• We will create a stimulation for the population of 10,000 college students
• Show each daily screen time in hours
• Collect random sample of 100 college students
• Use the sample mean to be able to estimate the mean of the population

• A point estimate is a single value that is used to calculate the estimate of an unknown population parameter
• Provides a single number to estimate of charachters like simple mean and population mean.

Example

• Population parameter: \(\mu\) = true average screen time

• Point estimate: \(\bar{x}\) = true average screen time

• the example above is to describe the concept of point estimation

• Stimulate the screen time in hours for the 10,000 college students
• Using the random sample of the 100 college students we calculate sample mean to find point estimate.

set.seed(123)
# 1. Stimulate population: 10,000 college students daily screen time in hours
population <- data.frame(screen_time = rnorm(10000, mean = 6, sd = 2))
# 2. Take sample of 100 college students
sample_data <- population[sample(1:10000, 100), , drop = FALSE]
# 3. Calculate the sample mean 
sample_mean <- mean(sample_data$screen_time)

sample_mean

## [1] 5.987638

• Histogram is distribution of daily screen times of the 10,000 students in stimulated population

library(ggplot2)
ggplot(population, aes(x = screen_time)) +
  geom_histogram(binwidth = 1, fill = "#8C1D40", color = "white") +
  labs(
    title = "Histogram of Screen Time (population)",
    x = "Screen Time in hours",
    y = "Number of College Students"
  ) +
  theme_minimal(base_size = 9 )

• Similar with distribution but we look at random sample of 100 students to look at estimate of populations true average screen time

ggplot(sample_data, aes(x = screen_time)) +
  geom_histogram(binwidth = 1, fill = "#004C97", color = "white") +
   labs(
    title = "Histogram of Screen Time (Sample of 100 students)",
    x = "Screen Time in hours",
    y = "Number of College Students"
  ) +
  theme_minimal(base_size = 9 )

• With statistics and point estimation as we know from previous slide we use a single value to use as a best guess to look for unknown population perimeter
• In this example im using the point estimate for the population mean \(\mu\) is the sample mean \(\bar{x}\) \[ \hat{\mu} = \bar{x} \frac{1}{n} \sum_{i=1}^{n} x_i \] with this formula we find the arithmetic mean of a sample of size \(n\)

• we have this slide to show more interactive to show vision of data related to point estimation
• Bring in a second variable to make this plot visual in 3d we can use related subject of daily study time
• blue dots to represent individual students study and screen time
• orange dot for average screen and study time of the sample

• This is an understanding for point estimation throughout the slides.
• We learned the fundamental idea of point estimation in statistics and in the scenarios it can be used in.
• Point estimation was able to give single value guess to find population parameter based on sample data.
• The statistics and visualization helps better understanding in point estimation.
• Thank You and hope you learned what polint estimation is through these slides :)!