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How to Calculate Point Estimates in R?

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  • Last Updated : 26 Jan, 2022
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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 parameterPopulation ParameterPoint Estimate
Proportionπ
Meanμx̄ 

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].


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