Statistics: Central Tendency, Frequency, and Distributions

Flashcards covering concepts of central tendency, frequency distributions, and related statistical notations and graphs.

Measures of Central Tendency

Indicates where the center of a distribution tends to be located, including mean, median, and mode.

The Mode

The most frequently occurring score in a data set, often used with nominal data.

Unimodal Distribution

A distribution with one hump, used when classifying categories.

Bimodal Distribution

A distribution with two scores that are tied for the most frequently occurring score, appearing as two distinct humps on a graph.

The Median

The score at the 50th percentile, summarizing ordinal or highly skewed interval or ratio scores.

The Mean

The average of all the scores, calculated by adding all scores and dividing by the total number of scores (N), often used with interval or ratio data.

Sigma (
∑
)

A symbol meaning 'sum up'.

N (statistical notation)

The total number of scores in a study or data set.

Relative Frequency (rel. f)

The proportion of time a score occurs, calculated as its simple frequency (f) divided by the total number of scores (N).

Cumulative Frequency (cf)

The frequency of all scores at or below a particular score, found by adding simple frequencies for all scores below the score plus the score's own frequency.

Percentile

The percent of all scores in the data that are at or below a particular score, calculated using its cumulative frequency (cf) divided by N, then multiplied by 100.

Grouped Frequency Distributions

A type of distribution where scores are combined to form small groups, and the total frequency, relative frequency, cumulative frequency, and percentile are reported for each group.

Deviation

A score's distance separating it from the mean, calculated as the raw score (X) minus the mean (X̄).

Frequency (f)

The number of times a score occurs within a data set.

Distribution (data)

The general name for any organized set of data.

Simple Frequency Distribution

A display showing the number of times each distinct score occurs in a set of data.

Frequency Distribution Graph

A visual representation showing scores on the X-axis and their frequency on the Y-axis.

Simple Frequency Bar Graph

A graph used for nominal and ordinal data, displaying frequencies with separate bars.

Histogram

A graph used for a small range of different interval or ratio scores, displaying frequencies with contiguous bars.

Frequency Polygon

A graph used for a large number of different scores, displaying frequencies with connected dots above each score.

Normal Distribution

A bell-shaped curve that is symmetrical, also known as the normal curve, where most data points cluster around the mean.

Tails of Distribution

The far left and right portions of a normal curve, containing low-frequency extreme scores.

Skewed Distributions

Distributions that are not symmetrical, having only one pronounced tail extending more to one side than the other.

Negative Skewed Distribution

A skewed distribution containing a tail of extremely low scores that have low frequency, pulling the mean to the left.

Positive Skewed Distribution

A skewed distribution containing a tail of extreme high scores that have low frequency, pulling the mean to the right.

Rectangular Distribution

A symmetrical distribution shaped like a rectangle, where all scores have approximately the same frequency.