Presentation of Data: Frequency Distributions
Frequency distributions provide a structured way to present both discrete and continuous data in tabular form.
Discrete Data
For discrete data, a frequency distribution table typically includes:
- Possible values or categories of the variable
- Frequency (count) of each value or category
- Relative frequency (proportion of total)
Continuous Data
For continuous data, we typically use class intervals:
- Class intervals (ranges of values)
- Frequency of observations in each interval
- Relative frequency of each interval
In the IB Math AA SL course, class intervals are given as inequalities without gaps. For example, the first interval in the height example would be written as $100 \leq h < 110$.
Histograms
Histograms are graphical representations of frequency distributions for continuous data. They consist of adjacent rectangles with areas proportional to the frequencies of the class intervals they represent.
Frequency Histograms with Equal Class Intervals
In a frequency histogram:
- The x-axis represents the variable's values (class intervals)
- The y-axis represents the frequency
- Each bar's height corresponds to the frequency of its class interval
- Bars are adjacent, with no gaps between them
Cumulative Frequency
Cumulative frequency (CF) represents the running total of frequencies up to each class interval. It's particularly useful for finding median, quartiles, and percentiles.
Cumulative Frequency Graphs
A cumulative frequency graph, also known as an ogive, is created by:
- Calculating the cumulative frequencies
- Plotting these against the upper boundaries of each class interval
- Connecting the points with a smooth curve
Using CF Graphs for Statistical Measures
CF graphs are powerful tools for finding various statistical measures:
