Measures of Central Tendency of Ungrouped Data

Practice flashcards covering definitions, formulas, and distribution shapes for Measures of Central Tendency as presented in the Grade 8 Quarter 1 lecture notes.

Ungrouped Data

Raw data collected in its actual form, such as individual shoe sizes, ages, or the number of absences of students.

Grouped Data

Raw information that has been organized, categorized, and bundled into distinct intervals or "classes" rather than being kept as a list of individual numbers.

Measures of Central Tendency

A single value that attempts to describe a set of data by identifying the central position within that set of data; also called measures of central location.

Mean

The sum of the data values divided by the number of values; it is also referred to as the arithmetic mean and acts as the balance point of a distribution.

Extreme Value (Outlier)

A number that is significantly greater or significantly less than most of the other numbers in a distribution; it greatly affects the mean.

Mean Formula (Ungrouped Data)

$\bar{x} = \frac{\Sigma x}{N}$ where $\bar{x}$ is the mean, $\Sigma x$ is the sum of all values, and $N$ is the number of values.

$\Sigma$ (Sigma)

A Greek letter used to indicate summation.

Median

The middle or central value of an ordered distribution; also known as the halfway marker, it splits data perfectly into two equal halves (50% above, 50% below).

Median Calculation (Odd Number of Values)

The median value identified as the $\frac{n + 1}{2}th$ term after arranging the data in increasing or decreasing order.

Median Calculation (Even Number of Values)

The average of the two middle values in a data set that has been ordered.

Mode

The most frequent value in a set of data, also known as the peak popularity.

Unimodal Mode

A collection of data or numbers that contains exactly one mode.

Bimodal Mode

A set of data including two modes, indicating there are two data values that possess the highest frequencies.

Trimodal Mode

A collection of data including three modes, meaning three data values hold the highest frequencies.

Multimodal Mode

A set of data including four or more than four modes.

Skewed

A dataset that is unbalanced rather than perfectly symmetrical like a bell curve, characterized by values stretched out further on one side than the other.

Symmetrical Distribution (Normal)

A distribution where the mean, median, and mode are all perfectly identical and located right at the center peak of the curve.

Negatively Skewed (Left-Skewed)

A distribution where the long tail extends toward the lower values on the left and $\text{Mean} < \text{Median} < \text{Mode}$. stage

Positively Skewed (Right-Skewed)

A distribution where the long tail extends toward the higher values on the right and $\text{Mean} > \text{Median} > \text{Mode}$.