FEUCAT Mathematics — Statistics & ProbabilitySlides
Presentation-style slides for Statistics & Probability — the fastest way to cover the chapter if you are reviewing on your phone between classes or shifts. Covers everything Far Eastern University tests on this chapter in the FEUCAT Mathematics subtest.
Exam context
On the FEUCAT 2026, the Mathematics subtest carries a "Core section" weight in Far Eastern University's pattern. Statistics & Probability lands at position 8th out of 9 in the standard review order. Target score is Competitive overall score, and roughly a meaningful share of items come from Mathematics on a typical FEUCAT paper.
Statistics & Probability - Slides
Statistics and Probability are fundamental mathematical concepts that help us collect, organize, analyze, and interpret data to make informed decisions. In this chapter, we'll explore measures of central tendency, data analysis techniques, probability calculations, and counting principles through step-by-step problem-solving approaches essential for UPCAT and other college entrance examinations.
Slides
Introduction to Statistics & Probability
Statistics and probability are interconnected fields that help us understand patterns in data and predict future outcomes. These concepts are widely used in business, science, medicine, and everyday decision-making.
Notes
This overview helps students understand the scope and interconnection of statistical and probability concepts they'll encounter in college entrance exams.
Topic
Introduction
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mindmap root((Statistics & Probability)) Data Analysis Collection Organization Interpretation Central Tendency Mean Median Mode Probability Basic Rules Events Sample Space Counting Permutations Combinations Factorial
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Overview of main topics in Statistics and Probability
Population vs Sample
Understanding the difference between population and sample is crucial for statistical analysis. We use samples to make conclusions about populations when studying the entire population is impractical.
Notes
Emphasize that proper sampling techniques ensure the sample represents the population accurately.
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Fundamentals
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flowchart TD A[Population<br/>All Grade 12 Students<br/>in Philippines] --> B[Random Sampling] B --> C[Sample<br/>500 Selected Students] C --> D[Analysis] D --> E[Inferences about<br/>Entire Population]
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mermaid_flowchart
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Process of sampling from population to make statistical inferences
The Mean - Step-by-Step Calculation
The mean represents the average value of a dataset. It's calculated by adding all values and dividing by the count of values. This measure is sensitive to outliers, which can pull the mean away from the center.
Notes
Practice with different datasets to master mean calculation. Show how outliers affect the mean.
Topic
Measures of Central Tendency
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flowchart TD A[Data Set: 85, 90, 78, 92, 88] --> B[Step 1: Add all values] B --> C[85 + 90 + 78 + 92 + 88 = 433] C --> D[Step 2: Count values] D --> E[n = 5] E --> F[Step 3: Divide] F --> G[Mean = 433 ÷ 5 = 86.6]
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Step-by-step process for calculating the mean of a dataset
The Median - Finding the Middle Value
The median divides a dataset into two equal halves. It's particularly useful when dealing with skewed distributions or datasets with outliers, as it better represents the center of the data.
Notes
Always arrange data in order first. Practice identifying middle positions for both odd and even datasets.
Topic
Measures of Central Tendency
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flowchart TD A[Original Data] --> B[Step 1: Arrange in Order] B --> C{Is n odd or even?} C -->|Odd| D[Median = Middle Value<br/>Position = n+1/2] C -->|Even| E[Median = Average of<br/>Two Middle Values] D --> F[Final Answer] E --> F
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Decision tree for finding the median based on whether the dataset size is odd or even
The Mode - Most Frequent Value
The mode identifies the most common value in a dataset. Unlike mean and median, mode can be applied to both numerical and categorical data, making it versatile for different types of analysis.
Notes
Create frequency tables to easily identify modes. Remember that mode is the only measure that can be used with categorical data.
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Measures of Central Tendency
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flowchart TD A[Count Frequency of Each Value] --> B{How many values have<br/>highest frequency?} B -->|None tied| C[Unimodal<br/>One Mode] B -->|Two tied| D[Bimodal<br/>Two Modes] B -->|Three+ tied| E[Multimodal<br/>Multiple Modes] B -->|All equal| F[No Mode]
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Classification system for determining the type of mode in a dataset
Range and Measures of Dispersion
Range provides a basic measure of how spread out data values are. While easy to calculate, it only considers the two extreme values and doesn't account for the distribution of values in between.
Notes
While range is easy to calculate, emphasize its limitations and introduce concepts of variance and standard deviation for more comprehensive analysis.
Topic
Measures of Dispersion
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flowchart LR A[Data Set] --> B[Find Maximum] A --> C[Find Minimum] B --> D[Range = Max - Min] C --> D D --> E[Measure of Spread]
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Simple process for calculating range as a measure of data spread
Fundamental Counting Principle
The Fundamental Counting Principle helps us count the total number of outcomes when multiple events occur in sequence. Each event's outcomes are multiplied together to get the total possibilities.
Notes
Practice with real-world examples like outfit combinations, menu choices, or license plate possibilities to reinforce understanding.
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Counting Principles
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flowchart TD A[Event 1<br/>m ways] --> C[Total Outcomes<br/>m × n ways] B[Event 2<br/>n ways] --> C C --> D[Example:<br/>Shirt 3 ways<br/>Pants 4 ways<br/>Total: 3 × 4 = 12]
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Visual representation of the Fundamental Counting Principle with multiplication
Factorial Notation and Calculation
Factorial notation represents the product of all positive integers from 1 to n. It's essential for calculating permutations and combinations, showing how many ways objects can be arranged.
Notes
Emphasize the recursive nature of factorials and how they can be simplified in calculations. Practice computing factorials mentally for small numbers.
Topic
Counting Principles
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flowchart TD A[n!] --> B[n × n-1!] B --> C[Keep multiplying<br/>by decreasing integers] C --> D[Until you reach 1] D --> E[Example: 5!] E --> F[5 × 4 × 3 × 2 × 1 = 120]
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mermaid_flowchart
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Step-by-step breakdown of factorial calculation process
Permutations - Order Matters
Permutations count arrangements where the order of selection matters. ABC is different from BAC. This is crucial when positions or sequence have significance in the problem.
Notes
Always identify whether order matters in the problem. Practice with examples like seating arrangements, ranking, and scheduling.
Topic
Permutations and Combinations
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flowchart TD A[Choose r objects from n objects] --> B[Does order matter?] B -->|Yes| C[Use Permutation<br/>nPr = n!/(n-r)!] B -->|No| D[Use Combination<br/>nCr = n!/r!(n-r)!] C --> E[Calculate step by step]
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Decision tree for choosing between permutations and combinations
Combinations - Order Doesn't Matter
Combinations count selections where order is irrelevant. Choosing students A, B, and C is the same as choosing C, A, and B. This applies when we only care about which items are selected, not their arrangement.
Notes
Emphasize that combinations are always smaller than or equal to permutations for the same values of n and r.
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Permutations and Combinations
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flowchart TD A[Combination Formula<br/>nCr = n!/r!(n-r)!] --> B[Step 1: Calculate n!] B --> C[Step 2: Calculate r!] C --> D[Step 3: Calculate (n-r)!] D --> E[Step 4: Divide n! by r!(n-r)!]
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Step-by-step process for calculating combinations
Basic Probability Concepts
Probability measures the likelihood of an event occurring, expressed as a fraction, decimal, or percentage. It forms the foundation for statistical inference and decision-making under uncertainty.
Notes
Start with simple experiments like coins and dice before moving to more complex scenarios. Emphasize that all outcomes must be equally likely.
Topic
Probability
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flowchart TD A[Random Experiment] --> B[Sample Space<br/>All possible outcomes] B --> C[Event E<br/>Favorable outcomes] C --> D[P(E) = n(E)/n(S)] D --> E[Express as fraction,<br/>decimal, or percentage]
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mermaid_flowchart
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Basic probability calculation process from experiment to final probability
Probability Rules and Properties
These fundamental rules allow us to calculate complex probabilities by breaking them down into simpler components. Understanding these rules is essential for solving multi-step probability problems.
Notes
Practice identifying when to use each rule. Draw Venn diagrams to visualize overlapping events for addition rule problems.
Topic
Probability
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Conditional Probability
Conditional probability calculates the likelihood of an event occurring given that another event has already happened. This concept is crucial when events are dependent on each other.
Notes
Use tree diagrams and tables to organize information in conditional probability problems. Practice with real-world scenarios like medical testing and quality control.
Topic
Probability
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flowchart TD A[Event A occurs] --> B[Reduces sample space] B --> C[Calculate P(B|A)] C --> D[P(A and B) / P(A)] D --> E[Result: Conditional Probability]
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Process of calculating conditional probability when one event has already occurred
Sampling Methods
Different sampling methods are used depending on the population structure and research goals. Each method has advantages and potential biases that must be considered.
Notes
Discuss advantages and disadvantages of each sampling method. Consider cost, time, and accuracy trade-offs in real research situations.
Topic
Sampling
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flowchart TD A[Population] --> B{Sampling Method} B -->|Random| C[Simple Random<br/>Equal probability for all] B -->|Groups| D[Stratified<br/>Sample from each stratum] B -->|Clusters| E[Cluster<br/>Select entire groups] B -->|Interval| F[Systematic<br/>Every kth member]
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Different sampling methods and their characteristics
Common Mistakes and Problem-Solving Tips
Recognizing common mistakes helps avoid errors in statistics and probability problems. Systematic problem-solving approaches improve accuracy and speed in exams.
Notes
Practice identifying problem types quickly. Develop a checklist for each type of problem to avoid common errors.
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Problem-Solving Strategies
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flowchart TD A[Read Problem Carefully] --> B{What type of problem?} B -->|Central Tendency| C[Arrange data first] B -->|Counting| D[Order matters?] B -->|Probability| E[Independent events?] C --> F[Calculate and verify] D --> F E --> F
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Problem-solving strategy for statistics and probability questions
References
- CET 2026 Comprehensive Lecture Notes - Mathematics
- Brainbox UPCAT and Other College Entrance - Mathematics Proficiency
- The UPCAT Champion CET - Quantitative Reasoning
- New Curriculum Civil Service 2026 Edition - Numerical
In summary
Statistics and Probability provide essential tools for analyzing data and making informed decisions under uncertainty. Master the step-by-step approaches for calculating measures of central tendency, understand when to use permutations versus combinations, and apply probability rules systematically. These concepts are fundamental for success in college entrance exams and future academic pursuits. Remember to always verify your answers and check that they make logical sense in the context of the problem.
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