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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.
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Box-and-whisker Plots
What is it?
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.
In simple words
- 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
Important terms
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.
What you should learn
- 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.
Examples
- IQR=640 in that example
- Median line inside
- Not the mean unless they coincide
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.
Recommended for Class 10
Full school-level explanation
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.
Five-number picture:
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.
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.
Remember
- IQR from the box
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.
Remember
- summary, not raw list
Examples
- Two boxes: compare medians
- Not Pearson r by itself
- Not cumulative frequency
Remember
- box = Q1 to Q3
- line = median
- 640
- median line
- IQR from the box
- summary, not raw list
- box = Q1 to Q3
- line = median
How the ideas connect
Worked: min=50, Q1=160, median=300, Q3=800, max=1000. Find IQR. IQR = Q3 - Q1 IQR = 800 - 160 IQR = 640
Deeper understanding
Go beyond memorising Box-and-whisker Plots. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked: min=50, Q1=160, median=300, Q3=800, max=1000. Find IQR. IQR = Q3 - Q1 IQR = 800 - 160 IQR = 640
Common mistakes
Exam focus
Core Idea
READING THE BOX
WHAT IT IS NOT
Worked Method
Exam focus
Quick revision
- box = Q1 to Q3
- line = median
- 640
- median line
- 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 b
- READING THE BOX: Min=50, Q1=160, median=300, Q3=800, max=1000: IQR=800-160=640. A long right box/whisker suggests a h
The line in the box is the median, not Q1 and not the mean.
For long answers on Box-and-whisker Plots: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- box = Q1 to Q3
- line = median
- 640
- median line
Important formulas
- box = Q1 to Q3
- line = median
- 640
Common exam traps
- The line in the box is the median, not Q1 and not the mean.
- Not the mean unless they coincide
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
The line in the box is the median, not Q1 and not the mean.
- Mistake
Not the mean unless they coincide
- Mistake
Not Pearson r by itself
- Mistake
Not cumulative frequency
- Mistake
The line in the box is the median, not Q1 and not the mean.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
box = Q1 to Q3
line = median
640
median line
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-out
box = Q1 to Q3
- 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-out
- Formula
- box = Q1 to Q3
- Example
- IQR=640 in that example
- Critical warning
- The line in the box is the median, not Q1 and not the mean.
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Exam Practice
Define
Q1. Define Box-and-whisker Plots.
Explain
Q2. Explain: READING THE BOX.
Example
Q3. Give one clear example of Box-and-whisker Plots and say why it fits.
Mistake
Q4. State one common mistake students make about Box-and-whisker Plots.
Exam note
Q5. Write a short exam note on Box-and-whisker Plots: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.