Point estimation is a statistical method used to determine a single, “best guess” value for an unknown population parameter based on sample data.

Examples

• Sample mean estimates the population mean.
• Sample proportion estimates the population proportion.

A population is the entire group, whereas a sample is only a subset.

Example

• Population: All of Arizona.
• Sample: 100 random Arizona residents.

The sample mean estimates the population mean.

\[ \bar{x} = \frac{\sum x_i}{n} \]

In this example, the sample mean estimates the average exam score.

The sample proportion estimates the population proportion.

\[ \hat{p} = \frac{x}{n} \]

Example: If 60 out of 100 people agree, then the sample proportion is 0.60.

We will use 20 exam scores as a sample.

## [1] 85.1

This number is the point estimate for the population mean exam score.

The following R code creates the histogram shown in the next slide.

ggplot(students, aes(scores)) +
  geom_histogram(
    bins = 5,
    fill = "red",
    color = "black"
  ) +
  labs(
    title = "Distribution of Exam Scores",
    x = "Exam Score",
    y = "Frequency"
  )

This histogram shows the distribution of the sample exam scores used for point estimation.

Point estimation gives one best estimate of a population parameter using sample data.