Standard Error Solved Examples
Example 1: Find the standard error for the sample data: 1, 2, 3, 4, 5.
Solution:
Mean of Given Data = (1+2+3+4+5)/5
μ = 15/5
μ = 3
Standard Deviation = √((1 – 3)2 + (2 – 3)2 + (3 – 3)2 + (4 – 3)2 + (5 – 3)2)/(5 – 1)
σ = √((4 + 1 + 0 + 1 + 4)/4)
σ = √(10/4)
σ = 1.5
SE = 1.5/√5
SE = 0.67
Example 2: Find the standard error for the sample data: 2, 3, 4, 5, 6.
Solution:
Mean of Given Data = (2+3+4+5+6)/5
μ = 20/5
μ = 4
Standard Deviation(σ) = √((2 – 4)2 + (3 – 4)2 + (4 – 4)2 + (5 – 4)2 + (6 – 4)2)/(5 – 1)
σ = √((4 + 1 + 0 + 1 + 4)/4)
σ = √(10/4)
σ = 1.58
SE = 1.58/√5
SE = 0.706
Example 3: Find the standard error for the sample data: 10, 20, 30, 40, 45.
Solution:
Mean of the given data = (10+20+30+40+45)/5
μ = 145/5
μ = 29
Standard Deviation(σ) = √((10 – 29)2 + (20 – 29)2 + (30 – 29)2 + (40 – 29)2 + (45 – 29)2)/(5 – 1)
σ = √(820/4)
σ = 14.317
SE = 14.317/√6
SE = 5.84
Example 4: Find the standard error for the sample data: 2, 6, 9, 5.
Solution:
Mean of Given Data = (2+6+9+5)/4
μ = 5.5
Standard Deviation = √((2 – 5.5)2 + (6 – 5.5)2 + (9 – 5.5)2 + (5 – 5.5)2)/(4 – 1)
σ = √(25/3)
σ = 2.88
SE = 2.8/√5.5
SE = 1.19
Example 5: Find the standard error for the sample data: 5, 8, 10, 12.
Solution:
Mean of Given Data(μ) = (5+8+10+12)/4
μ = 8.75
Standard Deviation = √((5 – 8.75)2 + (8 – 8.75)2 + (10 – 8.75)2 + (12 – 8.75)2)/(4 – 1)
σ = √(26.75/3)
σ = 2.98
SE = 2.98/√8.75
SE = 1.0074
Standard Error
Standard Error is the measure of the variability of a sample statistic used to estimate the variability of a population. Standard Error is important in dealing with sample statistics, such as sample mean, sample proportion, etc. Sample Error Formula is used to determine the accuracy of a sample that reflects a population. The standard error formula is the discrepancy between the sample mean and the population mean.
In this article, we will learn about, Standard Error, Standard Error Formula, Standard Error of Mean, Standard Error of Estimate, related Examples, and Error in detail.
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