Central Limit Theorem</a> states that the sampling distribution of the mean will approach a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

• Use in Hypothesis Testing: x̄ is frequently used in <a href="https://www.wikiwhat.page/kavramlar/hypothesis%20testing">hypothesis testing</a>, particularly when performing t-tests or z-tests to compare sample means to a hypothesized population mean or to compare the means of two different samples.

• Use in Control Charts: x̄ is a critical component of <a href="https://www.wikiwhat.page/kavramlar/control%20charts">control charts</a>, specifically the x̄ chart, used in statistical process control to monitor the stability of a process over time.