Statistics

Class Width

Finally, the class width for a class in a frequency distribution is found by subtracting the lower (or upper) class limit of one class from the lower (or upper) class limit of the next class

Open-ended Distribution

That is, the class has no specific beginning value or no specific ending value. A frequency distribution with an open-ended class is called an open-ended distribution.

Frequency Polygon

The frequency polygon is a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes. The frequencies are represented by the heights of the points.

Upper Class Limit

The upper class limit represents the largest data value that can be included in the class.

Raw data

When the data are in original form, they are called raw data

Cumulative Frequency Distribution

A cumulative frequency distribution is a distribution that shows the number of data values less than or equal to a specific value (usually an upper boundary).

Frequency Distribution

A frequency distribution is the organization of raw data in table form, using classes and frequencies.

Class Boundaries

Class Boundaries numbers are used to separate the classes so that there are no gaps in the frequency distribution.

Class

Each raw data value is placed into a quantitative or qualitative category called a class

Class Midpoint

The class midpoint Xm is obtained by adding the lower and upper boundaries and dividing by 2, or adding the lower and upper limits and dividing by 2:

Cumulative Frequency

The cumulative frequency is the sum of the frequencies accumulated up to the upper boundary of a class in the distribution.

Frequency

The frequency of a class then is the number of data values contained in a specific class.

Histogram

The histogram is a graph that displays the data by using contiguous vertical bars (unless the frequency of a class is 0) of various heights to represent the frequencies of the classes.

Relative Frequency Graphs

The histogram, the frequency polygon, and the ogive shown previously were constructed by using frequencies in terms of the raw data. These distributions can be converted to distributions using proportions instead of raw data as frequencies. These types of graphs are called relative frequency graphs.

Lower Class Limit

The lower class limit represents the smallest data value that can be included in the class.

Grouped Frequency Distribution

When the range of the data is large, the data must be grouped into classes that are more than one unit in width, in what is called a grouped frequency distribution.

Ungrouped Frequency Distribution

When the range of the data values is relatively small, a frequency distribution can be constructed using single data values for each class. This type of distribution is called an ungrouped frequency distribution

Categorical Frequency Distribution

The categorical frequency distribution is used for data that can be placed in specific categories, such as nominal- or ordinal-level data. For example, data such as political affiliation, religious affiliation, or major field of study would use categorical frequency distributions.

Ogive

The ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution.