MH Police Bharti · Bite-size lessons
Average
About 6 min · Mathematics · English
Time worked out from the lesson's 340 words at 150 words a minute, plus a minute for each question.
Average is a topic in the Maharashtra Police Bharti mathematics section. Questions are straightforward once you master the basic formula and its variations. Examiners may test your ability to find the average of a given set, work backward to find a missing number, or handle scenarios where items are added, removed, or replaced.
Key ideas
- Average (Mean) is the sum of all observations divided by the number of observations. It represents the "central" value of a data set.
- Weighted Average applies when different items have different importance (weights). Multiply each value by its weight, sum them, then divide by total weight.
- Effect of Adding a Number: If a new number is added to a group, the new average shifts toward that number. If the new number equals the old average, average remains unchanged.
- Effect of Removing a Number: Removing a number above the average pulls the average down; removing one below pulls it up.
- Replacement Rule: When one item is replaced by another, change in sum = (new value – old value). This change divided by count gives shift in average.
Quick reference
- Average = Sum ÷ Count — memorize and apply instantly.
- Sum = Average × Count — the key to all backward problems.
- Weighted Average: Multiply each average by its group size, sum, then divide by total group size.
- Consecutive integers a to b: Average = (a + b) ÷ 2.
- First n natural numbers: Average = (n + 1) ÷ 2.
Check yourself: 3 questions
1. The average of five numbers is 48. If one number 56 is excluded, the average of the remaining four numbers is:
2. A cricket player has an average of 42 runs in 10 innings. How many runs must he score in the next innings to raise his average to 44?
3. The average weight of 8 men is increased by 2.5 kg when one of the men whose weight is 60 kg is replaced by a new man. What is the weight of the new man?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 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.