SSC CGL Maths · Averages

Replacements and Corrections

When the number of members stays the same, the average moves only because the total moves, and the change in the total is the count times the change in the average.

All Averages notes

Why this matters

Eight questions in the bank, all EASY: a person replaced, two people replaced, a mark misread, a constant added to every value. Each is one multiplication or one division once you see that the count has not changed.

Concept 1 of 2: Replacing members, or changing every value

A replacement keeps the count fixed. If the average of n members rises by r, the total has risen by n times r, and all of that extra came from the swap: the new member brought it in.

Definition

One member replaced: new member $=$ old member $+ n \times$ rise. If the average falls, the rise is negative and the new member is lighter, younger or lower.
Several members replaced: total of the new members $=$ total of the old ones $+ n \times$ rise. Here $n$ is the size of the whole group, not the number replaced.
Same number added to every value: the average goes up by that number. Subtracting works the same way.
Every value multiplied by the same number: the average is multiplied by it too.

Replacement and shifts

\text{New} = \text{Old} + n \times \text{rise} \qquad \overline{x + c} = \bar{x} + c \qquad \overline{cx} = c\,\bar{x}

nthe size of the group, which does not change
ca number added to, or multiplied into, every value

Worked example

The average weight of 8 men rises by 2.5 kg when a man weighing 65 kg is replaced by a new man. What does the new man weigh?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 16 Sep 2025, Shift 2 · Q55Easy

Example 1 · Averages · Replacements and Corrections

The average age of a committee of 9 members increases by 3 years when two men aged 42 and 44 years are replaced by two women. What is the average age of these two women?

Using n + 1 for a replacement

A replacement does not change the count, so the total changes by

n \times

rise. The

(n + 1)

form is only for a member who joins.

Multiplying the rise by the number replaced

If 2 members of a group of 9 are replaced and the average rises by 3, the total rises by

9 \times 3 = 27

, not

2 \times 3 = 6

: every member's share went up.

Drill 3 more on replacing members, or changing every value

Concept 2 of 2: Correcting a wrong entry

A misread value puts the total out by the difference between the true and the wrong value. The count is still right, so the average is out by that difference shared over the count.

Definition

Error $=$ correct value $-$ wrong value. Keep the sign.
Correct average $=$ wrong average $+$ error $\div n$ .
A correct value larger than the wrong one raises the average; a smaller one lowers it.
Several wrong entries: add their errors, with signs, before dividing.
Full method, when the numbers are awkward: wrong total $= n \times$ wrong average, fix the total, divide again.

Correcting an average

\text{Correct average} = \text{Wrong average} + \frac{\text{Correct value} - \text{Wrong value}}{n}

Worked example

The average of 25 numbers was found to be 40. Later it was found that 73 had been copied as 37. What is the correct average?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 22 Sep 2025, Shift 3 · Q67Easy

Example 2 · Averages · Replacements and Corrections

The average marks of

30

students in a class is

62

. If the marks of one student were wrongly entered as

82

instead of

62

, what is the CORRECT average?

Subtracting the wrong way round

The error is correct minus wrong. If 91 was misread as 19, the total was 72 too low, so the correct average is higher than the one found.

Moving the average by the whole error

The difference between the correct and wrong value is shared by all n values, so the average moves by the difference divided by n, not by the difference itself.

Drill 3 more on correcting a wrong entry

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Replacing members, or changing every value
Replacement and shifts
$\text{New} = \text{Old} + n \times \text{rise} \qquad \overline{x + c} = \bar{x} + c \qquad \overline{cx} = c\,\bar{x}$
Correcting a wrong entry
Correcting an average
$\text{Correct average} = \text{Wrong average} + \frac{\text{Correct value} - \text{Wrong value}}{n}$

Watch out for (4)

Using n + 1 for a replacement
→ Replacing members, or changing every value
Multiplying the rise by the number replaced
→ Replacing members, or changing every value
Subtracting the wrong way round
→ Correcting a wrong entry
Moving the average by the whole error
→ Correcting a wrong entry

Test yourself on Averages

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Averages chapter test Drill all 8 questions