2026-02-08
Point estimation is the estimation of an unknown parameter of a population by using sample data to define a single value to represent that parameter.
Point estimators can be found through multiple methods, such as:
In the examples provided in this presentation, we will be focusing on finding point estimators through calculating mean values.
The following formula is used to measure point estimators based on mean:
\(\bar{x}=(\sum x_i)/n\)
Where:
The following formula is used to measure point estimators based on variance:
\(s^2=\sum(x_i-\bar{x})^2/(n-1)\)
Where:
The dataset that will be used in the following examples includes 150 different observations of the lengths and widths of the petals and sepals across 3 different species of flowers: Setosa, versicolor, and virginica.
We could easily find the mean of any desired value, such as petal length, by using the following R code:
mean(subset(iris$Petal.Length, iris$Species == "setosa"))
## [1] 1.462
mean(subset(iris$Petal.Length, iris$Species == "versicolor"))
## [1] 4.26
mean(subset(iris$Petal.Length, iris$Species == "virginica"))
## [1] 5.552
However, with multiple variables across multiple species of flowers, it is more meaningful and interesting to visualize where the point estimation for the data set falls by plotting the means on a graph.
First, we will only look at one variable, petal length, across each of the 3 species of flowers using a simple box plot:
As expected, the plotted means match the calculated values in the previous slide. However, using different charts, we can look at multiple variables in the data and chart multiple point estimations at the same time.
In the chart above, the black cross marks represent the mean petal length and width for each respective species of flower.
By creating a 2-dimensional scatter plot, not only can we visualize the point estimation for the expected petal length of each species, but we can now also see the point estimation for the petal width.
Using a 3-dimensional scatter plot, we can also visualize the data across three different variables as well as plot the point estimations for these three variables. The mean values for each respective species of flower are plotted using black squares in the interactive chart below:
Point estimation is a useful tool to find the value of an unknown parameter for a population, and finding mean values is only one of multiple methods of point estimation.
Sometimes, it can be helpful to visualize the point estimators alongside the dataset using charts. Not only can this allow you to see the point estimation of multiple variables at the same time, but it also helps to compare the point estimators, either to other point estimators or to the rest of the dataset.