Solved Examples on Margin of Error Formula
Example 1: A random sample of 50 students has average pocket money of 2500 and a standard deviation of 567. Find the margin of error if c = 0.95.
Solution:
Given, n = 50
σ = 567
For c = 0.95 i.e. 95% confidence level, z = 1.96
M.O.E = 1.96 × 567 / √(50)
M.O.E. = 157.16
Example 2: 600 students were surveyed, and it was found that the average CGPA of the students was 8.7, with a population standard deviation of 0.2. Calculate the margin of error for the 90% confidence level.
Solution:
Given, n = 600
σ = 0.2
For confidence level of 90%, z = 1.645
M.O.E = 1.645 × 0.2 / √(600)
M.O.E. = 0.013
Example 3: In a survey, it was found that the average salary of 5000 employees was 350000, with a population standard deviation of 0.3. What is the margin of error at a 99% confidence level?
Solution:
Given, n = 5000
σ = 0.3
For 99% confidence level, z = 2.575
M.O.E = 2.575 × 0.3 / √(5000)
M.O.E. = 0.0109
Example 4: Find the margin of error when a population of 400 people is surveyed.
Solution:
Given, sample size = 400
∴M.O.E. = 1 / √(400)
= 1/20
= 0.05
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Margin of Error Formula
Margin of Error Formula: The margin of error is an important measure in statistics. The degree of error in random sampling surveys is known as the margin of error. It expresses random sampling error in the results of a survey. It depicts the confidence that the researchers should have in the data obtained from the survey. It tells the variance from the actual population in terms of the percentage points.
Example of Margin of Error: A 95% confidence interval with a 4% margin of error indicates that your statistic will, 95% of the time, be within 4% of the true population figure. A wider margin of error in statistics denotes a reduced chance of relying on a survey’s or poll’s findings, meaning that there will be less trust in the results’ ability to accurately reflect a community.
Table of Content
- What is a Margin of Error?
- Margin of Error Meaning
- Importance of Margin of Error
- Margin of Error Calculation
- Margin of Error Formula
- How to Calculate Margin of Error?
- Solved Examples on Margin of Error Formula
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