Mean, Median & Mode · Topic 1 of 6

➕ Mean (Average)

2 exam question types, fully solved

The mean (the everyday “average”) is the total of all the values shared out equally among them. It is the most-tested of the three averages, and almost every question reduces to one idea: turn the average into a total.

The one equation that runs everything

Definition: — add up the values, divide by how many there are.

• Convert first: rearrange to . Totals can be added and subtracted; averages cannot. Whenever a question gives a mean, multiply by the count to get the total.

• Missing value: .

• Excluded value: .

• Evenly-spaced shortcut: for an AP (consecutive / even / odd / multiples) the mean is just the middle, — never add them all.

• Weighted / combined: for unequal groups use — totals on top, counts (or weights) on the bottom. The heavier group pulls the answer towards itself, so averaging the averages is wrong unless the groups are equal.

📊Statistics ExplorerEnter up to 10 numbers

Numbers (comma-separated, max 10)

Using 8 values (max 10)

— Mean— Median● Mode (larger dot)● Other values

Sorted Array

23457779

Mean

(4 + 7 + 2 + 9 + 7 + 3 + 7 + 5) / 8

5.5

Median

Avg of positions 4 and 5 = (5 + 7) / 2

Mode

7 (unimodal)

Distribution insight: The mean is smaller than the median — the data is left-skewed (pulled by small outliers).

Empirical Check: Mode = 3×Median − 2×Mean

3×6 − 2×5.5 = 7 (actual mode: 7)

The mean of 7, 11, 15 is — the middle term, since they are evenly spaced.

Q1The mean of 5 numbers is 20. Their total sum is:

Q2The mean of 6 numbers is 30. If one number 50 is removed, the new mean of the remaining 5 is:

Q340 students average 60 marks and 60 students average 80 marks. The combined average is:

📚

Real exam questions — Mean & Weighted Mean

2 question types · 9 solved examples from real SSC papers

Every mean hides a total: $\text{total}=\text{mean}\times n$ . Convert first, then add or subtract whole totals. For weighted groups, divide $\sum w x$ by $\sum w$ — never average the averages unless the weights are equal.

How to solve this type

The mean is one line:

\text{Mean}=\dfrac{\sum x}{n}

— the total of all values divided by how many values there are. The single most useful rearrangement is

\text{total}=\text{mean}\times n

: whenever a question gives you a mean, multiply by the count to turn it into a total, because totals can be added and subtracted while means cannot.
Missing value:

\text{missing}=(\text{mean}\times n)-(\text{sum of the known values})

.
Excluded value:

\text{excluded}=(\text{old mean}\times\text{old }n)-(\text{new mean}\times\text{new }n)

.
Shortcut for evenly-spaced lists (an AP like consecutive / even / odd numbers): the mean is just the middle,

\dfrac{\text{first}+\text{last}}{2}

— no addition needed.

Find the mean of 12, 18, 24, 30, 36.

A26B20C24D22

Find the mean of all odd numbers from 1 to 19.

A9B8C10D11

The mean of 4 numbers is 15. Three of them are 12, 14 and 18. Find the fourth.

A14B15C17D16

The mean of five numbers is 28. If one number is excluded, the mean of the rest falls by 5. Find the excluded number.

A47B45C46D48

The mean of 8 numbers is 45. If the number 73 is removed, what is the new mean?

A41B43C44D42