The sampling error calculator is used to estimate the potential error or deviation between a sample statistic and the true population parameter (such as the population mean).

Sampling error occurs because the sample may not perfectly represent the entire population, leading to inherent variability in the data.

The sampling error calculator requires the following inputs:

• Sample Size: The number of observations or data points in the sample.
• Population Standard Deviation: The known or estimated standard deviation of the population.
• Confidence Level: The desired level of confidence, typically 90%, 95%, or 99%.

Sampling Error Calculation Chart

Sampling Error Formula

The formula for calculating the sampling error is:

Sampling Error = Z * (Population Standard Deviation / √Sample Size)

Where:

Z: The z-score corresponding to the desired confidence level (e.g., 1.65 for 90%, 1.96 for 95%, 2.58 for 99%)

Population Standard Deviation: The known or estimated standard deviation of the population

Sample Size: The number of observations or data points in the sample

Example

Let’s use the example where the researcher wants to estimate the mean height of all students in a university.

Given:

• Sample Size: 50 students
• Population Standard Deviation: 3 inches
• Confidence Level: 95%

To calculate the sampling error, we need to find the corresponding z-score for a 95% confidence level, which is 1.96.

Plugging the values into the formula:

Sampling Error = Z (Population Standard Deviation / √Sample Size)
Sampling Error = 1.96 (3 / √50)
Sampling Error = 0.84 inches

This means that the true population mean height is likely to be within 68 ± 0.84 inches, or between 67.16 inches and 68.84 inches, with a 95% confidence level.

The sampling error of 0.84 inches represents the potential deviation or margin of error in the estimate of the population mean, due to the inherent variability in the sample data and the fact that the sample may not perfectly represent the entire population.

How Do You Calculate Sampling Error?

To calculate the sampling error, you can follow these steps:

1. Choose the desired level of confidence, typically 90%, 95%, or 99%.
2. Find the corresponding z-score for the chosen confidence level. For example, the z-score for a 95% confidence level is 1.96.
3. Obtain the following information:
   • Sample Size (n)
   • Population Standard Deviation (σ)
4. Input the values into the sampling error formula: Sampling Error = Z * (Population Standard Deviation / √Sample Size) Where:
   • Z: The z-score corresponding to the desired confidence level
   • Population Standard Deviation: The known or estimated standard deviation of the population
   • Sample Size: The number of observations or data points in the sample

Suppose a market research firm wants to estimate the average monthly spending of all customers in a particular region.

They take a random sample of 75 customers and find the sample mean monthly spending to be $250, with a known population standard deviation of $50.

The firm wants to calculate the sampling error at a 90% confidence level.

Confidence Level: 90%

Z-score: For a 90% confidence level, the z-score is 1.65.

Sample Size: 75 customers

Population Standard Deviation: $50

Plugging the values into the sampling error formula:

Sampling Error = Z (Population Standard Deviation / √Sample Size)
Sampling Error = 1.65 ($50 / √75)
Sampling Error = $12.03

This means that the true population mean monthly spending is likely to be within $250 ± $12.03, or between $237.97 and $262.03, with a 90% confidence level.

The sampling error of $12.03 represents the potential deviation or margin of error in the estimate of the population mean, due to the inherent variability in the sample data and the fact that the sample may not perfectly represent the entire population.