topic 1

Population

All subjects or items of interest; size N.

Sample

A subset drawn from a population; size n.

Parameter

A characteristic of a population.

Statistic

A characteristic of a sample (sample statistic) that estimates a parameter.

Quantitative Variable

Variables with numeric values; a mean can be reported across individuals (e.g., age).

Categorical Variable

Variables with descriptive categories; counts or proportions can be reported (e.g., gender).

Histogram

A graph for single quantitative variables to show the pattern of variability, useful for large data sets, using class intervals (bins) on the horizontal axis and frequencies (counts) on the vertical axis.

Mean

The arithmetic average of a dataset; sum of values divided by the total number of values.

Median

The middle value when data are ordered. If n is odd, it's the middle value; if n is even, it's the mean of the two middle values.

Mode

The most frequent value in a dataset.

Standard Deviation (Sample)

Measures how much data values differ from each other, representing the typical distance of data points from the mean; calculated as s = \sqrt{\frac{\sum(x - \bar{x})^2}{n-1}}.

IQR (Interquartile Range)

The range between the third quartile (Q3) and the first quartile (Q1), calculated as Q3 - Q1. Used to define the middle 50% of the data and identify outliers.

Z-score (Standardized Score)

The number of standard deviations a given value x is above or below the mean; calculated as z = \frac{x - \mu}{\sigma} for population or z = \frac{x - \bar{x}}{s} for sample.