SL 4.2—Histograms, CF graphs, box plots

Before we can draw any graphs, we need to organise raw data into a frequency distribution , a structured table that groups data and counts how often values occur.

For discrete data (countable values like number of siblings), the table lists:

• Each possible value or category
• Its frequency (count)
• Its relative frequency (frequency ÷ total)

For continuous data (measured values like height or time), we group values into class intervals:

• Each interval covers a range of values
• Frequencies count how many observations fall within each interval

Class Interval: A range of values used to group continuous data in a frequency table, written as an inequality such as $a\le x<b$, where $a$ is the lower boundary and $b$ is the upper boundary.

Relative Frequency: The proportion of the total observations that fall within a given class, calculated as: $\text{Relative Frequency}=\frac{\text{frequency}}{\text{total frequency}}$

A histogram is the standard graph for displaying the frequency distribution of continuous data. It looks like a bar chart, but with one crucial difference: the bars are adjacent (no gaps), because the data is continuous.

Histogram: A graphical representation of a frequency distribution for continuous data, consisting of adjacent rectangles whose areas are proportional to the frequencies of their corresponding class intervals.

Key features of a histogram:

• The x-axis shows the variable's values, with class interval boundaries marked
• The y-axis shows frequency (for equal class widths, this is also proportional to area)
• Each bar spans one class interval
• Bar heights represent the frequency of that interval
• No gaps between bars , this reflects that the data is continuous