The sum of all values divided by the number of values. It incorporates every data point but is sensitive to extreme outliers (e.g., an unusually high compressive strength reading).

The middle value when the data is sorted in ascending or descending order. If there is an even number of observations, it is the arithmetic average of the two middle values. The median is robust and not heavily influenced by extreme outliers, making it a better measure of center for skewed data (e.g., income, or highly variable soil permeability).

The value that appears most frequently in the data set. A distribution can be unimodal, bimodal (two distinct peaks), or multimodal. It is primarily useful for categorical data (nominal level).

An approximation of the mean for grouped data calculated using the class midpoints and frequencies.

The difference between the maximum and minimum values in the dataset. It is a quick measure of total spread but is highly susceptible to extreme outliers.

The average of the squared differences from the mean. It quantifies the average squared distance of each data point from the center.

The positive square root of the variance. It is expressed in the same units as the original data (e.g., MPa, mm, seconds), making it far easier to interpret practically than variance.

A measure of relative variability. It expresses the standard deviation as a percentage of the mean, allowing for the comparison of dispersion across datasets with different units or vastly different means.

If the data distribution is approximately bell-shaped (normal):

• Approximately 68% of the data falls within one standard deviation of the mean ($\bar{x} \pm 1s$).
• Approximately 95% of the data falls within two standard deviations ($\bar{x} \pm 2s$).
• Approximately 99.7% of the data falls within three standard deviations ($\bar{x} \pm 3s$).

For any set of data (regardless of the shape of the distribution), the proportion of values that lie within $k$ standard deviations of the mean is at least $1 - \frac{1}{k^2}$, where $k > 1$.

• For $k=2$: At least 75% of the data falls within $\bar{x} \pm 2s$.
• For $k=3$: At least 88.9% of the data falls within $\bar{x} \pm 3s$.

Values that divide a sorted dataset into 100 equal parts. The $k^{\text{th}}$ percentile ($P_k$) is a value such that at least $k\%$ of the observations are less than or equal to this value, and $(100-k)\%$ are greater.

Values that divide the sorted data into four equal parts. They form the basis of the Five-Number Summary (Min, $Q_1$, Median, $Q_3$, Max) and the Box Plot visualization.

• $Q_1$ (First Quartile): 25th percentile ($P_{25}$)
• $Q_2$ (Second Quartile): 50th percentile (Median, $P_{50}$)
• $Q_3$ (Third Quartile): 75th percentile ($P_{75}$)

The range of the middle 50% of the sorted data. It is a robust measure of variability.

A measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.

• Positive Skew (Right-Skewed): The right tail is longer or fatter; the mass of the distribution is concentrated on the left. The Mean is typically greater than the Median.
• Negative Skew (Left-Skewed): The left tail is longer or fatter; the mass of the distribution is concentrated on the right. The Mean is typically less than the Median.
• Zero Skew: The distribution is perfectly symmetric (e.g., normal distribution). Mean equals Median.

A measure of the "tailedness" (heavy or light tails) of the probability distribution. It describes how much of the data is clustered in the extreme tails versus the center, relative to a normal distribution.

• Leptokurtic (High Kurtosis, $>3$): Heavy tails and a sharper, higher peak compared to a normal distribution. Indicates a higher propensity for extreme outliers (critical in risk assessment for extreme loads).
• Platykurtic (Low Kurtosis, $<3$): Light tails and a flatter peak. Fewer extreme outliers.
• Mesokurtic (Kurtosis $\approx 3$): The kurtosis of a standard normal distribution.