Averages in Aptitude Tests: Mean, Weighted Average, Shortcuts

Every placement aptitude test includes two or three averages questions, and all of them reduce to the same three moves: sum the values, count them, divide.

What Placement Tests Ask About Averages

Averages questions in campus aptitude tests fall into four types:

• Simple mean: given n values, find their average.
• Change in average: one element is added, removed, or replaced — find the new average or the missing value.
• Weighted average: two or more groups with different sizes are combined — find the combined average.
• Find the missing value: given the average and all-but-one values, find the unknown.

Identifying the type before calculating saves 20 to 30 seconds per question. Most students start computing before they have finished reading. The type determines the formula path; the formula path determines whether you need to reconstruct the sum first or apply a shortcut directly.

The arithmetic mean formula: Average = Sum of all values / Number of values.

All four question types use this formula. The methods below let you apply it faster.

The Deviation Method: A Faster Calculation Path

The deviation method replaces direct summation with differences from an assumed mean. It is faster whenever values are close together.

Steps:

• Step 1: Pick an assumed mean — ideally a round number near the middle of the data.
• Step 2: Calculate each value’s deviation from the assumed mean (value minus assumed mean).
• Step 3: Sum all deviations.
• Step 4: Divide the sum by the count of values.
• Step 5: Add that result to the assumed mean.

Example: Find the average of 71, 72, 73, 74, 75, 76. Assumed mean = 73.

• Deviations: 71 minus 73 = -2; 72 minus 73 = -1; 73 minus 73 = 0; 74 minus 73 = +1; 75 minus 73 = +2; 76 minus 73 = +3.
• Sum of deviations = (-2) + (-1) + 0 + 1 + 2 + 3 = 3.
• Average = 73 + (3/6) = 73 + 0.5 = 73.5.

Direct check: (71 + 72 + 73 + 74 + 75 + 76) / 6 = 441 / 6 = 73.5. Both paths agree.

The deviation method shines on consecutive-integer questions and on timed tests where adding six three-digit numbers manually introduces errors.

How Changes to Data Affect the Average

Three rules cover every change-in-average question on campus tests.

Adding a New Element

New Average = (Old Average × Old Count + New Value) / (Old Count + 1)

Since Old Sum = Old Average × Old Count, you only need the old average, old count, and the new value. No need to reconstruct the full data set.

If the new value is above the current average, the new average rises. If below, it falls. If exactly equal to the old average, the average stays unchanged.

Adding a Constant to Every Value

If every value increases by k, the average also increases by k. The same rule works in reverse: a uniform decrease of k reduces the average by k.

Multiplication works proportionally. If every value is multiplied by k, the new average equals Old Average × k.

Replacing an Element

New average = (Old Sum minus Old Value + New Value) / Count.

Shortcut: change in average = (New Value minus Old Value) / Count.

Weighted Averages: When Group Sizes Differ

Simple average works when every element has equal weight. Weighted average applies when groups of different sizes are combined.

Formula: Weighted Average = (Sum of [Each group average × Group size]) / Total count

Example: Group A has 20 people with average height 180 cm. Group B has 40 people with average height 170 cm.

• Numerator: (20 × 180) + (40 × 170) = 3600 + 6800 = 10400.
• Denominator: 20 + 40 = 60.
• Weighted Average: 10400 / 60 = 173.33 cm.

The intuition: Group B is twice as large as Group A, so the combined average sits two-thirds of the way from 180 toward 170, not at the midpoint of 175.

Solved Examples: Eight Question Types

All answers are derived from first principles and independently verified.

Example 1: Simple Mean

• Given: Heights of five students: 168, 170, 169, 174, and 166 cm.
• Find: Average height.
• Step 1: Sum = 168 + 170 + 169 + 174 + 166 = 847.
• Step 2: Average = 847 / 5 = 169.4 cm.

Example 2: New Score Added

• Given: A batsman’s average after 16 innings is 36. He scores 70 in the 17th inning.
• Find: New average.
• Step 1: Old sum = 16 × 36 = 576.
• Step 2: New sum = 576 + 70 = 646.
• Step 3: New average = 646 / 17 = 38.

Example 3: New Student Joins a Class

• Given: Average marks of 19 students is 50. A new student joins with 75 marks.
• Find: New class average.
• Step 1: Old sum = 19 × 50 = 950.
• Step 2: New sum = 950 + 75 = 1025.
• Step 3: New average = 1025 / 20 = 51.25.

Example 4: Newborn Baby and Age Average

• Given: Average age of 3 children is 8 years. A baby is born (age 0).
• Find: New average age.
• Step 1: Sum of existing ages = 3 × 8 = 24.
• Step 2: New sum = 24 + 0 = 24.
• Step 3: New average = 24 / 4 = 6 years.

Example 5: Find the Missing Value

• Given: Average of five numbers is 40. Four of them are 32, 38, 44, and 48.
• Find: The fifth number.
• Step 1: Required total = 5 × 40 = 200.
• Step 2: Sum of four known = 32 + 38 + 44 + 48 = 162.
• Step 3: Fifth number = 200 minus 162 = 38.

Example 6: Weighted Average

• Given: Data values 10, 20, 30 with weights 1, 2, 3 respectively.
• Find: Weighted average.
• Step 1: Numerator = (10 × 1) + (20 × 2) + (30 × 3) = 10 + 40 + 90 = 140.
• Step 2: Denominator = 1 + 2 + 3 = 6.
• Step 3: Weighted average = 140 / 6 = 23.33.

Example 7: Uniform Constant Added

• Given: Average of a set is 45. Every value in the set increases by 8.
• Find: New average.
• By the constant-addition rule: New average = 45 + 8 = 53. No recalculation needed.

Example 8: Replacing an Element

• Given: Average of 10 numbers is 20. One number was recorded as 15 but should be 35.
• Find: Corrected average.
• Step 1: Old sum = 10 × 20 = 200.
• Step 2: Corrected sum = 200 minus 15 + 35 = 220.
• Step 3: New average = 220 / 10 = 22.

Preparing Averages for Campus Tests

The eight examples above cover the full range of question types campus aptitude tests set on this topic. IndiaBix’s averages practice set uses the same question formats and is the most widely used independent drill resource.

The consistent pattern across all eight examples: convert averages to sums, make the change, convert back. That single habit (sum first, average last) removes the errors that cost marks on timed tests.

For how averages fits into the full placement test structure alongside logical reasoning and verbal ability, the campus placement evaluation test guide covers section breakdowns and timelines. The placement preparation book guide lists standard titles used across coaching programmes. Mu Sigma’s hiring process weights quantitative reasoning with an analytics lens; the Mu Sigma MuApt guide shows how pattern problems appear in analytics-company tests. For the broader quant toolkit, the time and work aptitude guide covers the same sum-convert-recombine structure across a different problem class. TCS NQT preparation material links from the TCS official careers page.

The weighted-sum logic from this article (multiply each group by its size, sum, divide by total) is the same operation that runs through most AI ranking and recommendation outputs. TinkerLLM’s exercises, starting at ₹299 on tinkerllm.com, apply that weighted reasoning to real AI tasks, making them a practical next step after the quant foundation you have built here.