Average
About 7 min · Elementary Mathematics · English
Time worked out from the lesson's 458 words at 150 words a minute, plus a minute for each question.
Average is one of the most straightforward topics in SSC GD Elementary Mathematics. The concept is simple: average represents the central value when a quantity is equally distributed among all members. Mastering average problems requires understanding the basic formula, knowing how to handle entry/exit of members, and quickly computing weighted averages. Students often lose marks on age-related average problems due to confusion about time shifts (years ago/years hence). This topic overlaps with ratio, percentage, and time-speed problems, so a strong grasp here builds confidence across multiple question types.
Key ideas
- Average (Mean) is the sum of all observations divided by the number of observations. Formula: Average = Total Sum ÷ Number of Items. This is the foundation of every average problem.
- Total Sum is always the product of average and count: Total = Average × Number of Items. This reverse calculation is crucial for solving most problems where the total is unknown.
- When a new member joins a group, calculate the new total by adding the new member's value to the old total, then divide by the new count. When a member leaves, subtract that member's value from the total.
- Weighted Average applies when different groups contribute differently. If group A has average x with n₁ members and group B has average y with n₂ members, the combined average = (n₁x + n₂y) ÷ (n₁ + n₂). Never just average the two averages unless group sizes are equal.
- In age problems, remember that when time passes, every person's age increases by the same amount, so the total age of a group increases by (number of people × years passed). The average age increases by exactly the same number of years when no one joins or leaves.
Quick reference
- Average = Total ÷ Count; Total = Average × Count — memorize both directions
- To find one unknown value: Unknown = (Average × Count) − Sum of Known Values
- Weighted average always lies between the individual averages, closer to the larger group
- In age problems: when n people age t years, total age increases by n × t
- Replacement effect: Change in average = (New Value − Old Value) ÷ Total Count
Check yourself: 3 questions
1. The average of five numbers is 42. If one number is excluded, the average of the remaining four numbers becomes 40. What is the excluded number?
2. The average age of 30 students in a class is 15 years. If the teacher's age is included, the average age increases by 1 year. What is the age of the teacher?
3. A batsman has an average score of 48 runs in 12 innings. How many runs must he score in his next innings to increase his average to 50?
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.
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