By Kishi

• Point estimation is the process of finding an approximate value of a parameter
• Common paramters include the mean and varianc
• In this presentation we will be taking a a look at mean for the parameter

The sample mean (\(\bar{x}\)) is an estimator of population mean (\(\mu\)):

\[ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i \] - \(\bar{x}\) is the sample mean - \(n\) is the sample size - \(x_i\) is the sample observations

The sample variance (\(s^2\)) is an estimator of the population variance (\(\sigma^2\)):

\[ s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2 \] - \(s^2\) is the sample variance - \(\bar{x}\) is the sample mean - \(x_i\) is the sample observations

In this example we will take a sample of 10 students heights in in and through this we will estimate the average height of all students

## [1] 66.2

-Bias is the difference between the expected value of the estimator and the value of the parameter that’s estimated

-Consistency: This showcases how close the point estimator stays to the value of the parameter as size increases

-Efficiency: The most efficient point estimator will be the one with the smallest variance

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• Point estimation is very important tool in statistics that helps estimate population parameters from data
• Sample mean and variance are some of the most common point estimators