MathematicsChapter 12: Basic Statistics
Quartiles, Deciles, Percentiles
Quartiles split data into four equal counts.
Learning objectives
- 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.
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% scored below that value. Above Q3 is about 25% of the data.
Mathematical form
IQR = 90 - 40 = 50
D1 = lowest 10
D5 = median). Percentile Pk has k
Q1=40
Where / symbols
- 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'.
Overview
Cuts of the ordered list:
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.
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'.
Examples D1 = 10% below · P70 = 70% below · D5 = median
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.
Worked example
- 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
In simple words
Percentile is not the percentage score on a test. It is the position in the class distribution.
Key points
- Q1 Q2 Q3
- Pk : k% below
- middle 50% = IQR
- percent below
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Quartiles, Deciles, Percentiles
Sticky Notes · Quick Revision
Core Idea
- 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'.
Worked Method
- 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 Misconception
- Percentile is not the percentage score on a test. It is the position in the class distribution.
FBISE Exam Check
- Percentile is not the percentage score on a test. It is the position in the class distribution.
60-second revision
- 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
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