## Types of Data

**Nominal:** Categorical data without an inherent order.

**Ordinal:** Categorical data with a defined order but not evenly spaced.

**Interval:** Numerical data with equal intervals but no true zero.

**Ratio:** Numerical data with equal intervals and a true zero.

## Measures of Central Tendency

Provide a central value for the data set.

**Mean (Average):** \(\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}\)

**Median:** Middle value when data is ordered.

**Mode:** Most frequently occurring value.

## Measures of Dispersion

Indicate the spread or variability of a data set.

**Range:** Difference between the highest and lowest values.

**Variance:** Average of the squared differences from the Mean.
\(\sigma^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n}\) for a population,
\(s^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}\) for a sample.

**Standard Deviation:** Square root of the variance. \(\sigma\) for population, \(s\) for sample.

**Interquartile Range (IQR):** Difference between the 75th percentile (Q3) and the 25th percentile (Q1).

## Skewness and Kurtosis

**Skewness:** Measure of the asymmetry of the probability distribution.

**Kurtosis:** Measure of the 'tailedness' of the probability distribution.

## Graphical Representations

Visualize data to identify patterns, trends, and outliers.

**Bar Chart:**Represents categorical data with rectangular bars.**Histogram:**Represents the distribution of numerical data.**Box Plot:**Visual representation of the five-number summary (Minimum, Q1, Median, Q3, Maximum).**Scatter Plot:**Shows the relationship between two quantitative variables.

## Z-Scores

Measure of how many standard deviations an element is from the mean.

\(z = \frac{x - \bar{x}}{\sigma}\) where \(x\) is a score from the population, \(\bar{x}\) is the mean of the population, and \(\sigma\) is the standard deviation of the population.

## Correlation

Measure of the strength and direction of a linear relationship between two variables.

\(r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}\)