Average Simple and Weighted Questions for BIHAR POLICE CONSTABLE

Simple Average Concept

Simple average is the sum of all values divided by the count of values. Think of it as 'fair share' — if everyone gets equal amount. In police exams, this appears in problems about average age of recruits, average salary of constables, or average marks in a test. The key insight: if you know the average and the count, you can find the total; if you know total and count, you find average. This reversibility is what examiners test.

• Simple Average = Sum of all values / Number of values
• Rearranged: Total Sum = Average × Count
• Used when all items have EQUAL weight or importance
• Common contexts: average age, average marks, average salary, average speed (if time is same)
• If one value changes, recalculate the new average using the new sum

Weighted Average Concept

Weighted average is used when different values have different importance or frequency. Imagine a class where 10 students scored 80 marks and 5 students scored 90 marks — you cannot simply average 80 and 90 to get 85. You must 'weight' each score by how many students got it. This is critical in police exams for problems involving multiple groups with different sizes, or items with different quantities. The formula multiplies each value by its weight, sums those products, then divides by the sum of weights.

• Weighted Average = (Sum of (Value × Weight)) / (Sum of Weights)
• Weight = frequency, quantity, or importance factor of each value
• Used when items have UNEQUAL importance or appear in different quantities
• Common contexts: average marks of multiple batches, average price per unit when buying different quantities, average speed over different distances
• Always check: do the groups have different sizes? If yes, use weighted average.

Identifying When to Use Which

This is where aspirants get confused. The exam will NOT tell you 'use weighted average' — you must recognize the pattern. If the problem mentions 'groups of different sizes' or 'different quantities' or 'different frequencies', it is weighted. If all items are treated equally or the problem is about a single homogeneous group, it is simple. Read carefully: words like 'batch', 'group', 'category', 'type', 'quantity', 'number of' are red flags for weighted average.

• Simple Average: single group, all items equal, no mention of quantities or batches
• Weighted Average: multiple groups/batches mentioned, or different quantities of same item
• Trick: if problem says 'average of averages', it is almost always weighted
• Watch for hidden weights: 'twice as many', 'three times', 'ratio 2:3' — these are weights
• Always write down the weights explicitly before calculating

Common Application Patterns in Police Exams

Bihar Police Constable exams love to test average in real-world scenarios. The most common are: (1) Age problems — 'average age of 5 constables is X, if one leaves and another joins, new average is Y'; (2) Salary/allowance problems — 'average salary of a batch'; (3) Marks problems — 'average marks of two batches of recruits'; (4) Speed/distance problems — 'average speed when travelling different distances at different speeds'. Each follows the same logic but requires careful reading to extract the numbers.

• Age problems: focus on 'who leaves, who joins' — recalculate sum and count
• Marks problems: always identify batch sizes — use weighted average if sizes differ
• Speed problems: if distances differ, use weighted average (distance is weight, not time)
• Salary problems: watch for 'one person earning X leaves' — subtract from total, recalculate
• Read twice: first for context, second to extract numbers and identify weights

• Treating weighted average as simple average: e.g., averaging 75 and 85 to get 80, ignoring that one group has 20 people and the other 30. Always multiply by weights first.
• Forgetting to update the count when a person leaves or joins: if average of 5 is 30 and one person leaves, the new count is 4, not 5. Recalculate total first, then divide by new count.
• Confusing 'average speed' with simple average of speeds: if you travel 100 km at 50 km/h and 100 km at 100 km/h, average speed is NOT 75 km/h. Use weighted average with distance as weight: (50*100 + 100*100)/(100+100) = 75 km/h. (This one happens to work out, but the method matters for other numbers.)
• Misidentifying weights: if a problem says 'ratio 2:3', that IS a weight — use 2 and 3 as weights, not as separate values.
• Arithmetic errors in sum: always double-check your sum before dividing. A single addition mistake ruins the answer.

• SIMPLE = Single group, all Equal weight. WEIGHTED = multiple groups, different Weights.
• Average = Fair Share. If shares are unequal (different group sizes), weight them.
• Formula shortcut: A = S/N (Average = Sum / Number). Rearrange as needed: S = A*N.
• Weighted = Multiply then Add then Divide: (v1*w1 + v2*w2 + ...) / (w1 + w2 + ...).

• Bihar Police Constable papers typically have 2-3 average questions in the numerical section. Expect 1 straightforward simple average and 1-2 weighted or application-based.
• Time management: simple average should take 30-45 seconds; weighted average 1-2 minutes if you set up the formula clearly. Do not rush — these are easy marks if you avoid careless errors.
• Recent papers show a trend toward 'average with replacement' problems (someone leaves, someone joins) — practice these specifically. They test both formula knowledge and logical thinking.
• Word problems are common — underline the numbers and weights as you read. Many aspirants miss a weight because they skim.
• Difficulty is usually easy to moderate, but a poorly read problem can look hard. Slow down, extract data, then calculate. Accuracy > Speed on this topic.