Average Questions for SSC MTS

What is Average

Average means sharing equally. If 5 friends together have 100 rupees, each gets 20 — that 20 is the average. In maths terms, Average is the Sum of all values divided by the Count of values. Simple as dividing a pizza equally among people.

• Average = Sum of all items divided by Number of items
• Sum = Average multiplied by Number of items (very useful shortcut)
• If all values are equal, average equals that common value
• Average always lies between the smallest and largest value in the group
• Increasing one item increases the average; decreasing one item decreases it

Effect of Adding or Removing a Number

A very common SSC MTS question type: a new person joins a group and the average changes — find the new person's value. Or one person leaves and average changes. The trick is: use Sum = Average x Count before and after the change, then find the missing value by subtraction.

• New person's value = New Sum minus Old Sum
• Old Sum = Old Average x Old Count
• New Sum = New Average x New Count
• If average increases after adding a number, new number is above old average
• If average decreases after adding a number, new number is below old average

Average of Consecutive Numbers

For consecutive numbers, even numbers, or odd numbers in a series, you do not need to add all — just find the middle value. For any evenly spaced sequence, average = (First + Last) divided by 2. This saves huge time in SSC MTS.

• Average of 1 to n = (n+1)/2
• Average of first n even numbers = n+1
• Average of first n odd numbers = n
• Average of any arithmetic sequence = (First term + Last term) / 2
• For consecutive numbers, average = middle number

Age-Based and Cricket/Score Problems

SSC MTS loves word problems on age averages (family, class) and score averages (batsman, student marks). These are just disguised sum problems. The moment you see average + someone joins or leaves or age changes — convert to Sum using Sum = Average x Count formula immediately.

• Average age increases by 1 each year for every member in the group
• If average after N years is asked — add N to current average directly
• Batting average problem: runs = average x innings played
• If a batsman improves average, new runs = new average x new innings
• Replace problems: old member out, new member in — difference in sum = difference in their values

• Using Count wrong: forgetting to increase Count by 1 when a new person is added — always update Count first
• Confusing increase in average with the new value being high — if average goes up by 2 and group has 5 people, new person is 10 above old average, not just 2 above
• In age problems after N years: students forget to add N to every member's age, so group average also increases by N — no separate calculation needed
• Averaging averages directly: average of two groups is NOT average of their averages unless group sizes are equal — always go back to total sum divided by total count
• Missing the word 'excluding' in cricket/score problems — if a score is excluded, reduce both sum and count, not just sum

• SCAN formula: Sum = Count x Average N(umber) — always convert average to sum first before doing anything
• Pizza rule: Average is how much each person gets if the total pizza is shared equally — more people same pizza, smaller slice (lower average)
• Change shortcut for replacement: Change in Average x Group Size = Difference between new and old member's value. Remember as A x G = D
• For consecutive numbers — just grab the middle one. Odd count series: middle number is the average. Even count series: average of two middle numbers

• SSC MTS typically asks 1-2 average questions per paper. Difficulty is easy — expect direct formula application or one-step word problems, not multi-step puzzles
• Most common pattern: group average changes when one person joins or leaves — master the Sum method and you crack these in 30-40 seconds
• Second most common pattern: consecutive number averages — use (First+Last)/2 and save time; never add all numbers manually
• Age-based average problems often say 'average age X years ago was Y' — add the years to find current average directly, no individual ages needed
• Avoid calculator-style addition in exam. If you see average of many numbers, check if they form an AP or symmetric series — middle value is the answer instantly