Statistics
Measures of Central Tendency
1. Mean (Average)
- Formula: Mean = Sum of observations / Number of observations
- Symbol: x̄ (x-bar) or μ (mu)
- Affected by extreme values
2. Median
- Definition: Middle value when data is arranged in order
- Odd n: Median = (n+1)/2 th term
- Even n: Median = Average of n/2 th and (n/2 + 1) th terms
- Not affected by extreme values
3. Mode
- Definition: Most frequently occurring value
- Data can have no mode, one mode, or multiple modes
- Best for categorical data
Relationship
- Empirical Formula: Mode = 3(Median) - 2(Mean)
- For symmetric distribution: Mean = Median = Mode
Measures of Dispersion
1. Range
- Formula: Range = Highest value - Lowest value
- Simplest measure of spread
2. Variance (σ²)
- Formula: σ² = Σ(x - x̄)² / n
- Average of squared deviations from mean
3. Standard Deviation (σ)
- Formula: σ = √Variance
- Most commonly used measure of dispersion
- Same unit as original data
Data Representation
- Bar Graph: For categorical data
- Histogram: For continuous data
- Pie Chart: For showing proportions
- Line Graph: For showing trends over time
Quick Tips
- Arrange data in ascending order for median
- Use mean for normally distributed data
- Use median when data has outliers
- Mode is useful for categorical data
- Standard deviation shows data spread around mean