Civil Service Exam (Subprofessional) Numerical Ability — Basic Statistics & Consecutive NumbersStudy Notes
Full study notes for Basic Statistics & Consecutive Numbers — built specifically for the Civil Service Exam (Subprofessional) 2026. These notes cover every concept, definition, formula, and worked example you need for the Numerical Ability subtest of the Civil Service Exam (Subprofessional), structured in the order Civil Service Commission (CSC) typically tests them.
Exam context
The Career Service Examination — Subprofessional Level is conducted by Civil Service Commission (CSC) and is scheduled for Bi-annual — March and August 2026. The Numerical Ability subtest is marked as "~25% weightage" in the official pattern, and Basic Statistics & Consecutive Numbers appears in position 9th of 9 in the Civil Service Exam (Subprofessional) Numerical Ability review rotation. Passing mark: 80%. Recent Civil Service Exam (Subprofessional) 2026 papers have drawn roughly 17 questions from this subject.
Basic Statistics & Consecutive Numbers - Study notes
Statistics and consecutive numbers are fundamental concepts in numerical ability that appear frequently in Philippine entrance exams and civil service examinations. Statistics help us understand and analyze data through measures like averages and weighted means, while consecutive numbers follow predictable patterns that can be used to solve various mathematical problems. Mastering these concepts will improve your problem-solving skills and prepare you for standardized tests.
Summary
Basic statistics and consecutive numbers are essential topics for success in Philippine entrance and civil service exams. Key statistical concepts include calculating simple and weighted averages, finding missing terms, and unit conversions. Fraction problems require careful identification of wholes and parts, while consecutive number problems involve setting up algebraic equations. Success depends on mastering the fundamental formulas, practicing systematic problem-solving approaches, and checking answers for reasonableness. Regular practice with exam-style problems will build confidence and speed in these crucial mathematical skills.
Sections
Statistics is the branch of mathematics that deals with collecting, analyzing, and interpreting data. The most common statistical measure is the average or mean, which gives us a central value that represents a set of numbers. There are different types of averages: simple average (arithmetic mean) and weighted average. The simple average treats all values equally, while weighted average gives different importance to different values based on their frequency or significance. Understanding these concepts is crucial for solving word problems in entrance exams.
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Understanding Basic Statistics
Examples
- Five students scored 16, 14, 22, 19, and 17 in a quiz. Average = (16+14+22+19+17)÷5 = 88÷5 = 17.6
- A family of five has average height 150cm. Four members are 153, 150, 151, 152cm. Fifth member: (150×5) - (153+150+151+152) = 750-606 = 144cm
Key Points
- Average (Mean) = Sum of all terms ÷ Number of terms
- Missing term = Sum of original terms - Sum of remaining terms
- Sum of all terms = Average × Number of terms
- Weighted average considers the importance of each value
- Statistical measures help analyze real-world data
There are four main formulas you need to master for solving average problems. First, the basic average formula divides the sum by the count. Second, when finding a missing term, subtract known values from the total sum. Third, when you know the average and need the total sum, multiply average by count. Fourth, weighted averages account for different frequencies or importance of values. These formulas are essential tools for civil service and entrance exam success.
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Types of Averages and Formulas
Examples
- Athlete scores 165, 135, 122, 154 in 4 games. For average 147 in 5 games: Total needed = 147×5 = 735. Fifth game = 735-(165+135+122+154) = 159
- Class has 26 boys (avg 40kg) and 14 girls (avg 35kg). Class average = [(26×40)+(14×35)]÷(26+14) = (1040+490)÷40 = 38.25kg
Key Points
- Simple Average: Add all values and divide by count
- Missing Term: Use total sum minus known values
- Total Sum: Multiply average by number of terms
- Weighted Average: Consider frequency of each value
- Always identify what the problem is asking for
Unit conversion is a critical skill that involves changing measurements from one unit to another. Common conversions include time (days to weeks), length (inches to feet, feet to yards), weight (ounces to pounds), and volume (pints to gallons). The key is knowing the conversion factors and setting up the problem correctly using dimensional analysis. Always write out the conversion factor as a fraction to help cancel units properly.
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Unit Conversion Problems
Examples
- 644 days to weeks: 644 days × (1 week/7 days) = 644÷7 = 92 weeks
- 15 feet rope divided into 90 parts: (15 feet × 12 inches/foot) ÷ 90 = 180 ÷ 90 = 2 inches per part
Key Points
- Learn common conversion factors (12 inches = 1 foot, 7 days = 1 week)
- Use dimensional analysis to cancel units
- Set up conversions as multiplication by fractions
- Check that final units match what the problem asks for
- Practice metric and imperial system conversions
Fraction word problems combine basic fraction operations with real-world scenarios. These problems often involve parts of a whole, such as portions of work completed, parts of a tank filled, or fractions of an inheritance. The key strategy is to identify what represents the whole (denominator) and what represents the part (numerator). Always read carefully to understand whether you're finding a fraction of something or combining fractions.
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Fraction Word Problems
Examples
- If 1/3 workers use public transport and 2/5 drive cars, fraction who walk = 1 - (1/3 + 2/5) = 1 - 11/15 = 4/15
- Tank is 7/9 full. After removing 27 liters, it's 4/9 full. Capacity: (7/9 - 4/9) × capacity = 27, so 3/9 × capacity = 27, capacity = 81 liters
Key Points
- Identify the whole and the parts in the problem
- Add fractions when combining parts
- Subtract fractions when finding remaining parts
- Multiply fractions when finding a fraction of a fraction
- Convert mixed numbers to improper fractions for easier calculation
Consecutive numbers are numbers that follow each other in order without gaps. Examples include 5, 6, 7, 8 (consecutive integers) or 2, 4, 6, 8 (consecutive even numbers). These problems often involve finding unknown numbers when given their sum or relationships between them. The key is to express all numbers in terms of one variable, then solve the resulting equation. Consecutive number problems frequently appear in entrance exams because they test both algebraic thinking and pattern recognition.
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Consecutive Numbers and Patterns
Examples
- Three consecutive integers sum to 48: Let first number = n, then n + (n+1) + (n+2) = 48, so 3n + 3 = 48, n = 15. Numbers are 15, 16, 17
- Two consecutive even numbers have product 168: Let first = n, second = n+2. Then n(n+2) = 168, n² + 2n - 168 = 0, solving gives n = 12, so numbers are 12 and 14
Key Points
- Consecutive integers: n, n+1, n+2, n+3...
- Consecutive even numbers: n, n+2, n+4, n+6...
- Consecutive odd numbers: n, n+2, n+4, n+6...
- Express all numbers in terms of one variable
- Set up equations based on given conditions
Successful problem-solving in statistics and number theory requires a systematic approach. First, read the problem carefully and identify what is being asked. Second, determine what information is given and what needs to be found. Third, choose the appropriate formula or method. Fourth, set up the equation or calculation properly. Fifth, solve step by step, checking units and reasonableness. Finally, verify your answer makes sense in the context of the problem.
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Problem-Solving Strategies
Examples
- When finding missing test scores, first calculate total points needed, then subtract known scores
- For mixture problems, set up weighted averages using quantities as weights
Key Points
- Read problems carefully and identify key information
- Choose the correct formula for the situation
- Set up equations systematically
- Check units throughout your calculations
- Verify answers make sense in real-world context
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