# 3. Frequency Distributions

## c. calculate and interpret relative frequencies and cumulative relative frequencies, given a frequency distribution;

## d. describe the properties of a data set presented as a histogram or a frequency polygon;

What is an interval (or a class) and what are its two characteristics?

An interval is a set of values within which an observation falls. An interval is defined by

- Each interval has an upper limit and a lower limit

- Intervals are all-inclusive and non-overlapping

What is a frequency distribution and what are its characteristics?

A frequency distribution is a tabular display of data organized into non-overlapping intervals.

- The range is unique, each value (observation) will fall into only one interval

- Total number of intervals will incorporate the entire population

What are the three different types of frequency distributions?

- Absolute frequency - the actual number of observations in an interval

- Relative frequency - divide the absolute frequency by the total number of observations

- Cumulative absolute/relative frequency - sum the frequencies as you move from the first to last interval

What are the rules when setting up classes for frequency distributions?

- Get the highest and lowest number from the distribution

- Create classes (groups) that are mutually exclusive and of equal size

- Assign each observation to its appropriate class

What is the difference between discrete and continuous data?

- Discrete data is data in a data set with a smaller number of unique values, like number of children, or number of shares compromising an index

- Continuous data is data that can be measured. It is on a continuous scale like height and time. Often has lots of decimal places.

What are the two ways to graphically represent continuous data?

1. Histograms - bar chart showing distribution of groupings of data

2. Frequency polygons - area chart showing percent of data under line

How do you get the relative frequency of a class?

Divide the number of occurrences in the class by the total observations. "The percentage of total observations falling within each interval"

##### Source:

- CFA