CEUET Mathematics — Statistics & ProbabilityCheat Sheet
Cheat sheet for CEUET Mathematics — Statistics & Probability. Compact, printable, and organised around the concepts Centro Escolar University tests most frequently in the CEUET 2026. Perfect for the week before exam day.
Exam context
Centro Escolar University runs the Centro Escolar University Entrance Test on Q3–Q4 2026. Its Mathematics section sits under a "Core" weighting, and Statistics & Probability is the 8th chapter in the 9-chapter CEUET Mathematics rotation. The CEUET passing mark is Competitive overall score, and the most recent 2026 paper drew about a meaningful share of questions from Mathematics.
Statistics & Probability - Cheat sheet
Your last-minute revision companion for mastering Statistics & Probability concepts, formulas, and problem-solving techniques for UPCAT and other CETs.
Sections
Formulas
Formula
Mean = Σx / n
Meaning
Σx = sum of all values, n = number of values
Watch Out
Don't confuse with median - mean uses ALL values and is affected by outliers
When To Use
Finding the average or central tendency of a dataset
Formula
Range = Maximum - Minimum
Meaning
Difference between highest and lowest values
Watch Out
Range is easily affected by extreme values (outliers)
When To Use
Finding the spread or dispersion of data
Formula
Variance = Σ(x - x̄)² / n
Meaning
x = individual values, x̄ = mean, n = number of values
Watch Out
Remember to square the deviations - don't forget this step
When To Use
Measuring how spread out data points are from the mean
Formula
Standard Deviation = √Variance
Meaning
Square root of variance
Watch Out
Always take the positive square root
When To Use
Expressing spread in the same units as the original data
Section Title
Basic Statistics Concepts
Important Facts
- Mean is affected by outliers, median is not
- For odd n: median = middle value; for even n: median = average of two middle values
- A dataset can have no mode, one mode, or multiple modes
- Arrange data in ascending order to find median easily
- Standard deviation is always non-negative
Key Definitions
Term
Population
Example
All students in a school
Definition
Complete set of all individuals or items of interest
Term
Sample
Example
50 randomly selected students from the school
Definition
Subset selected from a population for study
Term
Variable
Example
Height, age, test scores
Definition
Characteristic that can take different values
Term
Data
Example
Heights: 160cm, 165cm, 170cm
Definition
Actual values collected for variables
Term
Median
Example
For {3,5,7,9,11}, median = 7
Definition
Middle value when data is arranged in order
Term
Mode
Example
For {2,3,3,4,5}, mode = 3
Definition
Most frequently occurring value
Diagrams To Know
- Bar graphs for categorical data
- Histograms for continuous data
- Pie charts for parts of a whole
- Box plots showing quartiles
Formulas
Formula
Sample Size Rule: n ≥ 30 for normal approximation
Meaning
n = sample size
Watch Out
Smaller samples may not represent population well
When To Use
Determining if sample size is adequate for statistical inference
Section Title
Sampling Methods
Important Facts
- Random sampling reduces bias
- Larger samples generally give better estimates
- Convenience sampling may introduce bias
- Stratified sampling ensures representation of all groups
- Systematic sampling can miss patterns if list has cycles
Key Definitions
Term
Simple Random Sampling
Example
Drawing names from a hat
Definition
Every member has equal chance of selection
Term
Stratified Sampling
Example
Sample students from each grade level
Definition
Population divided into groups, sample from each proportionally
Term
Systematic Sampling
Example
Every 10th student from enrollment list
Definition
Select every kth member from ordered list
Term
Cluster Sampling
Example
Select random barangays, survey all households in those barangays
Definition
Divide into clusters, randomly select clusters, survey all in selected clusters
Term
Convenience Sampling
Example
Survey friends or classmates
Definition
Select easily accessible members (non-probability)
Formulas
Formula
Fundamental Counting Principle: k₁ × k₂ × k₃ × ... × kₙ
Meaning
k₁, k₂, etc. = number of ways for each event
Watch Out
Events must be independent - one doesn't affect the others
When To Use
Counting total ways for sequence of independent events
Formula
n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1
Meaning
n = positive integer, 0! = 1, 1! = 1
Watch Out
Remember that 0! = 1, not 0
When To Use
Counting arrangements of n distinct objects
Formula
ₙPᵣ = n!/(n-r)!
Meaning
n = total objects, r = objects to arrange
Watch Out
Order matters in permutations - AB ≠ BA
When To Use
Arrangements where order matters
Formula
ₙCᵣ = n!/[r!(n-r)!]
Meaning
n = total objects, r = objects to choose
Watch Out
Order doesn't matter in combinations - AB = BA
When To Use
Selections where order doesn't matter
Common Values
Value
1
Symbol
0!
Quantity
0!
Value
1
Symbol
1!
Quantity
1!
Value
2
Symbol
2!
Quantity
2!
Value
6
Symbol
3!
Quantity
3!
Value
24
Symbol
4!
Quantity
4!
Value
120
Symbol
5!
Quantity
5!
Section Title
Counting Principles
Important Facts
- For permutations: order matters, use ₙPᵣ
- For combinations: order doesn't matter, use ₙCᵣ
- ₙCᵣ = ₙCₙ₋ᵣ (choosing r is same as leaving n-r)
- ₙP₀ = 1 and ₙC₀ = 1
- ₙPₙ = n! (all arrangements of n objects)
Key Definitions
Term
Permutation
Example
Arranging 3 books: ABC, ACB, BAC are different
Definition
Arrangement where order matters
Term
Combination
Example
Choosing 3 books: ABC = ACB = BAC
Definition
Selection where order doesn't matter
Term
Factorial
Example
5! = 5 × 4 × 3 × 2 × 1 = 120
Definition
Product of all positive integers up to n
Formulas
Formula
P(E) = n(E)/n(S)
Meaning
n(E) = favorable outcomes, n(S) = total outcomes
Watch Out
Ensure all outcomes are equally likely
When To Use
Finding probability of any event
Formula
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Meaning
P(A ∪ B) = A or B, P(A ∩ B) = A and B
Watch Out
Don't forget to subtract P(A ∩ B) to avoid double counting
When To Use
Probability of either event A or B occurring
Formula
P(A') = 1 - P(A)
Meaning
P(A') = probability of complement of A
Watch Out
Complement means everything except A
When To Use
Finding probability of event NOT happening
Formula
P(A ∩ B) = P(A) × P(B) [if independent]
Meaning
For independent events only
Watch Out
Only works when events are independent
When To Use
Probability of both independent events occurring
Formula
P(B|A) = P(A ∩ B)/P(A)
Meaning
P(B|A) = probability of B given A occurred
Watch Out
P(A) cannot be zero
When To Use
Conditional probability when events are dependent
Section Title
Probability
Important Facts
- Probability is always between 0 and 1
- P(impossible) = 0, P(certain) = 1
- Sum of all probabilities in sample space = 1
- For mutually exclusive events: P(A ∩ B) = 0
- For independent events: P(B|A) = P(B)
Key Definitions
Term
Sample Space
Example
Rolling die: S = {1,2,3,4,5,6}
Definition
Set of all possible outcomes
Term
Event
Example
Getting even number: E = {2,4,6}
Definition
Subset of sample space
Term
Mutually Exclusive
Example
Getting heads and tails in one coin toss
Definition
Events cannot occur simultaneously
Term
Independent Events
Example
Two coin tosses
Definition
One event doesn't affect the other
Term
Conditional Probability
Example
P(rain | cloudy sky)
Definition
Probability of B given A has occurred
Diagrams To Know
- Tree diagrams for sequential events
- Venn diagrams for event relationships
- Probability tables for conditional probability
Must Remember
- P(E) = Favorable outcomes ÷ Total outcomes (basic probability)
- 0! = 1 (crucial for permutation/combination formulas)
- ₙPᵣ for arrangements (order matters), ₙCᵣ for selections (order doesn't matter)
- P(A') = 1 - P(A) (complement rule)
- Mean uses all values, median is middle value, mode is most frequent
- For mutually exclusive events: P(A ∩ B) = 0
- For independent events: P(A ∩ B) = P(A) × P(B)
- Sample space contains ALL possible outcomes
- Variance = average of squared deviations from mean
- Probability always between 0 and 1, inclusive
Last Minute Tips
- Always check if events are independent before multiplying probabilities
- For combination problems, ask yourself: does order matter? If no, use ₙCᵣ
- When finding median, always arrange data in order first
- In probability trees, multiply along branches, add across different paths
- Check your probability answers - they should never exceed 1 or be negative
Comparison Tables
Rows
Values
- Sum ÷ Count
- Normal distributions
- Yes - very sensitive
Property
Mean
Values
- Middle value
- Skewed distributions
- No - resistant to outliers
Property
Median
Values
- Most frequent
- Categorical data
- No - shows typical value
Property
Mode
Columns
- Measure
- Definition
- When to Use
- Affected by Outliers
Table Title
Mean vs Median vs Mode
Rows
Values
- Yes
- ₙPᵣ = n!/(n-r)!
- Arranging letters ABC
Property
Permutation
Values
- No
- ₙCᵣ = n!/[r!(n-r)!]
- Choosing 3 from 5 students
Property
Combination
Columns
- Type
- Order Matters?
- Formula
- Example
Table Title
Permutations vs Combinations
Rows
Values
- Equal chance for all
- Unbiased
- May miss groups
Property
Simple Random
Values
- Sample from each stratum
- Represents all groups
- Complex to implement
Property
Stratified
Values
- Every kth member
- Easy to implement
- May miss patterns
Property
Systematic
Values
- Random clusters, all members
- Cost effective
- Less precise
Property
Cluster
Columns
- Method
- Process
- Advantage
- Disadvantage
Table Title
Sampling Methods Comparison
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