Civil Service Exam (Subprofessional) Numerical Ability — Basic Statistics & Consecutive NumbersFlash Cards

What is the formula for calculating the average or mean of a set of numbers?

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?

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?

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?

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?

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?

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?

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?

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.

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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.