STAT C1000 Chapter 2: Frequency Distributions and Graphs

Vocabulary practice flashcards covering terminology, formulas, distribution types, and graph types from STAT C1000 Chapter 2.

Frequency Distribution

A table that shows how a data set is partitioned among all of several categories by listing all of the categories along with the number of data values in each category.

Class

A quantitative or qualitative category within a frequency distribution.

Frequency

The number of times a data value, or category of data values, occurs in a data set.

Relative Frequency

A ratio of a class frequency to the total number of values, typically expressed as a percentage in descriptive statistics.

Categorical Frequency Distribution

A frequency distribution used to organize qualitative (categorical) data.

Ungrouped Frequency Distribution

A frequency distribution used for quantitative data in which each class consists of an individual data value.

Grouped Frequency Distribution

A frequency distribution used for quantitative data in which data values are grouped into class intervals.

Class Limits

The smallest and biggest numbers that belong in each category, which should always have the same number of decimal points as the original data.

Class Boundaries

Numbers used to separate categories so there are no gaps in the frequency distribution, usually written with one more decimal place than the data.

Class Width

The difference between lower (or upper) class limits or boundaries from consecutive classes, calculated as $\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}}$ and rounded up.

Lower Class Boundary

The absolute lowest edge of a class, found by subtracting a value such as $0.5$ or $0.05$ from the lower class limit depending on the decimal precision of the data.

Upper Class Boundary

The absolute upper edge of a class, found by adding a value such as $0.5$ or $0.05$ to the upper class limit depending on the decimal precision of the data.

Class Midpoint

The value in the middle of a class, calculated as $\frac{\text{lower limit} + \text{upper limit}}{2}$.

Cumulative Frequency Distribution

A tabular distribution showing the sum of frequencies for a given class and all previous classes, where class limits are replaced with the phrase 'less than lower-class-boundary'.

Histogram

A graph that displays data using contiguous vertical bars of varying height, where the horizontal axis represents class boundaries and the vertical axis represents frequencies.

Frequency Polygon

A line graph that uses line segments connected to points located directly above class midpoint values, with the horizontal axis labeled with midpoints and vertical axis labeled with class frequencies.

Ogive

A cumulative frequency graph (line graph) depicting cumulative frequencies, where the initial ordered pair is (lowest class boundary, zero) and the final ordered pair is (highest class boundary, total frequency).

Normal Distribution

A distribution where frequencies start low, increase to one or two high frequencies, and then decrease to a low frequency, forming an approximately symmetric 'bell curve'.

Skewed Distribution

A distribution where frequencies start high and go lower or vice versa; characterized as Skewed-Left (more data on the right) or Skewed-Right (more data on the left).

Uniform Distribution

A distribution in which all class frequencies are equal or nearly equal.

Bar Graph

A visual representation for qualitative data using vertical or horizontal bars to display class frequencies or relative frequencies, often drawn with gaps between bars.

Pareto Chart

A specific type of bar graph for qualitative data that arranges bars in descending order according to frequency.

Pie Chart

A circular graph depicting qualitative data as slices, where the angle size of each slice in degrees is found by multiplying its relative frequency percentage by $360^\text{o}$.

Time-series Graph

A graph displaying quantitative data collected at different points in time, with time on the horizontal axis and the observed variable on the vertical axis.

Dotplot

A visual display in which each individual data value is plotted as a point (dot) above a horizontal axis.

Stemplot

An exploratory data analysis graph for quantitative data that separates each value into two parts: a stem (leftmost digits) and a leaf (rightmost digit).

Back-to-back Stem and Leaf plot

A stemplot that uses a single central column of stems with leaves extending outward on both sides to compare two data distributions.