Frequency Distributions and Graphs (Chapter 2)

60 vocabulary flashcards covering key terms and concepts from the frequency distributions chapter.

Frequency distribution

An organized tabulation showing how many individuals occur in each category of a measurement scale.

Score

A single measured value obtained from a participant on a scale.

Scale of measurement

The type of data scale (nominal, ordinal, interval, ratio) that determines how data are categorized and analyzed.

Categories

The distinct values or ranges that make up a measurement scale.

X values

The measurement categories listed in a frequency distribution table.

Frequency (f)

The count of individuals whose score falls in a given category.

Proportion (p)

The fraction of the total sample in a category; p = f/N.

Relative frequency

Another term for proportion; frequency relative to the total.

Percentage (%)

The proportion expressed as a percent: (f/N) × 100.

Frequency distribution table

A table with columns for X values and their frequencies.

Grouped frequency distribution

A distribution that groups scores into class intervals rather than listing all scores.

Class interval

A range of scores forming one category in a grouped table; all intervals have same width.

Range

Difference between the highest and lowest scores.

N (sample size)

Total number of scores in the data.

Sum of scores

The total of all scores, ΣX.

Sum of squared scores

The total of each score squared, ΣX^2.

Real limits

Precise bounds of class intervals when data are continuous (e.g., 39.5 to 40.5).

Apparent limits

The stated lower and upper bounds of a class interval (e.g., 40–49).

Interval width

The size of each class interval (e.g., 5, 10, 2).

Number of intervals

How many class intervals appear in a grouped table.

Midpoint

The center value of a class interval, computed as (low + high)/2.

Histogram

A graph with bars above each category; height equals frequency; bars touch for continuous data.

Polygon

A graph where a dot is placed above each score or interval and connected by lines.

Bar graph

A graph for nominal/ordinal data with spaces between bars.

X-axis

The horizontal axis representing the score categories.

Y-axis

The vertical axis representing frequencies.

Abscissa

Another term for the X-axis.

Ordinate

Another term for the Y-axis.

Normal distribution

A symmetric, bell-shaped distribution with most scores near the center.

Symmetrical distribution

A distribution that is mirror-imaged around the center.

Skewed distribution

An asymmetrical distribution with frequencies tapering toward one end.

Positive skew

Tail toward higher values (right side).

Negative skew

Tail toward lower values (left side).

Tail

The tapering end of a skewed distribution.

Central tendency

The center of a distribution (mean, median, mode) where data cluster.

Variability

How spread out the scores are around the central tendency.

Interval scale

A scale with equal intervals between values and no true zero required.

Ratio scale

A scale with equal intervals and a true zero representing absence.

Nominal scale

Categorical data without inherent order.

Ordinal scale

Categorical data with natural order but unequal intervals.

Proportion column

Column in a frequency distribution table showing the proportion p for each category.

Percentage column

Column showing the percentage values for each category.

Real limits example

Example: a 50–54 interval has real limits 49.5 to 54.5.

Apparent limits example

Example: the 50–59 interval may be shown with apparent limits 50 and 59.

Break in axis

A deliberate gap on a graph to omit ranges; can mislead if not used carefully.

Population distribution

The distribution of scores for an entire population; often shown with relative frequencies or smooth curves.

Continuous variable

A variable that can take on an infinite number of values within a range.

Discrete variable

A variable with distinct, separated values (e.g., integers).

10-interval guideline

Aim for about 10 class intervals when constructing grouped tables.

Simple interval width

Choose interval width that is a simple number (e.g., 2, 5, 10) for ease of use.

Bottom score a multiple of width

The lowest value in the first interval should be a multiple of the interval width.

All intervals equal width

Class intervals should have the same width and cover the range with no gaps or overlaps.

Cover range with no gaps

Class intervals should collectively include every score without omissions or overlaps.

Real vs apparent limits difference

Real limits reflect continuous measurement; apparent limits are the stated interval endpoints.

Sum of frequencies equals N

The total of all frequencies in a distribution equals the sample size N.

X f columns

In a frequency table, X lists category values and f lists their frequencies.

Sum X f (X×f)

An alternative way to compute ΣX by summing each X times its frequency.

Sum of squares ΣX^2

The total of each score squared; used in computing variance and related metrics.

SPSS frequency distribution

A statistical software procedure that outputs a frequency table and graphs.

Purpose of frequency distribution

To simplify data, organize it, and reveal patterns in the scores.