Point estimation is a single value to represent what we use to roughly estimate what is an unknown value for the population group only using sample data.

Example: Graded average score from the entire class of an assignment in DAT301

A population is the full group we want to study while a sample is a smaller group selected from the population.

The goal is to use the sample to estimate something about the population.

The population mean is written as: # latex math notation \[ \mu = \frac{1}{N}\sum_{i=1}^{N}x_i \]

Usually, \(\mu\) is unknown.

The sample mean is written as:

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

We use \(\bar{x}\) as a point estimate for \(\mu\).

\[ \hat{\mu} = \bar{x} \]

Suppose a sample of assignment grade for DAT301 is:

70, 75, 80, 85, 90

The point estimate is:

\[ \bar{x} = \frac{70 + 75 + 80 + 85 + 90}{5} = 80 \]

So, the estimated average grade is 80.

#create interactive plot of sample size and error
plot_ly(error_data,
        x = ~sample_sizes,
        y = ~avg_errors,
        type = "scatter",
        mode = "lines+markers") %>%
        layout(title = "Sample Size vs. Average Estimation Error",
        xaxis = list(title = "Sample Size"),
        yaxis = list(title = "Average Error"))

#create sample scores
scores = c(70, 75, 80, 85, 90)

#calcs point estimates
sample_mean = mean(scores)

#print
sample_mean

Point estimation uses sample data to estimate an unknown population value.

The sample mean is one of the most common point estimates.

Larger samples from population will give more accurate results.