Chapter 2: Frequency Distributions

Vocabulary flashcards covering key concepts, formulas, graph types, and distribution shapes from Chapter 2 on Frequency Distributions.

Frequency Distribution

An organized tabulation showing the number of individuals located in each category of a measurement scale.

$$\Sigma fX$$

The calculation used to obtain the sum of scores by multiplying each score ($X$) by its frequency ($f$) and then adding the products.

Proportions

Also called relative frequency, it describes the fraction of the total group associated with each score and is calculated using the formula $p = \frac{f}{N}$.

Percentage

A relative measure obtained by converting a proportion using the formula $\text{Percentage} = p \times 100$.

Grouped Frequency Distribution Table

A frequency distribution table created by grouping individual scores into class intervals when there are many different scores.

Abscissa

The horizontal axis, or $X$-axis, of a frequency distribution graph.

Ordinate

The vertical axis, or $Y$-axis, of a frequency distribution graph.

Histogram

A frequency distribution graph for interval and ratio data that uses touching bars to represent frequencies, with categories placed on the $X$-axis and bar height representing frequency.

Polygon

A frequency distribution graph for interval and ratio data that uses dots connected by continuous lines, with dots placed above each score or interval midpoint to represent frequency.

Modified Histogram

A graph that uses stacks of blocks to display frequency, where each block represents one individual and does not require a vertical frequency scale.

Bar Graph

A frequency distribution graph used for nominal and ordinal data, characterized by spaces between bars to show distinct categories.

Relative Frequencies

Frequencies used in population distribution graphs that show values in relation to the total number rather than exact absolute numbers.

Smooth Curves

Curved lines used for numerical scores measured on interval or ratio scales in large populations to replace the jagged shapes of histograms and polygons.

Symmetrical Distribution

A distribution shape in which one side of the distribution is approximately a mirror image of the other.

Skewed Distribution

A distribution shape where scores tend to pile up toward one end and gradually taper toward the other end.

Tail

The section of a distribution where scores taper off toward one end.

Positive Skew

A skewed distribution where the tail points toward the right or positive direction.

Negative Skew

A skewed distribution where the tail points toward the left or negative direction.

Percentile Rank

The percentage of individuals in a distribution with scores at or below a particular value.

Cumulative Frequency

The total number of individuals who have scores at or below a particular score, calculated by adding frequencies from the lowest score upward.

Cumulative Percentage

The percentage of individuals located at or below each score category.

Real Limits

The boundaries between scores on a continuous number line located halfway between two adjacent scores, calculated as $\text{Real Limits} = X \pm \frac{1}{2}(\text{unit of measurement})$.

Interpolation

A mathematical process used to estimate intermediate values not directly reported in a table, based on the assumption of a constant rate of change across an interval.

Stem-and-Leaf Display

A method of organizing data that separates each score into two parts (stem and leaf), allowing every individual score in the dataset to remain identifiable.

Stem

The first digit or digits of a score in a stem-and-leaf display.

Leaf

The final digit of a score in a stem-and-leaf display.