UP Police Constable · Bite-size lessons
Average
About 7 min · Numerical & Mental Ability · English
Time worked out from the lesson's 491 words at 150 words a minute, plus a minute for each question.
Average (or arithmetic mean) is a topic in the Numerical & Mental Ability section of the UP Police Constable exam. Questions on average can be disguised in word problems involving ages, marks, income, temperature, or cricket scores. The topic tests your ability to quickly compute the central value of a data set and solve real-world problems where quantities are added or removed from a group.
Key ideas
- Average is the sum of all observations divided by the number of observations. It represents the central or typical value of a dataset.
- Formula relationship: Average = Total Sum / Number of Items, which rearranges to Total Sum = Average × Number of Items. This second form is critical for solving most exam problems.
- Weighted Average applies when different groups have different counts. The combined average is NOT the simple average of the two averages; you must account for the weight (count) of each group.
- Effect of Adding/Removing: When a new element is added or an old one removed, the average changes. Calculate the new total sum, then divide by the new count.
- Replacement Impact: When one element replaces another, the change in average reveals the difference between the new and old elements.
Watch out for
- Averaging the averages without weights → When combining groups, don't just add averages and divide by 2. Always multiply each average by its count, sum the totals, then divide by the combined count.
- Confusing individual change with total change → If 5 people each gain 3 kg, total weight increases by 15 kg, not 3 kg. Always multiply individual change by the number of items.
- Wrong formula for speed average → Average speed is NOT (speed₁ + speed₂) / 2. It's total distance / total time. For equal distances: Average speed = 2xy / (x + y) (harmonic mean).
Quick reference
- Average = Sum / Count; Sum = Average × Count (use the second form to find totals)
- Weighted average needs counts: (n₁A₁ + n₂A₂) / (n₁ + n₂)
- Replacement impact: n(New Avg − Old Avg) = (New Item − Old Item)
- When n people age by t years: total age increases by n×t; average age increases by t
- Average of 1 to n = (n+1)/2; Average of n consecutive numbers = (First + Last)/2
Check yourself: 3 questions
1. The average age of 5 students in a class is 14 years. If one student of age 12 years leaves the class, what will be the new average age of the remaining students?
2. A batsman has an average score of 45 runs in 8 innings. How many runs must he score in his 9th innings to increase his average to 48 runs?
3. The average weight of 30 students in a class is 40 kg. If the weight of the teacher is included, the average weight increases by 1 kg. What is the weight of the teacher?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
Read the full noteFlashcards for this topic
Saves this lesson and its 3 questions in this browser on this phone. No sign-in; nothing about you is saved or sent. A saved copy is not updated until you save it again. Parts that load from the server when you use them (the AI tutor, adaptive practice, sign-in) still need a connection.