• point estimation
• sample data
• ggplot
• plotly plot

• Point estimation is a statistical method used to estimate an unknown parameter based on observed data from a sample. It involves calculating a single value, known as a point estimator, which serves as the best guess for the true value of the parameter. Point estimation provides a single value as an estimate, without providing information about the uncertainty associated with that estimate.

\[ \hat{\theta} = g(X_1, X_2, \ldots, X_n) \] where: represents the point estimator. X_1, X_2, , X_n are random variables representing the observed data from a sample. g is a function that maps the sample data to the parameter of interest.

# Generating example data for point estimation
set.seed(123)  # for reproducibility

sample_data <- rnorm(50, mean = 8, sd = 2)

sample_mean <- mean(sample_data)

sample_sd <- sd(sample_data)

cat("Sample Data:", toString(sample_data), "\n")

## Sample Data: 6.87904870689558, 7.53964502103344, 11.1174166282982, 8.14101678284915, 8.25857547032189, 11.4301299737666, 8.92183241197841, 5.46987753078693, 6.62629429621295, 7.10867605980008, 10.4481635948789, 8.71962765411473, 8.80154290118811, 8.22136543189024, 6.88831773049185, 11.5738262736062, 8.99570095645848, 4.06676568674072, 9.40271180312737, 7.05441718454413, 5.86435258802631, 7.56405017068341, 5.94799110338552, 6.54221754141772, 6.74992146430149, 4.62661337851517, 9.67557408898905, 8.30674623567303, 5.72372612597611, 10.5076298421399, 8.85292844295363, 7.40985703401546, 9.79025132209004, 9.75626697506608, 9.64316216327497, 9.37728050820018, 9.10783530707518, 7.87617657884656, 7.38807467252017, 7.23905799797523, 6.61058604215897, 7.5841654439608, 5.46920729686347, 12.337911930677, 10.41592399661, 5.7537828335933, 7.19423032940185, 7.06668929275356, 9.55993023667263, 7.83326186705634

cat("Sample Mean:", sample_mean, "\n")

## Sample Mean: 8.068807

cat("Sample Standard Deviation:", sample_sd, "\n")

## Sample Standard Deviation: 1.85174

This red line is the mean value which is the point estimator, in this case the majority data is below the point estamate line.

In this graph, it once again shows the red line, which is the mean as the point estamator.