Basic Statistics & Consecutive Numbers - Exam Answer Templates
Proper answer writing in numerical ability questions requires clear step-by-step solutions, correct formulas, and accurate calculations. Students often lose marks not because they don't know the concept, but because they don't present their solutions systematically. These templates show exactly how to structure answers for maximum marks in Basic Statistics and Consecutive Numbers questions.
Answer templates
Find the average of 16, 14, 22, 19, and 17.
Examiner tip
Always show the addition step explicitly - examiners look for complete working
Model answer
Given numbers: 16, 14, 22, 19, and 17
Formula: Average = Sum of all terms ÷ Number of terms
Sum = 16 + 14 + 22 + 19 + 17 = 88
Number of terms = 5
Average = 88 ÷ 5 = 17.6
Therefore, the average is 17.6.
Answer structure
- Line 1: Write given numbers and formula [0.5 marks]
- Line 2: Calculate the sum correctly [1 mark]
- Line 3: Apply formula and find average [0.5 marks]
Scoring breakdown
Criteria
Correct sum calculation (88)
Criteria
Correct final answer (17.6) with proper working
Common mark deductions
- Not showing the sum calculation
- Arithmetic errors
- Not stating the final answer clearly
Key phrases to include
- Sum of all terms
- Number of terms
- Average =
- Therefore
The average height of a family of five is 150 cm. If the heights of 4 family members are 153, 150, 151 and 152 cm, find the height of the fifth member.
Examiner tip
This is a classic 'missing term' problem - always find the total first, then subtract
Model answer
Given: Average height of 5 members = 150 cm
Heights of 4 members: 153, 150, 151, 152 cm
To find: Height of fifth member
Formula: Sum of all terms = Average × Number of terms
Total height of 5 members = 150 × 5 = 750 cm
Sum of 4 known heights = 153 + 150 + 151 + 152 = 606 cm
Height of fifth member = 750 - 606 = 144 cm
Therefore, the height of the fifth member is 144 cm.
Answer structure
- Line 1: State given information and what to find [0.5 marks]
- Line 2: Find total sum using average formula [1 mark]
- Line 3: Calculate sum of known terms [1 mark]
- Line 4: Find missing term by subtraction [0.5 marks]
Scoring breakdown
Criteria
Correct calculation of total sum (750)
Criteria
Correct sum of four known heights (606)
Criteria
Correct final answer (144 cm)
Common mark deductions
- Not finding total sum first
- Addition errors in the four heights
- Subtraction errors
Key phrases to include
- Sum of all terms = Average × Number of terms
- Height of fifth member
- Therefore
A class has 26 boys and 14 girls. The average weight of boys is 40 kg and the average weight of girls is 35 kg. Find the average weight of the students.
Examiner tip
Weighted average problems require finding the total for each group first - never average the averages directly
Model answer
Given: 26 boys with average weight 40 kg
14 girls with average weight 35 kg
To find: Average weight of all students
Formula: Weighted Average = Sum of weighted terms ÷ Total number of terms
Total weight of boys = 26 × 40 = 1,040 kg
Total weight of girls = 14 × 35 = 490 kg
Total weight of all students = 1,040 + 490 = 1,530 kg
Total number of students = 26 + 14 = 40
Average weight = 1,530 ÷ 40 = 38.25 kg
Therefore, the average weight of the students is 38.25 kg.
Answer structure
- Line 1: Identify this as weighted average problem [0.5 marks]
- Line 2: Calculate total weight of each group [1 mark]
- Line 3: Find combined totals [1 mark]
- Line 4: Apply weighted average formula [0.5 marks]
Scoring breakdown
Criteria
Correct total weights (1,040 kg and 490 kg)
Criteria
Correct combined total (1,530 kg)
Criteria
Correct final average (38.25 kg)
Common mark deductions
- Using simple average instead of weighted average
- Calculation errors in multiplication
- Wrong final division
Key phrases to include
- Weighted Average
- Total weight
- Combined total
- Therefore
What part of a gallon is 5 pints? (Given: 1 gallon = 8 pints)
Examiner tip
Always use the given conversion factor and express the answer as a proper fraction
Model answer
Given: 1 gallon = 8 pints
To find: What part of a gallon is 5 pints
Method: 5 pints × (1 gallon ÷ 8 pints)
= 5 pints × 1/8 gallon per pint
= 5/8 gallon
Therefore, 5 pints is 5/8 of a gallon.
Answer structure
- Line 1: State the conversion factor [0.5 marks]
- Line 2: Set up the proportion correctly [1 mark]
- Line 3: Calculate and express as fraction [0.5 marks]
Scoring breakdown
Criteria
Correct setup using conversion factor
Criteria
Correct final answer as fraction (5/8)
Common mark deductions
- Not using the given conversion
- Incorrect fraction
- Not simplifying the fraction
Key phrases to include
- Conversion factor
- proportion
- Therefore
If 1/3 workers take public transportation and 2/5 drive cars, what fraction of workers walk to work?
Examiner tip
Remember that all fractions must add up to 1 (the whole group)
Model answer
Given: 1/3 take public transportation, 2/5 drive cars
To find: Fraction who walk to work
Fraction using transportation or cars = 1/3 + 2/5
= 5/15 + 6/15 = 11/15
Fraction who walk = Total - (Transportation + Cars)
= 1 - 11/15 = 15/15 - 11/15 = 4/15
Therefore, 4/15 of the workers walk to work.
Answer structure
- Line 1: Add fractions for transportation and cars [1 mark]
- Line 2: Subtract from 1 to find remaining fraction [1 mark]
Scoring breakdown
Criteria
Correct addition of fractions (11/15)
Criteria
Correct subtraction from 1 (4/15)
Common mark deductions
- Errors in adding fractions
- Not finding common denominator
- Arithmetic mistakes
Key phrases to include
- Common denominator
- Total fraction
- Therefore
644 days is how many weeks?
Examiner tip
For 1-mark questions, show the operation and give the final answer with units
Model answer
644 days ÷ 7 days per week = 92 weeks
Answer structure
- Single line: Division with correct answer [1 mark]
Scoring breakdown
Criteria
Correct division and final answer (92 weeks)
Common mark deductions
- Division errors
- Not stating units
Key phrases to include
- days per week
- weeks
A water tank is 7/9 full. When 27 liters of water are drawn out, the tank is 4/9 full. What is the total capacity of the tank?
Examiner tip
The difference in fractions equals the amount drawn out - this is the key insight
Model answer
Given: Initially 7/9 full, after drawing 27 liters it becomes 4/9 full
To find: Total capacity of tank
Let x be the total capacity of the tank.
Water drawn out = 7/9 x - 4/9 x = 3/9 x = 1/3 x
Given that water drawn out = 27 liters
Therefore: 1/3 x = 27
x = 27 × 3 = 81 liters
Therefore, the total capacity of the tank is 81 liters.
Answer structure
- Line 1: Set up equation with variable [1 mark]
- Line 2: Express water drawn as fraction of capacity [1 mark]
- Line 3: Solve equation to find capacity [1 mark]
Scoring breakdown
Criteria
Correct setup: 7/9 x - 4/9 x = 3/9 x
Criteria
Correct equation: 1/3 x = 27
Criteria
Correct final answer: 81 liters
Common mark deductions
- Not setting up the equation correctly
- Fraction arithmetic errors
- Not solving for x properly
Key phrases to include
- Let x be
- Water drawn out
- Therefore
An athlete scored 165, 135, 122 and 154 in his first 4 games. What score must he make on his next game so that his average for the five games will be 147?
Examiner tip
Always work backwards from the target average to find what total is needed
Model answer
Given: Scores in first 4 games: 165, 135, 122, 154
Required average for 5 games = 147
To find: Score needed in 5th game
Required total for 5 games = Average × Number of games
= 147 × 5 = 735
Sum of first 4 games = 165 + 135 + 122 + 154 = 576
Score needed in 5th game = 735 - 576 = 159
Therefore, he must score 159 in his next game.
Answer structure
- Line 1: Calculate required total using target average [1 mark]
- Line 2: Find sum of existing scores [1 mark]
- Line 3: Find missing score by subtraction [1 mark]
Scoring breakdown
Criteria
Correct total required (735)
Criteria
Correct sum of 4 scores (576)
Criteria
Correct 5th score (159)
Common mark deductions
- Not finding the required total first
- Addition errors
- Subtraction errors
Key phrases to include
- Required total
- Sum of first 4 games
- Therefore
If 3 feet = 1 yard, how many yards are there in 45 feet?
Examiner tip
Use the given conversion factor correctly and show the division
Model answer
45 feet × (1 yard ÷ 3 feet) = 45 ÷ 3 = 15 yards
Answer structure
- Single line: Conversion calculation with answer [1 mark]
Scoring breakdown
Criteria
Correct conversion and final answer (15 yards)
Common mark deductions
- Using wrong conversion
- Division errors
Key phrases to include
- conversion factor
- yards
A 12-meter yarn is cut so that one part is 1/3 of the other. How long is the longer segment?
Examiner tip
Always check that both segments add up to the total length
Model answer
Given: Total length = 12 meters
One part is 1/3 of the other
To find: Length of longer segment
Let x = length of shorter segment
Then longer segment = 12 - x
Given: x = 1/3(12 - x)
3x = 12 - x
3x + x = 12
4x = 12
x = 3 meters (shorter segment)
Longer segment = 12 - 3 = 9 meters
Therefore, the longer segment is 9 meters.
Answer structure
- Line 1: Define variable and relationship [0.5 marks]
- Line 2: Set up equation from given condition [1 mark]
- Line 3: Solve equation correctly [1 mark]
- Line 4: Find both segments and identify longer one [0.5 marks]
Scoring breakdown
Criteria
Correct equation setup: x = 1/3(12-x)
Criteria
Correct solution: x = 3
Criteria
Correct longer segment: 9 meters
Common mark deductions
- Not setting up equation properly
- Algebraic errors
- Not identifying which segment is longer
Key phrases to include
- Let x
- equation
- longer segment
- Therefore
The average age of 13 persons in a club was 21. What should be the age of the new person joining so as to increase the average by 4?
Examiner tip
Remember that increasing average by 4 means new average is 21 + 4 = 25
Model answer
Given: 13 persons with average age 21
New average required = 21 + 4 = 25
To find: Age of new person
Total age of 13 persons = 13 × 21 = 273
Total age of 14 persons = 14 × 25 = 350
Age of new person = 350 - 273 = 77
Therefore, the new person should be 77 years old.
Answer structure
- Line 1: Calculate current total age [1 mark]
- Line 2: Calculate required total for new average [1 mark]
- Line 3: Find age of new person by subtraction [1 mark]
Scoring breakdown
Criteria
Correct current total (273)
Criteria
Correct new total (350)
Criteria
Correct age of new person (77)
Common mark deductions
- Not calculating the new average first
- Arithmetic errors
- Wrong approach to the problem
Key phrases to include
- Total age
- New average
- Therefore
Average expenditure of a person for the first 3 days is 350 and for the next 4 days is 420. What is the average expenditure for the whole week?
Examiner tip
This is a weighted average over different time periods
Model answer
Given: First 3 days average = 350, Next 4 days average = 420
To find: Average for whole week (7 days)
Total expenditure for first 3 days = 3 × 350 = 1,050
Total expenditure for next 4 days = 4 × 420 = 1,680
Total expenditure for 7 days = 1,050 + 1,680 = 2,730
Average for whole week = 2,730 ÷ 7 = 390
Therefore, the average expenditure for the whole week is 390.
Answer structure
- Line 1: Calculate total for each period [1 mark]
- Line 2: Find overall average [1 mark]
Scoring breakdown
Criteria
Correct totals (1,050 and 1,680)
Criteria
Correct weekly average (390)
Common mark deductions
- Not finding totals first
- Division errors
- Wrong number of days
Key phrases to include
- Total expenditure
- Average for whole week
- Therefore
If a string is 25 inches long, what is its length in millimeters? (1 inch = 25.4 mm)
Examiner tip
Use the exact conversion factor given in the question
Model answer
25 inches × 25.4 mm/inch = 635 mm
Answer structure
- Single line: Multiplication with conversion factor [1 mark]
Scoring breakdown
Criteria
Correct conversion: 635 mm
Common mark deductions
- Using wrong conversion factor
- Multiplication errors
Key phrases to include
- conversion factor
- mm
Ms. Alvarez inherited 6/7 of her mother's estate. She sold 2/3 of her share. What part of the entire estate did she sell?
Examiner tip
When finding a fraction of a fraction, multiply the fractions together
Model answer
Given: Inherited 6/7 of estate, sold 2/3 of her share
To find: What part of entire estate was sold
Part of estate sold = (6/7) × (2/3)
= (6 × 2)/(7 × 3) = 12/21 = 4/7
Therefore, she sold 4/7 of the entire estate.
Answer structure
- Line 1: Set up multiplication of fractions [1 mark]
- Line 2: Simplify to lowest terms [1 mark]
Scoring breakdown
Criteria
Correct multiplication setup: (6/7) × (2/3)
Criteria
Correct simplified answer: 4/7
Common mark deductions
- Not multiplying fractions
- Not simplifying the answer
- Arithmetic errors
Key phrases to include
- multiplication of fractions
- Therefore
Jan cuts up a rope so that he has 25 pieces of 6⅕ cm long each. What was the original length of the rope?
Examiner tip
Always convert mixed numbers to improper fractions before multiplying
Model answer
Given: 25 pieces, each 6⅕ cm long
To find: Original length of rope
Length of each piece = 6⅕ = 31/5 cm
Original length = 25 × 31/5 = 775/5 = 155 cm
Therefore, the original length of the rope was 155 cm.
Answer structure
- Line 1: Convert mixed number to improper fraction [1 mark]
- Line 2: Multiply by number of pieces [1 mark]
Scoring breakdown
Criteria
Correct conversion: 6⅕ = 31/5
Criteria
Correct final answer: 155 cm
Common mark deductions
- Not converting mixed number properly
- Multiplication errors
- Wrong final calculation
Key phrases to include
- mixed number
- improper fraction
- Therefore
Mark wise strategy
Direct calculation with final answer and units
Do
- Show the operation clearly
- Include units in final answer
- Double-check arithmetic
Don't
- Skip showing the calculation
- Forget units
- Round prematurely
Formula, substitution, calculation, final answer
Do
- State the formula
- Show substitution step
- Calculate step by step
- State final answer clearly
Don't
- Skip formula
- Jump steps
- Make calculation errors
- Forget to conclude
Complete working with clear steps and explanations
Do
- Define variables if needed
- Show all major steps
- Check intermediate calculations
- Verify final answer makes sense
Don't
- Skip variable definition
- Rush calculations
- Omit checking work
- Give unclear final statement
Comprehensive solution with detailed explanation
Do
- Break into clear sub-steps
- Explain reasoning
- Show multiple methods if applicable
- Verify answer
- Connect to real-world context
Don't
- Write in paragraph form
- Skip explanations
- Ignore units throughout
- Rush the verification
General answer writing tips
- Always write the formula first before substituting values
- Show all calculation steps clearly - never skip steps even if they seem obvious
- Label your final answer clearly and include appropriate units
- For average problems, always state what you're finding (sum, number of terms, etc.)
- Use proper mathematical notation and avoid shortcuts in exam answers
- Double-check your arithmetic - calculation errors cost valuable marks
- For word problems, identify what is given and what needs to be found
- Round final answers appropriately and as specified in the question
Diagrams
Basic Statistics Concepts Overview
Visual overview of all basic statistics concepts covered in the chapter, showing the relationship between different types of average problems
Average Problem Solving Flowchart
Step-by-step flowchart showing how to identify and solve different types of average problems systematically
Unit Conversion Process
Systematic approach to handling unit conversion problems with proper factor identification and application