Average Questions in Aptitude Tests: How to Solve Them
Average questions are among the most common question types in numerical reasoning assessments. Employers like Google, Deloitte, Unilever, JP Morgan and the Civil Service all include numerical reasoning in their hiring process, and questions about averages appear in nearly every test. Whether you are calculating a simple mean from a data table, working out a weighted average, or identifying the median in a skewed data set, these questions test your ability to interpret numbers quickly under time pressure.
The good news is that average questions follow predictable patterns. Once you understand the core formulas and recognise the question types, you can answer them with confidence. This guide covers every type of average question you will encounter, provides worked examples, and gives you a clear preparation strategy.
Types of Averages You Need to Know
Aptitude tests can ask about several different types of averages. Each measures central tendency in a different way, and using the wrong method is one of the most common errors candidates make. Here is a breakdown of the four types you should be prepared for.
Arithmetic Mean is the most frequently tested average. You add up all the values and divide by the number of values. If a company reports quarterly revenues of 12, 15, 18 and 11 million pounds, the mean revenue is (12 + 15 + 18 + 11) / 4 = 14 million pounds. This is the calculation most people think of when they hear the word "average."
Weighted Average applies when different values carry different levels of importance. Instead of treating every number equally, you multiply each value by its weight before summing. This type appears in questions about grading systems, portfolio returns, and composite scores. If a candidate scores 72 on a written test worth 30% and 88 on a practical assessment worth 70%, the weighted average is (72 x 0.30) + (88 x 0.70) = 21.6 + 61.6 = 83.2.
Median is the middle value when all numbers are arranged in order. For the set 3, 7, 9, 15, 22, the median is 9. When there is an even number of values, you take the mean of the two middle numbers. Median questions tend to appear when the data set contains extreme outliers that would distort the mean.
Mode is the value that occurs most frequently. In the set 4, 7, 7, 9, 12, the mode is 7. Mode appears less often in aptitude tests than mean or median, but it can show up in questions about the most common result in a survey or the most popular category in a data set.
💡Before you start calculating, identify which type of average the question is asking for. The word "average" on its own almost always means arithmetic mean, but look for clues like "weighted," "middle value," or "most frequent" that signal a different calculation.
How Average Questions Appear in Real Tests
Average questions in professional aptitude tests rarely ask you to compute a simple mean from a list of numbers. Instead, they embed the calculation within a realistic business scenario, often requiring you to extract the right data from a table or chart before you can begin.
Here are the most common formats you will encounter:
| Question Format | What You Need to Do | Typical Difficulty | Time Needed |
|---|---|---|---|
| Simple mean from a table | Read values from a data table, sum them, divide by count | Low | 45-60 seconds |
| Weighted average | Identify weights and values, apply the weighted formula | Medium | 60-90 seconds |
| Find a missing value | Use Sum = Mean x Count to reverse-engineer one unknown value | Medium | 60-90 seconds |
| Compare averages across groups | Calculate separate averages for two or more groups, then compare | Medium-High | 75-90 seconds |
| Effect of adding or removing a value | Determine how the average changes when one data point is added or removed | High | 75-90 seconds |
| Median from grouped data | Identify the median class or value from a frequency table | Medium | 60-75 seconds |
Employers like Deloitte and JP Morgan typically use data-heavy numerical reasoning tests where you must read a table of financial figures, identify the relevant rows and columns, and then perform the average calculation. The Civil Service numerical test similarly presents information in tables and charts, requiring careful data extraction before any arithmetic.
💡The calculation itself is usually straightforward. The real challenge is extracting the correct numbers from the data presented and choosing the right formula under time pressure.
Worked Examples: Step-by-Step Solutions
Working through examples is the most effective way to build speed and confidence. Here are three representative problems covering the most common average question types.
Example 1: Simple Mean from a Data Table
A company reports the following monthly sales figures (in thousands): January 42, February 38, March 51, April 45, May 39, June 55. What is the average monthly sales figure for the first half of the year?
Step 1: Sum all values. 42 + 38 + 51 + 45 + 39 + 55 = 270. Step 2: Divide by the number of months. 270 / 6 = 45. Answer: The average monthly sales figure is 45 thousand.
Example 2: Weighted Average
A graduate assessment at Unilever consists of three components: an online numerical test worth 25%, a group exercise worth 35%, and an interview worth 40%. A candidate scores 78 on the numerical test, 82 on the group exercise, and 91 on the interview. What is the candidate's overall weighted score?
Step 1: Multiply each score by its weight. 78 x 0.25 = 19.5. Then 82 x 0.35 = 28.7. Then 91 x 0.40 = 36.4. Step 2: Sum the weighted values. 19.5 + 28.7 + 36.4 = 84.6. Answer: The candidate's overall weighted score is 84.6.
Example 3: Finding a Missing Value
The average score of 8 candidates on a Google aptitude test is 74. Seven of the scores are 68, 71, 73, 75, 79, 80, and 82. What is the eighth score?
Step 1: Calculate the required total sum. Sum = Mean x Count = 74 x 8 = 592. Step 2: Add the known scores. 68 + 71 + 73 + 75 + 79 + 80 + 82 = 528. Step 3: Subtract to find the missing value. 592 - 528 = 64. Answer: The eighth score is 64.
These three patterns cover the vast majority of average questions you will see in professional aptitude tests. If you can solve each type within 90 seconds, you are well prepared for test day.
Practise these question types with full numerical reasoning tests to build your speed and accuracy under timed conditions.
Common Mistakes and How to Avoid Them
Even candidates with strong mathematical ability lose marks on average questions because of avoidable errors. Understanding these pitfalls before test day helps you steer clear of them when the pressure is on.
Mistake 1: Using simple mean when weighted average is required. This is the single most common error. If a question mentions percentages, proportions, or different weightings for each component, you must use the weighted average formula. A simple sum-and-divide approach will give you the wrong answer every time.
Mistake 2: Miscounting the number of values. When data is presented in a table with many rows, it is easy to miss a row or count a header as a data point. Always verify your count before dividing.
Mistake 3: Confusing median with mean. These two measures can produce very different results, especially when the data contains outliers. The set 10, 12, 14, 15, 95 has a mean of 29.2 but a median of 14. If you calculate the wrong measure, your answer will be far off.
Mistake 4: Forgetting to sort before finding the median. The median requires values to be in ascending or descending order. If you pick the middle number from an unsorted list, you will almost certainly get the wrong answer.
Mistake 5: Rounding too early. In multi-step problems, rounding intermediate results can cause your final answer to differ from the correct option. Keep full precision throughout your calculation and only round at the very end.
💡Most errors on average questions are not mathematical failures but reading errors and formula selection mistakes. Read the question twice before you calculate, and always check whether the question specifies a particular type of average.
Strategies for Speed and Accuracy
In a timed numerical reasoning test, speed matters as much as correctness. Here are proven strategies that help you solve average questions faster without sacrificing accuracy.
Estimate before you calculate. Glance at the numbers and form a rough mental estimate of the answer. If the values are 42, 38, 51, 45, 39, and 55, you can see they cluster around 45. This estimate helps you catch major calculation errors instantly. If your calculated answer is 67, you know something went wrong.
Use the sum-first approach. For missing value problems, always start by calculating the total sum using Sum = Mean x Count. This single formula unlocks the solution to a wide range of question types.
Simplify weighted calculations. When weights are simple fractions, convert them mentally. A weight of 25% is simply one quarter. A weight of 50% means you just halve the value. Working with fractions rather than decimals can be faster for mental arithmetic.
Eliminate answer options. If you have four multiple-choice answers and your estimate tells you the average should be around 45, you can immediately rule out options like 32 or 61. This technique is especially valuable when time is running short.
Practise with realistic data tables. The challenge in professional tests is not the arithmetic but the data extraction. Practise reading complex tables quickly so you can identify the right numbers without hesitation. Tests from providers like SHL and Aon frequently present data in multi-column tables with distractors.
If you are preparing for a specific employer, find out which test provider they use. For detailed guidance on building a preparation plan, read our guide on how to pass an aptitude test and explore common numerical reasoning mistakes to identify your weak areas.
💡Estimation is your most powerful speed tool. A quick mental estimate before calculating catches errors early and helps you select the right answer faster in multiple-choice formats.
Average Questions Across Different Industries
Different employers emphasise different average question styles. JP Morgan and Deloitte favour weighted averages involving portfolio returns and composite performance scores across quarterly data. Google's numerical tests lean toward data interpretation where you calculate averages from charts comparing product lines or regions. Unilever combines numerical tests with case-study scenarios involving average sales per store or weighted market segment scores. The Civil Service numerical test draws heavily on government tables, asking you to calculate average expenditure across departments or compare median figures between regions.
The underlying mathematics is always the same. What changes is the data context. Practising with varied formats prepares you for any scenario. For a comprehensive look at numerical preparation, see our complete numerical reasoning preparation guide.
Start building your skills today with practice tests covering averages, percentages, ratios and data interpretation.
Frequently Asked Questions
When should I use weighted average instead of simple mean?
Use a weighted average whenever the question assigns different weights or proportions to values. Common scenarios include exam components with different percentage weightings and investment portfolios with varying allocations. If every value contributes equally, use the simple arithmetic mean. Look for percentage signs, the word "weighted," or phrases like "accounts for 40% of the total" as signals that a weighted calculation is needed.
How do I find a missing value when I know the average?
Use the formula Sum = Mean x Count to calculate the total sum first. Then add up the values you know and subtract that partial sum from the total. For example, if the average of 5 numbers is 20, the total sum is 100. If the four known numbers add up to 76, the missing number is 24. This reverse-engineering technique appears frequently in tests from SHL, Aon and other major providers.
Is the median ever tested in aptitude assessments?
Yes. Median questions appear in numerical reasoning tests, particularly when data sets include outliers. Employers may ask which measure of central tendency is most appropriate, or ask you to calculate the median directly. Sort all values in ascending order and pick the middle one. For an even number of values, take the mean of the two middle numbers.
What is the difference between mean, median and mode?
The mean sums all values and divides by the count. The median is the middle value in a sorted list. The mode is the most frequently occurring value. The mean is sensitive to outliers, while the median resists them. The mode is useful for identifying the most common category. Aptitude tests may ask you to choose the most appropriate measure for a given data set.
How much time should I spend on an average question in a timed test?
Most numerical reasoning tests allow roughly 60 to 90 seconds per question. Simple mean calculations should take under 60 seconds. Weighted average and missing-value questions often require the full 90 seconds. If a question takes longer, make your best estimate, select the closest answer, and move on.
Can I use a calculator for average questions in aptitude tests?
This depends on the test provider. SHL and Aon typically include an on-screen calculator. Some employers disable it to test mental arithmetic. The Civil Service numerical test generally permits a calculator. Your test invitation will specify which tools are allowed. Even when a calculator is available, practising mental arithmetic speeds up your work.
Prepare With Assessment-Training.com
Average questions are a scoring opportunity in numerical reasoning tests. The formulas are simple, the patterns are predictable, and dedicated practice turns these questions into reliable points on test day. Candidates who invest a few hours in targeted preparation consistently outperform those who walk into the test unprepared.
Focus your preparation on three areas: master the core formulas for mean, weighted average, median and mode; practise extracting data from complex tables and charts; and build speed by working through timed practice sets. This combination of knowledge, skill and speed is exactly what employers like Google, Deloitte, Unilever, JP Morgan and the Civil Service are looking for.
Get started with the complete test package at Assessment-Training.com and give yourself the preparation advantage that makes the difference between passing and failing your numerical reasoning assessment.