• This presentation focuses on point estimation.
• Point estimation is the process of using sample data to estimate unknown population parameters.
• In this presentation, we will explore how point estimation is used with sample means and demonstrate it through visualizations.

The means of 50 random samples of numbers between 1 and 100

Here we visualize the distribution of a sample of 10 random numbers from the dataset, which we used to calculate the sample means in the previous slide.

This plot shows how the data from a random sample is spread out, helping us understand the sample we used for point estimation from slide 2.

The formula for the sample mean (\(\bar{x}\)) is given by:

\[ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i \]

where \(x_i\) represents each value in the sample, and \(n\) is the sample size.

An estimator \(\hat{\theta}\) is said to be unbiased if:

\[ E(\hat{\theta}) = \theta \]

where \(E(\hat{\theta})\) is the expected value of the estimator, and \(\theta\) is the true population parameter.

A simple R code that generates a 2D scatter plot using a set random seed sample points.

# Generate random data for two variables (X and Y) between 1 and 100
set.seed(123) # Random num. generator using seed "123"
x <- sample(1:100, 20) #Generates 20 numbers between 1 and 100
y <- sample(1:100, 20) #Generates 20 numbers between 1 and 100

# Creates a simple scatter plot based off the above parameters
plot(x, y, main = "Scatter Plot of Random Sample Points", 
     xlab = "X values", ylab = "Y values")