Standard deviation measures the spread of data around the mean. Standard error of the mean (SEM) estimates the uncertainty of the sample mean. Both are essential for analyzing experimental data and reporting scientific results.

Key Formulas:

• Mean: μ = (Σx) / n
• Sample Variance: s² = Σ(x - μ)² / (n - 1)
• Population Variance: σ² = Σ(x - μ)² / n
• Sample Std Dev: s = sqrt(s²)
• Population Std Dev: σ = sqrt(σ²)
• SEM: s / sqrt(n)

Applications:

• Experimental data analysis
• Reporting scientific results
• Comparing variability between groups