Statistics: Frequency Distributions & Graphs

Definitions

Raw Data

Data collected in original form.

Frequency

The number of times a certain value or class of values occurs.

Frequency Distribution

The organization of raw data in table form with classes and frequencies.

Categorical Frequency Distribution

A frequency distribution in which the data is only nominal or ordinal.

Ungrouped Frequency Distribution

A frequency distribution of numerical data. The raw data is not grouped.

Grouped Frequency Distribution

A frequency distribution where several numbers are grouped into one class.

Class Limits

Separate one class in a grouped frequency distribution from another. The limits could actually appear in the data and have gaps between the upper limit of one class and the lower limit of the next.

Class Boundaries

Separate one class in a grouped frequency distribution from another. The boundaries have one more decimal place than the raw data and therefore do not appear in the data. There is no gap between the upper boundary of one class and the lower boundary of the next class. The lower class boundary is found by subtracting 0.5 units from the lower class limit and the upper class boundary is found by adding 0.5 units to the upper class limit.

Class Width

The difference between the upper and lower boundaries of any class. The class width is also the difference between the lower limits of two consecutive classes or the upper limits of two consecutive classes. It is not the difference between the upper and lower limits of the same class.

Class Mark (Midpoint)

The number in the middle of the class. It is found by adding the upper and lower limits and dividing by two. It can also be found by adding the upper and lower boundaries and dividing by two.

Cumulative Frequency

The number of values less than the upper class boundary for the current class. This is a running total of the frequencies.

Relative Frequency

The frequency divided by the total frequency. This gives the percent of values falling in that class.

Cumulative Relative Frequency (Relative Cumulative Frequency)

The running total of the relative frequencies or the cumulative frequency divided by the total frequency. Gives the percent of the values which are less than the upper class boundary.

Histogram

A graph which displays the data by using vertical bars of various heights to represent frequencies. The horizontal axis can be either the class boundaries, the class marks, or the class limits.

Frequency Polygon

A line graph. The frequency is placed along the vertical axis and the class midpoints are placed along the horizontal axis. These points are connected with lines.

Ogive

A frequency polygon of the cumulative frequency or the relative cumulative frequency. The vertical axis the cumulative frequency or relative cumulative frequency. The horizontal axis is the class boundaries. The graph always starts at zero at the lowest class boundary and will end up at the total frequency (for a cumulative frequency) or 1.00 (for a relative cumulative frequency).

Pareto Chart

A bar graph for qualitative data with the bars arranged according to frequency.

Pie Chart

Graphical depiction of data as slices of a pie. The frequency determines the size of the slice. The number of degrees in any slice is the relative frequency times 360 degrees.

Pictograph

A graph that uses pictures to represent data.

Stem and Leaf Plot

A data plot which uses part of the data value as the stem and the rest of the data value (the leaf) to form groups or classes. This is very useful for sorting data quickly.