Introduction to Box Plots and Cumulative Frequency
In statistics, we often need to summarize and visualize large sets of data so we can quickly understand patterns, spread, and central tendencies. Two powerful tools for doing this are box plots (also called box-and-whisker diagrams) and cumulative frequency graphs.
These visual representations help us answer questions like:
- What is the "middle" of the data?
- How spread out are the values?
- Are there any unusually high or low values?
- How does one data set compare to another?
Imagine you have the test scores of 200 students. You could list all 200 numbers — but that's overwhelming. A box plot or cumulative frequency graph is like a snapshot of the data: it captures the essential story in a single picture.
Before we dive into constructing these displays, let's make sure we're comfortable with the key statistical measures they rely on.
Key Statistical Measures: Median, Quartiles, and the Five-Number Summary
The middle value of an ordered data set. If there are values, the median is the value at position . For an even number of values, the median is the mean of the two middle values.
The median of the lower half of the data (not including the overall median if is odd). Approximately 25% of the data falls below .
The median of the upper half of the data. Approximately 75% of the data falls below .
The difference between the upper and lower quartiles: . It measures the spread of the middle 50% of the data.
A set of five values that summarize a data set: minimum, , median (), , and maximum.
Finding the five-number summary
Data (already ordered): 3, 5, 7, 8, 12, 14, 15, 18, 21
- Minimum = 3
- Maximum = 21
- Median (): There are 9 values, so the median is the 5th value = 12
- Lower half: 3, 5, 7, 8 →
- Upper half: 14, 15, 18, 21 →
- IQR =
13 more sections in this topic
Pick this up in your Library: it holds the whole topic, notes, cheatsheet and questions.