CAPS Mathematical Literacy Grade 12: BoxandWhisker Plots Revision Notes
Introduction
Boxandwhisker plots are a type of graphical representation used in statistics to display the distribution of a dataset. They are particularly useful for identifying the spread of the data, detecting outliers, and comparing different sets of data.
Importance
Understanding boxandwhisker plots is important for interpreting data distributions, which is a critical skill in data analysis. They help in visualizing the fivenumber summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. This information is crucial in many realworld applications such as comparing test scores, analyzing financial data, and more.
Key Points

Components of a BoxandWhisker Plot:
 Box: Represents the interquartile range (IQR), which contains 50% of the data.
 Whiskers: Extend from the box to the minimum and maximum values within 1.5 times the IQR from Q1 and Q3.
 Median (Q2): The middle value of the data set, represented by a line inside the box.
 Outliers: Data points outside the whiskers, often shown as dots or asterisks.

FiveNumber Summary:
 Minimum: The smallest data point.
 Q1 (First Quartile): The median of the first half of the dataset.
 Median (Q2): The middle value of the dataset.
 Q3 (Third Quartile): The median of the second half of the dataset.
 Maximum: The largest data point.

Drawing a BoxandWhisker Plot:
 Order the data from least to greatest.
 Identify the fivenumber summary.
 Draw a number line including the range of the dataset.
 Draw a box from Q1 to Q3.
 Mark the median inside the box.
 Extend whiskers from the box to the minimum and maximum values.
 Plot any outliers.
RealWorld Applications
Example Problem:
Given the dataset: 21, 23, 24, 25, 29, 33, 49, draw a boxandwhisker plot.
Solution:
1. Order the data: 21, 23, 24, 25, 29, 33, 49.
2. Fivenumber summary:
– Minimum: 21
– Q1: 23
– Median (Q2): 25
– Q3: 33
– Maximum: 49
3. Draw the plot:
– Draw a box from 23 (Q1) to 33 (Q3).
– Draw a line at 25 (Median).
– Extend whiskers from 21 (Minimum) to 49 (Maximum).
Common Misconceptions and Errors
 Confusing quartiles: Quartiles divide the data into four equal parts, not the dataset into four equal data points.
 Incorrectly identifying outliers: Outliers are points outside 1.5 times the IQR, not just any points far from the mean.
Practice and Review
Practice Questions:
1. Given the dataset [12, 15, 14, 10, 21, 20, 18], draw a boxandwhisker plot.
2. The following are examination results out of 50: [35, 40, 46, 42, 38, 49, 50, 32]. Identify the outliers if any.
Solutions:
Detailed stepbystep solutions and explanations can solidify understanding.
Examination Tips:
– Keywords: “fivenumber summary,” “interquartile range (IQR),” “outliers”
– Efficient Time Management: Start with drawing the number line and identifying the fivenumber summary.
Connections and Extensions
Interdisciplinary Links:
– Economics: Use boxandwhisker plots to compare economic indicators like income distributions.
– Biology: Analyze the spread of biological data such as heights or weights in a population.
Encourage exploring connections to understand the versatility and utility of boxandwhisker plots across different fields.
Summary and Quick Review
 Boxandwhisker plots visualize data distribution, highlighting the spread and outliers.
 Fivenumber summary: Minimum, Q1, Median, Q3, Maximum.
 Useful for comparing multiple data sets and understanding overall data distribution.
Additional Resources
By mastering boxandwhisker plots, students will be better equipped to analyze and interpret data effectively in various academic and realworld scenarios.
For further reading and practice, refer to the CAPS Mathematical Literacy Grade 12 study guide【4:1†source】【4:5†source】.