Measures of Central Tendency for Ungrouped Data (Grade 8 Review)

Statistics

Branch of mathematics concerned with collecting, organizing, presenting, analyzing, and interpreting data (COPIE).

Data

Facts, numbers, or observations used for analysis and decision-making.

Qualitative Data

Describes qualities or characteristics; cannot be measured numerically. Examples: civil status, skin color.

Quantitative Data

Represents quantities; can be measured or counted. Examples: annual income, age, number of children.

Nominal Data

A subtype of qualitative data with labels that have no inherent order. Example: civil status.

Ordinal Data

A subtype of qualitative data with categories that have an inherent order. Example: satisfaction level (satisfied, neutral, unsatisfied).

Discrete Data

A subtype of quantitative data involving whole-number counts. Example: number of books.

Continuous Data

A subtype of quantitative data involving measured values that may include decimals. Example: temperature or weight.

Ungrouped Data

Raw list of individual values; no class intervals or frequency groupings. Example: 90, 85, 88, 79, 93.

Measures of Central Tendency

A single value that represents the 'center,' 'typical value,' or 'central location' of a dataset.

Mean

The arithmetic average of a dataset, calculated by summing all values and dividing by the number of values (Formula: \bar{x} = \frac{\sum x}{n}).

Median

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

Mode

The value(s) that appear most frequently in a dataset.

Unimodal

A dataset with only one mode.

Bimodal

A dataset with two modes.

Multimodal

A dataset with three or more modes.