Introductory Statistics: Central Tendency and Variability

Vocabulary practice flashcards generated from the introductory statistics lecture notes covering distributions, central tendency measures, and variability calculations.

Ceiling Effect

An effect that occurs when scores cluster at an upper limitation that cannot be exceeded, often producing a negatively skewed distribution.

Floor Effect

An effect that occurs when scores cannot go any lower than the lowest possible score or floor, often producing a positively skewed distribution.

Symmetrical Distribution

A balanced distribution shape where both sides are mirror images of each other, typical of a normal distribution where the mean, median, and mode are all equal.

Positively Skewed Distribution

A distribution where one side is more spread out, forming a tail that points toward the higher end of the scale.

Negatively Skewed Distribution

A distribution where the tail points toward the lower end of the scale due to scores clustering near high limitations.

Unimodal Distribution

A distribution having only one mode or single peak frequency.

Bimodal Distribution

A distribution having two distinct modes or peak frequencies.

Multimodal Distribution

A distribution having several peak frequencies where more than two scores occur with the same highest frequency.

Rectangular Distribution

A distribution where the frequency of all scores or variables across the distribution is pretty much the same.

Leptokurtic

A distribution curve that is tall and peaked because scores are clustered closely together around the central mean.

Mesokurtic

A standard normal distribution curve representing a moderate middle peak.

Platykurtic

A distribution curve that is very broad and flat due to high variability among the scores.

Parameter

A numerical value that describes a population, represented by Greek letter symbols such as $\text{mu}$ ($\frac{}{}$) or $\text{sigma}$ ($\frac{}{}$).

Statistic

A numerical value that describes a sample, represented by English letter symbols such as $m$ or $s$.

Percentile Rank

A measure indicating a score's position relative to the rest of the distribution based on the percentage or number of scores that fall strictly below it.

Percentage

A simple calculation of an individual score relative to a total value out of $100$.

Mean

The average score in a distribution that measures distance, balancing the exact distances of scores above and below it so that $\text{sum}(x - m) = 0$.

Median

The middle score that divides a rank-ordered distribution into two equal halves by total number of scores, corresponding to the $50\text{th}$ percentile.

Mode

The single score or variable value that occurs most frequently within a dataset.

Deviation Score

The distance and direction of an individual score $x$ from its mean, calculated as $x - m$ for a sample or $x - \text{mu}$ for a population.

Sum of Squares (SS)

The sum of the squared deviation scores, expressed as $\text{sum}(x - m)^2$ or $\text{sum}(x - \text{mu})^2$, which eliminates negative values.

Variance

The average squared deviation of scores around the mean, calculated by dividing the sum of squares by the total number of scores $N$.

Standard Deviation

The square root of the variance, representing the average distance that scores deviate around the mean.

Range

A crude measure of total spread calculated as the upper real limit of the highest score minus the lower real limit of the lowest score.