Basic Statistics & Consecutive Numbers - Flashcards
This comprehensive flashcard set covers fundamental concepts in basic statistics (mean, median, mode, weighted averages) and consecutive numbers problems commonly tested in Philippine civil service and college entrance exams. These flashcards are designed to help Grade 12 students master essential numerical ability skills through active recall and practice with exam-style problems.
Flashcards
What is the formula for calculating the average or mean of a set of numbers?
Answer
Average/Mean = Sum of all terms ÷ Number of terms. For example, if you have scores 16, 14, 22, 19, and 17: Average = (16+14+22+19+17) ÷ 5 = 88 ÷ 5 = 17.6
How do you find a missing term when you know the average?
Answer
Missing term = Sum of original terms - Sum of remaining terms. First, calculate the total sum using: Sum = Average × Number of terms. Then subtract the known terms. Example: If average of 5 numbers is 150 and four are 153, 150, 151, 152, then missing term = (150×5) - (153+150+151+152) = 750 - 606 = 144
What is the weighted average formula and when is it used?
Answer
Weighted Average = Sum of weighted terms ÷ Total number of terms. Used when different groups have different sizes. Example: 26 boys (avg weight 40kg) and 14 girls (avg weight 35kg). Weighted average = [(26×40) + (14×35)] ÷ (26+14) = [1040+490] ÷ 40 = 38.25kg
A student scored 165, 135, 122, and 154 in four games. What score is needed in the fifth game for an average of 147?
Answer
Step 1: Total needed = 147 × 5 = 735
Step 2: Current total = 165+135+122+154 = 576
Step 3: Score needed = 735 - 576 = 159
Therefore, the student needs to score 159 in the fifth game.
How many days are in one week? How do you convert days to weeks?
Answer
1 week = 7 days. To convert days to weeks: Days ÷ 7 = Weeks. Example: 644 days = 644 ÷ 7 = 92 weeks. Always divide the number of days by 7 to get the number of weeks.
How many inches are in one foot? What fraction of a foot is 4 inches?
Answer
1 foot = 12 inches. To find what fraction 4 inches is of a foot: 4 inches ÷ 12 inches = 4/12 = 1/3. Therefore, 4 inches is 1/3 of a foot.
How many ounces are in one pound? What part of a pound is 14⅔ ounces?
Answer
1 pound = 16 ounces. Convert 14⅔ to improper fraction: 14⅔ = 44/3 ounces. Fraction of pound = (44/3) ÷ 16 = (44/3) × (1/16) = 44/48 = 11/12. Therefore, 14⅔ ounces is 11/12 of a pound.
A rope 15 feet long is divided into 90 equal parts. How many inches is each part?
Answer
Step 1: Convert feet to inches: 15 feet × 12 inches/foot = 180 inches
Step 2: Divide by number of parts: 180 inches ÷ 90 parts = 2 inches per part
Therefore, each part is 2 inches long.
How many millimeters are in one inch? Convert 25 inches to millimeters.
Answer
1 inch = 25.4 millimeters. To convert: 25 inches × 25.4 mm/inch = 635 millimeters. This conversion is important for international measurements and scientific calculations.
How many pints are in one gallon? What part of a gallon is 5 pints?
Answer
1 gallon = 8 pints. To find what part 5 pints is: 5 pints ÷ 8 pints = 5/8 of a gallon. Remember this relationship for volume conversions in cooking and measurements.
If ⅓ of workers take public transportation and ⅖ drive cars, what fraction walk to work?
Answer
Step 1: Add fractions using common denominator (15): 1/3 + 2/5 = 5/15 + 6/15 = 11/15
Step 2: Subtract from total (whole): 1 - 11/15 = 15/15 - 11/15 = 4/15
Therefore, 4/15 of workers walk to work.
A water tank can be filled in 2¼ hours. What part of the tank can be filled in 1 hour?
Answer
If the whole tank is filled in 2¼ hours, then in 1 hour: 1 ÷ 2¼ = 1 ÷ 9/4 = 1 × 4/9 = 4/9 of the tank. This represents the rate of filling per hour.
A gas gauge shows ⅜ full. 60 liters are needed to fill it completely. What is the tank capacity?
Answer
If ⅜ is filled and 60 liters fills the remaining ⅝: Let x = capacity. Then ⅝x = 60, so x = 60 × 8/5 = 96 liters. The tank capacity is 96 liters.
A 12-meter yarn is cut so one part is ⅓ of the other. How long is the longer segment?
Answer
Let x = shorter part, then longer part = 12-x. Given: x = ⅓(12-x)
Solving: x = 4 - ⅓x, so x + ⅓x = 4, thus 4x/3 = 4, x = 3
Longer segment = 12 - 3 = 9 meters
Three countries produce 1/6, 2/5, and 3/15 of world rice. What fraction do they produce together?
Answer
Add fractions using LCD = 30: 1/6 + 2/5 + 3/15 = 5/30 + 12/30 + 6/30 = 23/30. The three countries together produce 23/30 of the world's rice production.
Ms. Alvarez inherited 6/7 of her mother's estate and sold 2/3 of her share. What part of the entire estate did she sell?
Answer
Multiply the fractions: (6/7) × (2/3) = 12/21 = 4/7. She sold 4/7 of the entire estate. When finding a fraction of a fraction, multiply the numerators together and denominators together.
A tank is 7/9 full. After 27 liters are drawn out, it's 4/9 full. What is the tank capacity?
Answer
The difference in fractions: 7/9 - 4/9 = 3/9 = 1/3. This 1/3 of capacity equals 27 liters. So capacity = 27 ÷ (1/3) = 27 × 3 = 81 liters.
What are consecutive numbers and how do you find their sum?
Answer
Consecutive numbers are numbers that follow each other in order (like 5, 6, 7). For n consecutive integers starting from a: Sum = n × (first term + last term) ÷ 2. Or if starting from a: Sum = na + n(n-1)/2
How do you find three consecutive numbers whose sum is 48?
Answer
Let the numbers be n, n+1, n+2. Then: n + (n+1) + (n+2) = 48, so 3n + 3 = 48, thus 3n = 45, n = 15. The three consecutive numbers are 15, 16, 17.
A conference room is 6/7 full. After 18 people leave, it's 6/14 full. What is the seating capacity?
Answer
Simplify 6/14 = 3/7. Difference: 6/7 - 3/7 = 3/7. This 3/7 of capacity = 18 people. So capacity = 18 ÷ (3/7) = 18 × 7/3 = 42 people.
Diagrams
Basic Statistics and Consecutive Numbers Concept Map
This mind map shows the hierarchical relationship between all major topics covered in Basic Statistics and Consecutive Numbers, helping students understand how concepts connect and build upon each other.
Average Problem Solving Process
This flowchart guides students through the systematic approach to solving different types of average problems, showing decision points and verification steps.
Unit Conversion Strategy
This flowchart provides a systematic approach to unit conversion problems, emphasizing the importance of setting up proportions correctly and checking answers for reasonableness.