MMW Module 10

Measures of Central Tendency

A typical value of a set of data or observations where values tend to cluster, with the three major types being the mean, median, and mode.

Mean ($\bar{x}$)

The most commonly used "average," calculated as the sum of all given values in a distribution divided by the total number of observations ($n$).

Median ($md$)

The middle value in a distribution when data is arranged in ascending or descending order.

Mode ($mo$)

The simplest measure of central tendency, defined as the score or item that occurs most frequently in a dataset.

Mode Classifications

Classifications of mode based on frequency count: Unimodal (1 mode), Bimodal (2 modes), Trimodal (3 modes), Multimodal (many modes), or No Mode (no score repeats).

Unweighted Mean Formula (Ungrouped Data)

The formula used to calculate the simple average of ungrouped data: $\bar{x} = \frac{\sum x}{n}$.

Repeated Values Mean Formula (Ungrouped Data)

The mean formula used when ungrouped values repeat with known frequencies: $\bar{x} = \frac{\sum fx}{n}$, where $fx$ is the product of each score ($x$) and its frequency ($f$).

Weighted Mean Formula ($\bar{x}_w$)

The mean formula used when certain values are assigned specific weights or levels of importance (e.g., GPA calculation): $\bar{x}_w = \frac{\sum wx}{\sum w}$.

Median of Ungrouped Data (Odd $n$)

When the total number of observations ($n$) is odd, the median is the exact middle value of the ordered dataset.

Median of Ungrouped Data (Even $n$)

When the total number of observations ($n$) is even, the median is the average of the two middle values of the ordered dataset.