Point estimation involves using sample data to estimate unknown population parameters. This process is fundamental in statistical analysis for making inferences about a population.

• Point Estimator: A statistic that provides the best guess for a population parameter.
• Population Mean (\(\mu\)): Estimated by the sample mean (\(\bar{x}\)).
• Population Proportion (\(p\)): Estimated by the sample proportion (\(\hat{p}\)).

The sample mean is calculated as:

\[\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i\] This serves as an unbiased estimator of the population mean, \(\mu\).

## Sample mean:  50.32515

The sample proportion, \(\hat{p}\), is an estimator of the population proportion, \(p\), and is calculated as:

\[\hat{p} = \frac{x}{n}\] where \(x\) is the number of successes, and \(n\) is the sample size.

## Sample proportion:  0.63

# Generating sample data
set.seed(42)
sample_data <- rnorm(100, mean = 50, sd = 10)

# Calculating sample mean
sample_mean <- mean(sample_data)
cat("Sample mean: ", sample_mean, "\n\n")

library(ggplot2)
ggplot(data.frame(Value = sample_data), aes(x = Value)) +
  geom_histogram(binwidth = 5, fill = "salmon", color = "black") +
  geom_vline(aes(xintercept = sample_mean), color = "turquoise", 
             linetype = "dashed", size = 1) +
  labs(title = "Sample Data Distribution", x = "Value", y = "Frequency")