• A point estimate provides a single value as an estimate of a population parameter.
• Common point estimators include: sample mean (\(\bar{x}\)), sample proportion (\(\hat{p}\)), and sample variance (\(s^2\)).

• Unbiasedness: Expected value equals the true parameter.
• Efficiency: Has the smallest variance among all unbiased estimators.
• Consistency: Improves as sample size increases.

Given a sample \(x_1, x_2, ..., x_n\), the sample mean is:

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

This is a point estimate of the population mean \(\mu\).

# Sample of weights (in kg)
weights <- c(70, 72, 68, 75, 74, 69, 71, 73, 70, 72)
mean(weights)  # Point estimate of population mean

## [1] 71.4

\[ Var(\bar{x}) = \frac{\sigma^2}{n} \]

This variance decreases as \(n\) increases — meaning the estimate becomes more precise.