Draw histograms for grouped data, and construct ogives (cumulative frequency curves) to find median graphically.
When class intervals are unequal, bar heights must be adjusted (frequency density) to keep the area proportional to frequency, not just the height.
A class interval 0-10 has frequency 20, and another 10-30 has frequency 30. Find the adjusted height for the second interval relative to a standard width of 10.
Width=20, so adjusted height=30×(10/20)=15, matching the standard width scale
Why can't histogram bars simply use raw frequency as height when intervals are unequal?
Because the area of each bar (not just the height) must represent the frequency proportionally, so unequal widths need height adjustment
An ogive is a cumulative frequency curve. The median can be found graphically by locating where the cumulative frequency equals n/2 on the ogive.
A data set has 40 total observations. At what cumulative frequency value would you read off the median from the ogive?
n/2=20, so find where the ogive crosses cumulative frequency 20
Why is the ogive method useful for large or grouped data sets?
Because it allows the median to be estimated visually without needing exact individual data values, using only cumulative frequency
1. A class interval 0-20 has frequency 40. Find the frequency density (using standard width 10).
2. A data set has 60 total observations. At what cumulative frequency would the median be located?
3. What is plotted on the x-axis and y-axis of an ogive?
4. A less-than ogive and a more-than ogive intersect. What does the x-coordinate of their intersection represent?
5. Why must histogram bars have no gaps between them, unlike a bar chart?