Measures of Central Tendency and Spread

A set of vocabulary flashcards covering the definitions, symbols, and classifications of measures of central tendency such as mean, median, and mode for both ungrouped and grouped data.

Measure of Central Tendency

A single value that attempts to describe a set of data by identifying the central position within that set of data, sometimes called a measure of central location or summary statistics.

Arithmetic Mean

The most common measure of central tendency, calculated by taking the sum of all values divided by the total number of values.

$$\mu$$

The symbol, pronounced as $\text{mew}$, used to represent the mean of a population.

$$\bar{X}$$

The symbol, pronounced as $\text{X-bar}$, used to represent the mean of a sample.

Weighted Mean

A measure denoted by the symbol $\bar{x}_w$ that considers the proper weights assigned to the observed values according to their relative importance.

Grouped Data

Data that are arranged in a frequency distribution, often used when the number of items is too large to analyze individually.

Midpoint ($M$)

For grouped data, the value determined for each class interval using the formula $M = \frac{LL+UL}{2}$.

Median ($Mdn$)

The score-point which divides a ranked distribution into two equal parts; it is the value below which lies $50\%$ of the data.

Median for Even Data

When the number of scores ($n$) is even, the median is calculated as the average of the two middle values.

Mode ($Mo$)

The simplest measure of central tendency, identified by locating the score or item value which occurs most frequently in a distribution.

Unimodal

A distribution that contains only one mode.

Multimodal

A distribution that contains two or more modes.

Bimodal

A distribution that is characterized by having exactly two modes.

Trimodal

A distribution that is characterized by having exactly three modes.

Modal Class

The specific class interval in a frequency distribution that has the highest frequency.

$$LTCB$$

The Lower True Class Boundary, often calculated as $LL - 0.5$ for the purpose of computing the median or mode of grouped data.

$$cf <$$

The cumulative frequency less than, which is used in steps to determine the location of the median class in grouped data.