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Quartiles, Deciles, Percentiles
Quartiles split data into four equal counts. Deciles into ten (D1 = lowest 10%, D5 = median). Percentile Pk has k% of observations below it. P70 means 70% scored below that value. Above Q3 is about 25% of the data.
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Quartiles, Deciles, Percentiles
What is it?
Quartiles split data into four equal counts. Deciles into ten (D1 = lowest 10%, D5 = median). Percentile Pk has k% of observations below it. P70 means 70% scored below that value. Above Q3 is about 25% of the data.
In simple words
- Quartiles split data into four equal counts.
- QUARTILES: Q2 is the median.
- DECILES AND PERCENTILES: D1 marks 10% below.
- Worked-method reminder: about 25% score above 90
Important terms
QUARTILES, DECILES, PERCENTILES: Quartiles split data into four equal counts. Deciles into ten (D1 = lowest 10%, D5 = median). Percentile Pk has k% of observations below it. P70 means 70% scored below that value. Above Q3 is about 25% of the data.
QUARTILES: Q2 is the median. IQR is the middle half's spread. If Q3=90, about 25% score above 90. Box plots use these five: min, Q1, median, Q3, max.
DECILES AND PERCENTILES: D1 marks 10% below. P70 is the 70th percentile. They are the same idea as quartiles with different cuts. Do not confuse '70% below' with 'the 70th student only'.
What you should learn
- Explain quartiles, deciles, percentiles using the correct definitions, conditions, and notation.
- Apply Q1 Q2 Q3, Pk : k% below correctly in routine and exam-style questions.
- Show each important step, simplify the result, and check that it satisfies the original conditions.
Examples
- Q2 = median = D5
- Above Q3 ~ 25%
- IQR = Q3-Q1
QUARTILES
Q2 is the median. IQR is the middle half's spread. If Q3=90, about 25% score above 90. Box plots use these five: min, Q1, median, Q3, max.
DECILES AND PERCENTILES
D1 marks 10% below. P70 is the 70th percentile. They are the same idea as quartiles with different cuts. Do not confuse '70% below' with 'the 70th student only'.
Recommended for Class 10
Full school-level explanation
Quartiles split data into four equal counts. Deciles into ten (D1 = lowest 10%, D5 = median). Percentile Pk has k% of observations below it. P70 means 70% scored below that value. Above Q3 is about 25% of the data.
Cuts of the ordered list:
WHAT — QUARTILES, DECILES, PERCENTILES
Quartiles split data into four equal counts. Deciles into ten (D1 = lowest 10%, D5 = median). Percentile Pk has k% of observations below it. P70 means 70% scored below that value. Above Q3 is about 25% of the data. The symbols and conditions are part of the mathematics, so include them when stating the rule.
WHY — Why this topic matters
Quartiles, Deciles, Percentiles 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 QUARTILES, then DECILES AND PERCENTILES. Worked: Q1=40, Q2=70, Q3=90. IQR and % above 90. IQR = 90 - 40 = 50 above Q3 is the top quarter about 25% score above 90 Finish by checking signs, restrictions, units, and whether the answer matches the question.
QUARTILES
Q2 is the median. IQR is the middle half's spread. If Q3=90, about 25% score above 90. Box plots use these five: min, Q1, median, Q3, max.
Remember
- middle 50% = IQR
Examples
- Q2 = median = D5
- Above Q3 ~ 25%
- IQR = Q3-Q1
DECILES AND PERCENTILES
D1 marks 10% below. P70 is the 70th percentile. They are the same idea as quartiles with different cuts. Do not confuse '70% below' with 'the 70th student only'.
Remember
- percent below
Examples
- D1 = 10% below
- P70 = 70% below
- D5 = median
Remember
- Q1 Q2 Q3
- Pk : k% below
- IQR 50, about 25%
- position not test percent
- middle 50% = IQR
- percent below
- Q1 Q2 Q3
- Pk : k% below
How the ideas connect
Worked: Q1=40, Q2=70, Q3=90. IQR and % above 90. IQR = 90 - 40 = 50 above Q3 is the top quarter about 25% score above 90
Deeper understanding
Go beyond memorising Quartiles, Deciles, Percentiles. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked: Q1=40, Q2=70, Q3=90. IQR and % above 90. IQR = 90 - 40 = 50 above Q3 is the top quarter about 25% score above 90
Common mistakes
Exam focus
Core Idea
QUARTILES
DECILES AND PERCENTILES
Worked Method
Exam focus
Quick revision
- Q1 Q2 Q3
- Pk : k% below
- IQR 50, about 25%
- position not test percent
- QUARTILES, DECILES, PERCENTILES: Quartiles split data into four equal counts. Deciles into ten (D1 = lowest 10%, D5 = median). Percen
- QUARTILES: Q2 is the median. IQR is the middle half's spread. If Q3=90, about 25% score above 90. Box plots use
Percentile is not the percentage score on a test. It is the position in the class distribution.
For long answers on Quartiles, Deciles, Percentiles: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Q1 Q2 Q3
- Pk : k% below
- IQR 50, about 25%
- position not test percent
Important formulas
- Q1 Q2 Q3
- Pk : k% below
- IQR 50, about 25%
Common exam traps
- Percentile is not the percentage score on a test. It is the position in the class distribution.
- Do not treat QUARTILES and DECILES AND PERCENTILES as the same step; each has a different purpose.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Percentile is not the percentage score on a test. It is the position in the class distribution.
- Mistake
Do not treat QUARTILES and DECILES AND PERCENTILES as the same step; each has a different purpose.
- Mistake
Do not jump straight to the answer; omitted signs, brackets, restrictions, or construction reasons can change the result.
- Mistake
Percentile is not the percentage score on a test. It is the position in the class distribution.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Q1 Q2 Q3
Pk : k% below
IQR 50, about 25%
position not test percent
Quartiles split data into four equal counts. Deciles into ten (D1 = lowest 10%, D5 = median). Percentile Pk has k% of observations below it. P70 means 70% score
middle 50% = IQR
- Definition
- Quartiles split data into four equal counts. Deciles into ten (D1 = lowest 10%, D5 = median). Percentile Pk has k% of observations below it. P70 means 70% score
- Formula
- middle 50% = IQR
- Example
- Q2 = median = D5
- Critical warning
- Percentile is not the percentage score on a test. It is the position in the class distribution.
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Exam Practice
Define
Q1. Define Quartiles, Deciles, Percentiles.
Explain
Q2. Explain: QUARTILES.
Example
Q3. Give one clear example of Quartiles, Deciles, Percentiles and say why it fits.
Mistake
Q4. State one common mistake students make about Quartiles, Deciles, Percentiles.
Exam note
Q5. Write a short exam note on Quartiles, Deciles, Percentiles: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.