A point estimate represents a number that we calculate from sample data to estimate some population parameter. This serves as our best possible estimate of what the true population parameter may be.

The following table shows the point estimate that we use to estimate population parameters:

Measurement |
Population parameter |
Point estimate |
---|---|---|

Mean | μ (population mean) | x (sample mean) |

Proportion | π (population proportion) | p (sample proportion) |

The following examples explain how to calculate point estimates for a population mean and a population proportion in R.

**Example 1: Point Estimate of Population Mean**

Suppose we would like to estimate the mean height (in inches) of a certain type of plant in a certain field. We gather a simple random sample of 13 plants and measure the height of each plant.

The following code shows how to calculate the sample mean:

#define data data <- c(8, 8, 9, 12, 13, 13, 14, 15, 19, 22, 23, 23, 24) #calculate sample mean mean(data, na.rm = TRUE) [1] 15.61538

The sample mean is **15.6 **inches. This represents our point estimate for the population mean.

We can also use the following code to calculate a 95% confidence interval for the population mean:

#find sample size, sample mean, and sample standard deviation n <- length(data) xbar <- mean(data, na.rm = TRUE) s <- sd(data) #calculate margin of error margin <- qt(0.975,df=n-1)*s/sqrt(n) #calculate lower and upper bounds of confidence interval low <- xbar - margin low [1] 12.03575 high <- xbar + margin high [1] 19.19502

The 95% confidence interval for the population mean is **[12.0, 19.2]** inches.

**Example 2: Point Estimate of Population Proportion**

Suppose we would like to estimate the proportion of people in a certain city that support a certain law. We survey a simple random sample of 20 citizens.

The following code shows how to calculate the sample proportion:

#define data data <- c('Y', 'Y', 'Y', 'N', 'N', 'Y', 'Y', 'Y', 'N', 'Y', 'N', 'Y', 'Y', 'N', 'N', 'Y', 'Y', 'Y', 'N', 'N') #find total sample size n <- length(data) #find number who responded 'Yes' k <- sum(data == 'Y') #find sample proportion p <- k/n p [1] 0.6

The sample proportion of citizens who support the law is **0.6**. This represents our point estimate for the population proportion.

We can also use the following code to calculate a 95% confidence interval for the population mean:

#find total sample size n <- length(data) #find number who responded 'Yes' k <- sum(data == 'Y') #find sample proportion p <- k/n #calculate margin of error margin <- qnorm(0.975)*sqrt(p*(1-p)/n) #calculate lower and upper bounds of confidence interval low <- p - margin low [1] 0.3852967 high <- p + margin high [1] 0.8147033

The 95% confidence interval for the population proportion is **[0.39, 0.81]**.

**Additional Resources**

How to Calculate Five Number Summary in R

How to Find Confidence Intervals in R

How to Plot a Confidence Interval in R