Measures of Central Tendency

Vocabulary flashcards covering measures of central tendency, formulas, data distribution shapes, and related statistical terminology.

Measures of Central Tendency

A single value used to identify the center of a data set, representing a typical, precise yet simple, and representative value of the distribution.

Statistic

A characteristic or measure obtained by using the data values from a sample.

Parameter

A characteristic or measure obtained by using all the data values from a specific population.

Mean

The arithmetic average found by adding the data values and dividing by the total number of values, symbolized by $\bar{X}$ for a sample and $\mu$ for a population.

Mean for Grouped Data

An approximation of the mean calculated using $\bar{X} = \frac{\Sigma f \cdot X_m}{n}$, where $f$ is the frequency of each class, $X_m$ is the class midpoint, and $n$ is the total number of values.

Median

The midpoint of an ordered data array, symbolized by $MD$, which divides the observations into two equal parts.

Mode

The value or values that occur most frequently in a data set.

Unimodal

Refers to a data set that has only one value occurring with the greatest frequency.

Bimodal

Refers to a data set that has two values occurring with the same greatest frequency.

Multimodal

Refers to a data set that has more than two values occurring with the same greatest frequency.

Modal Class

The class with the largest frequency in a grouped frequency distribution.

Midrange

A rough estimate of the average defined as the sum of the lowest and highest values in the data set divided by $2$, symbolized by $MR = \frac{\text{lowest value} + \text{highest value}}{2}$.

Weighted Mean

A type of mean calculated by multiplying each value $X$ by its corresponding weight $w$ and dividing the sum of the products by the sum of the weights: $\bar{X} = \frac{\Sigma w X}{\Sigma w}$.

Outliers

Extremely high or low data values that significantly affect the mean and midrange.

Positively Skewed Distribution

A distribution where most data values cluster at the lower end (left) and the tail extends to the right; the mean is to the right of the median, and the mode is to the left.

Symmetric Distribution

A distribution in which data values are evenly distributed on both sides of the mean; when unimodal, the mean, median, and mode are equal and located at the center.

Negatively Skewed Distribution

A distribution where most data values cluster at the upper end (right) and the tail extends to the left; the mean is to the left of the median, and the mode is to the right.