Sampling Error Formula (original) (raw)

Last Updated : 23 Jul, 2025

Sampling error technique is employed to compute the total selection bias in statistical analysis, as the name implies. To refresh your memory, sampling error is a statistical mistake caused by the nature of sampling. The atypical-ness of the observations in the samples collected causes statistical analysis errors.

Because sampling is used to identify the characteristics of a full population, the discrepancy between the sample values and the population is referred to as sampling error. It's important to remember that calculating the precise value of sampling is impossible because the population value is unknown, yet sampling error may typically be calculated using statistical models of a sample.

**Sampling Error Formula

**SE = Z x σ/√n

where,

**Sample Problems on Sampling Error

**Question 1. Find the sampling error at a 95% confidence level given the standard deviation of the population is 0.23 and the sample size is 2145.

**Solution:

Given: Z = 95%, σ = 0.23 and n = 2145

Since, SE = Z x σ/√n

= 1.96 x (0.23/√2145)

= 1.96 x 0.00496608

**SE = 0.009733

**Question 2. Find the sampling error at a 90% confidence level given the standard deviation of the population is 0.2 and the sample size is 100.

**Solution:

Given: Z = 92%, σ = 0.2 and n = 100

Since, SE = Z x σ/√n

= 1.645 x (0.2/√100)

= 1.645 x 0.02

**SE = 0.0329

**Question 3. Find the sampling error at a 99% confidence level given the standard deviation of the population is 0.2 and the sample size is 36.

**Solution:

Given: Z = 99%, σ = 0.2 and n = 100

Since, SE = Z x σ/√n

= 2.58 x (0.2/√36)

= 2.58 x 0.0333

**SE = 0.085914

**Question 4. Find the sampling error at a 99% confidence level given the standard deviation of the population is 0.9 and the sample size is 49.

**Solution:

Given: Z = 99%, σ = 0.9 and n = 49

Since, SE = Z x σ/√n

= 2.58 x (0.9/√49)

= 2.58 x 0.1285

**SE = 0.33153

**Question 5. Find the sampling error at a 95% confidence level given the standard deviation of the population is 0.3 and the sample size is 81.

**Solution:

Given: Z = 95%, σ = 0.3 and n = 81

Since, SE = Z x σ/√n

= 1.96 x (0.3/√81)

= 1.96 x 0.03333

**SE = 0.0653268

**Question 6. Find the sampling error at a 95% confidence level given the standard deviation of the population is 0.15 and the sample size is 225.

**Solution:

Given: Z = 95%, σ = 0.15 and n = 225

Since, SE = Z x σ/√n

= 1.96 x (0.15/√225)

= 1.96 x 0.01

SE = 0.0196

**Question 7. Find the sampling error at a 90% confidence level given the standard deviation of the population is 0.5 and the sample size is 400.

**Solution:

Given: Z = 90%, σ = 0.5 and n = 400

Since, SE = Z x σ/√n

= 1.645 x (0.5/√400)

= 1.645 x 0.025

SE = 0.041125

**Question 8. Find the sampling error at a 95% confidence level given the standard deviation of the population is 0.4 and the sample size is 64.

**Solution:

Given: Z = 95%, σ = 0.4 and n = 64

Since, SE = Z x σ/√n

= 1.96 x (0.4/√64)

= 1.96 x 0.05

SE = 0.098

**Question 9. Find the sampling error at a 99% confidence level given the standard deviation of the population is 0.35 and the sample size is 121.

**Solution:

Given: Z = 99%, σ = 0.35 and n = 121

Since, SE = Z x σ/√n

= 2.58 x (0.35/√121)

= 2.58 x 0.0314

SE = 0.081012

**Question 10. Find the sampling error at a 90% confidence level given the standard deviation of the population is 0.25 and the sample size is 50.

**Solution:

Given: Z = 90%, σ = 0.25 and n = 50

Since, SE = Z x σ/√n

= 1.645 x (0.25/√50)

= 1.645 x 0.0354

SE = 0.058227

Practice Questions - Sampling Error Formula

**1. A survey estimates the mean height of students in a school to be 160 cm with a standard deviation of 12 cm. If the sample size is 100 students, calculate the sampling error at a 95% confidence level.

**2. In a poll of 400 voters, the proportion of people who favor a new policy is 0.45. Calculate the sampling error for the proportion at a 90% confidence level.

**3. A sample of 250 households reports an average monthly electricity bill of 120withastandarddeviationof120 with a standard deviation of 120withastandarddeviationof15. Determine the sampling error at a 99% confidence level.

**4. A researcher surveys 50 students to find the average time spent on homework per week. The mean time reported is 6 hours with a standard deviation of 1.5 hours. Calculate the sampling error at a 95% confidence level.

**5. In a study, the mean weight of 200 apples is found to be 150 grams with a standard deviation of 20 grams. Find the sampling error at a 95% confidence level.

**6. A random sample of 500 people indicates that 60% of them prefer online shopping. Calculate the sampling error for the proportion at a 95% confidence level.

**7. The mean annual salary of a sample of 80 teachers is 50,000withastandarddeviationof50,000 with a standard deviation of 50,000withastandarddeviationof5,000. Determine the sampling error at a 90% confidence level.

**8. In a survey, a sample of 150 customers reports a mean satisfaction score of 4.2 out of 5 with a standard deviation of 0.8. Calculate the sampling error at a 95% confidence level.

**9. A study finds that the average lifespan of 30 electronic devices is 5 years with a standard deviation of 1 year. Determine the sampling error at a 99% confidence level.

**10. A sample of 120 students shows that the average number of books read per year is 10 with a standard deviation of 3 books. Calculate the sampling error at a 95% confidence level.