How to Calculate Point Estimates in R?

Point estimation is a technique used to find the estimate or approximate value of population parameters from a given data sample of the population. The point estimate is calculated for the following two measuring parameters:

Measuring parameter	Population Parameter	Point Estimate
Proportion	π	p
Mean	μ	x̄

This article focuses upon how we can calculate point estimates in R Programming Language.

The point estimate of the population proportion

Point estimation of population proportion can be calculated by using the below mathematical formula,

Syntax: p′ = x / n

Here,

• x : Signifies the number of successes
• n : Signifies the sample size.
• p′ is the point estimate of population proportion

Example:

Let’s say we want to estimate the proportion of students in a class who are present on a particular day. The sample data consist of 20 data elements.

R

# define data
data <- c('Present', 'Absent', 'Absent', 'Absent',
          'Absent', 'Absent', 'Present', 'Present',
          'Absent', 'Present',
          'Present', 'Present', 'Present', 'Present',
          'Present', 'Present', 'Absent', 'Present',
          'Present', 'Present')

# find total sample size
n <- length(data)

# find number who are present
k <- sum(data == 'Present')

# find sample proportion
p <- k/n

# print
print(paste("Sample proportion of students who are present", p))

Output:

Example:

Note that we can calculate the 95% confidence interval for the population proportion by using the following source code,

R

# define data
data <- c('Present', 'Absent', 'Absent', 'Absent',
          'Absent', 'Absent', 'Present', 'Present',
          'Absent', 'Present',
          'Present', 'Present', 'Present', 'Present',
          'Present', 'Present', 'Absent', 'Present',
          'Present', 'Present')

# find total sample size
total <- length(data)

# find number who responded 'Yes'
favourable <- sum(data == 'Present')

# find sample proportion
ans <- favourable/total

# calculate margin of error
margin <- qnorm(0.975)*sqrt(ans*(1-ans)/total)

# calculate lower and upper bounds of
# confidence interval
low <- ans - margin
print(low)

high <- ans + margin
print(high)

Output:

Hence, The 95% confidence interval for the population proportion is [0.440, 0.859].

The point estimate of a population mean

Point estimation of population mean can be calculated by using mean() function in R. The syntax is given below,

Syntax: mean(x, trim = 0, na.rm = FALSE, …)

Here,

• x: It is the input vector
• trim: It is used to drop some observations from both end of the sorted vector
• na.rm: It is used to remove the missing values from the input vector

Example:

Let’s say we want to estimate the population mean of heights of the students in a class. The sample data consist of 20 data elements.

R

#define data
data <- c(170, 180, 165, 170, 165,
          175, 160, 162, 156, 159,
          160, 167, 168, 174, 180,
          167, 169, 180, 190, 195)

#calculate sample mean
ans <- mean(data, na.rm = TRUE)

#print the mean height
print(paste("The sample mean is", ans))

Output:

Hence, The sample means the height is 170.6 cm.

Example:

Note that we can calculate the 95% confidence interval for the population mean by using the following source code,

R

# define data
data <- c(170, 180, 165, 170, 165, 175,
          160, 162, 156, 159, 160, 167,
          168, 174, 180, 167, 169, 180,
          190, 195)

# Total number of students
total <- length(data)

# Point estimate of mean
favourable <- mean(data, na.rm = TRUE)
s <- sd(data)

# calculate margin of error
margin <- qt(0.975,df=total-1)*s/sqrt(total)

# calculate lower and upper bounds of
# confidence interval
low <- favourable - margin
print(low)

high <- favourable + margin
print(high)

Output:

Hence, The 95% confidence interval for the population mean is [165.782, 175.417].