MathematicsChapter 12: Basic Statistics
Box-And-Whisker Plots
A box plot shows min, Q1, median, Q3, max.
Learning objectives
- Explain box-and-whisker plots using the correct definitions, conditions, and notation.
- Apply box = Q1 to Q3, line = median correctly in routine and exam-style questions.
- Show each important step, simplify the result, and check that it satisfies the original conditions.
Definition
A box plot shows min, Q1, median, Q3, max. The box runs from Q1 to Q3 (the IQR). A line inside the box is the median. Whiskers go to the extremes (or to non-outlier fences in a fuller story). It displays spread and skew, not a frequency table.
Mathematical form
IQR = Q3 - Q1
IQR = 800 - 160
IQR = 640
min=50
Where / symbols
- BOX-AND-WHISKER PLOTS
- A box plot shows min, Q1, median, Q3, max. The box runs from Q1 to Q3 (the IQR). A line inside the box is the median. Whiskers go to the extremes (or to non-outlier fences in a fuller story). It displays spread and skew, not a frequency table.
- READING THE BOX
- Min=50, Q1=160, median=300, Q3=800, max=1000: IQR=800-160=640. A long right box/whisker suggests a high-side spread.
- WHAT IT IS NOT
- It does not show every point (that is a scatter or dot plot). It is not an ogive. Comparing two box plots can hint at a shift, not automatically a correlation r.
Relationship
- box = Q1 to Q3
- line = median
Overview
Five-number picture:
Reading the Box
Min=50, Q1=160, median=300, Q3=800, max=1000: IQR=800-160=640. A long right box/whisker suggests a high-side spread.
Examples IQR=640 in that example · Median line inside · Not the mean unless they coincide
What It Is Not
It does not show every point (that is a scatter or dot plot). It is not an ogive. Comparing two box plots can hint at a shift, not automatically a correlation r.
Examples Two boxes: compare medians · Not Pearson r by itself · Not cumulative frequency
WHAT — BOX-AND-WHISKER PLOTS
A box plot shows min, Q1, median, Q3, max. The box runs from Q1 to Q3 (the IQR). A line inside the box is the median. Whiskers go to the extremes (or to non-outlier fences in a fuller story). It displays spread and skew, not a frequency table. The symbols and conditions are part of the mathematics, so include them when stating the rule.
WHY — Why this topic matters
Box-And-Whisker Plots matters because statistics turns raw data into useful information about position, spread, and relationship. Probability describes chance, while graphs and summary measures support fair comparisons.
HOW — How to solve and explain it
Start by identifying what is given and what must be found. Work through READING THE BOX, then WHAT IT IS NOT. Worked: min=50, Q1=160, median=300, Q3=800, max=1000. Find IQR. IQR = Q3 - Q1 IQR = 800 - 160 IQR = 640 Finish by checking signs, restrictions, units, and whether the answer matches the question.
Worked example
- min=50, Q1=160, median=300, Q3=800, max=1000. Find IQR.
- IQR = Q3 - Q1
- IQR = 800 - 160
- IQR = 640
In simple words
The line in the box is the median, not Q1 and not the mean.
Key points
- box = Q1 to Q3
- line = median
- IQR from the box
- summary, not raw list
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Box-And-Whisker Plots
Sticky Notes · Quick Revision
Core Idea
- A box plot shows min, Q1, median, Q3, max. The box runs from Q1 to Q3 (the IQR). A line inside the box is the median. Whiskers go to the extremes (or to non-outlier fences in a fuller story). It displays spread and skew, not a frequency table.
READING THE BOX
- Min=50, Q1=160, median=300, Q3=800, max=1000: IQR=800-160=640. A long right box/whisker suggests a high-side spread.
WHAT IT IS NOT
- It does not show every point (that is a scatter or dot plot). It is not an ogive. Comparing two box plots can hint at a shift, not automatically a correlation r.
Worked Method
- Worked: min=50, Q1=160, median=300, Q3=800, max=1000. Find IQR.
- IQR = Q3 - Q1
- IQR = 800 - 160
- IQR = 640
Common Misconception
- The line in the box is the median, not Q1 and not the mean.
FBISE Exam Check
- The line in the box is the median, not Q1 and not the mean.
60-second revision
- A box plot shows min, Q1, median, Q3, max.
- READING THE BOX: Min=50, Q1=160, median=300, Q3=800, max=1000: IQR=800-160=640.
- WHAT IT IS NOT: It does not show every point (that is a scatter or dot plot).
- Worked-method reminder: IQR = 640
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.