Measures of Central Tendency (Statistical Averages):
- Arithmetic Mean ($\bar{X}$), Median (M), Mode (Z) - most important.
- Geometric Mean, Harmonic Mean - sometimes used.
Measures of Dispersion:
- Variance ($\sigma^2$), Standard Deviation ($\sigma$) - most often used.
- Mean Deviation, Range - also used.
- Coefficient of Standard Deviation, Coefficient of Variation - for comparison.
Measures of Asymmetry (Skewness):
- Based on mean & mode, or mean & median.
- Based on quartiles or moments.
Measures of Relationship:
- Karl Pearson’s coefficient of correlation (variables).
- Yule’s coefficient of association (attributes).
- Multiple correlation coefficient, partial correlation coefficient, regression analysis.
Other Measures

Most widely used measure.
Defined as the square root of the average of squares of deviations from the arithmetic mean.
Formula: $\sigma = \sqrt{\frac{\sum f_i (X_i - \bar{X})^2}{N}}$ (where $f_i$ is frequency, $N = \sum f_i$)
Coefficient of Standard Deviation: $\sigma / \bar{X}$ (relative measure for comparison).
Coefficient of Variation (CV): $(\sigma / \bar{X}) \times 100$
Variance: $\sigma^2$ (used in ANOVA).
Advantages:
- Very satisfactory measure of dispersion.
- Amenable to mathematical manipulation (algebraic signs not ignored).
- Less affected by sampling fluctuations.
- Popular in estimation and hypothesis testing.

Symmetrical Distribution: Normal curve, bell-shaped. Mean = Median = Mode. No skewness.
Asymmetrical (Skewed) Distribution: Curve is distorted.
Positive Skewness: Distorted to the right. Tail on the right. Mode < Median < Mean ($Z < M < \bar{X}$).
Negative Skewness: Distorted to the left. Tail on the left. Mean < Median < Mode ($\bar{X} < M < Z$).
Significance: Studies formation of series, indicates curve shape (normal or otherwise).
Measurement: Difference between mean, median, or mode.

Measure of "flat-toppedness" or "peakedness" of a curve.
Mesokurtic: Normal curve (bell-shaped).
Leptokurtic: More peaked than normal curve.
Platykurtic: Flatter than normal curve.
Significance: Crucial for statistical methods as many assume specific distribution curve nature.