Average Formula Questions for CLAT

📑 On this page

⚡ Average in 3 lines

Average = Sum ÷ Count. Flip it whenever you can: Sum = Average × Count, because totals can be added and subtracted while averages can't. The average is a balance point: amounts above it exactly cancel amounts below it. The trap: without both the total and the count, the answer is "cannot be determined".

🎬 The 30-second story

The hostel-night bill

“I paid ₹420 for the pizzas. Legend behaviour.”

🍕

Aarav

Four friends order dinner for a hostel movie night.

“Drinks were ₹180. Meher did dessert for ₹260, Rohan fries for ₹340.”

🥤

Zoya

Total spend: ₹1,200.

“So who pays whom? Four separate UPI requests?”

📱

Meher

The group chat panics.

“₹1,200 ÷ 4 = ₹300 each. Two transfers. Done.”

⚖️

Zoya

One division settles the night.

Tara's maths: That ₹300 is the average: each person's share if the bill is split equally. Aarav is +120 and Rohan +40; Zoya is −120 and Meher −40. The overs and unders cancel perfectly, and that cancelling is what an average is.

What does an average actually mean?

An average answers one question: if everyone had the same amount, how much would each have? Pool everything into one pot (the sum), then share it equally (divide by the count). It's also called the arithmetic mean; in CLAT the two words mean the same thing.

🧮 The formula

The average, built from scratch

🪣

Sum of all values

pour it into one pot

👥

Number of values

how many share it

⚖️

Average

each one's fair share

📌 Convert every average into a total, instantly

Read "the average of 8 values is 45"? Write total = 360 in your rough space. Averages can't be added across groups; totals can. Almost every CLAT average question is: build a total, adjust it, divide once at the end.

Why is the average a balance point?

The four amounts sit at different heights, and the average is the line where they balance. Whatever sticks out above the line exactly fills the gaps below it. So the deviations from the average always add up to zero.

📊 The data

Who paid what (average = ₹300)

Aarav · +120 above

₹420

Rohan · +40 above

₹340

Meher · −40 below

₹260

Zoya · −120 below

₹180

Above the ₹300 line: 120 + 40 = 160. Below it: 40 + 120 = 160. Surplus = shortfall, every time.

Friend	Paid	Paid − ₹300	Settles by
Aarav	₹420	+120	receives ₹120
Rohan	₹340	+40	receives ₹40
Meher	₹260	−40	pays ₹40
Zoya	₹180	−120	pays ₹120
Total	₹1,200	0	books balance

→ scroll to see more

Two consequences follow. The average always lies between the smallest and largest value, or the deviations couldn't cancel. And one big value drags it: had Aarav paid ₹1,000, the average would jump to ₹445 though three people paid far less.

What is the formula for average, and how do you use all three forms?

🧩 At a glance

One formula, three disguises

➗Average = Sum ÷ Count

When you know every value.

✖️Sum = Average × Count

When you're given an average. CLAT's favourite form.

🔢Count = Sum ÷ Average

Rare: finds "how many" from a total and an average.

✍️ Worked example Warm-up ⏱ 30 sec

Meher's five mock scores

Meher scores 64, 71, 58, 77 and 80 in five CLAT mocks. What is her average?

1
Add: 64 + 71 + 58 + 77 + 80 = 350.
2
Divide by the count: 350 ÷ 5 = 70.
3
Sanity check: 70 sits between 58 and 80.

Answer: Average score = 70

⚡ Balance check

Guess 70. Deviations: −6, +1, −12, +7, +10. They sum to 0, so 70 is exact.

✍️ Worked example CLAT level ⏱ 50 sec

The missing day of follower gains

Zoya's page gained an average of 1,240 followers a day over 7 days. The first six days brought 1,100, 1,350, 980, 1,420, 1,260 and 1,190. What about day 7?

1
Average to total: 7 × 1,240 = 8,680.
2
Six known days: 1,100 + 1,350 + 980 + 1,420 + 1,260 + 1,190 = 7,300.
3
Day 7 = 8,680 − 7,300 = 1,380.

Answer: Day 7 = 1,380 followers

⚡ Deviation route

Deviations from 1,240: −140, +110, −260, +180, +20, −50, summing to −140. The balance must close at zero, so day 7 = 1,240 + 140 = 1,380.

✍️ Worked example Tricky ⏱ 40 sec

Consecutive numbers, then three more

The average of 7 consecutive integers is 40. The next 3 consecutive integers are added. What is the new average?

1
For evenly spaced numbers, the average is the middle term. 40 is the 4th of 7, so the list is 37 to 43.
2
Add 44, 45 and 46. The list is now 37 to 46.
3
New average = (first + last) ÷ 2 = (37 + 46) ÷ 2 = 41.5.

Answer: New average = 41.5

⚡ The exam-hall shortcut

Check by totals: 7 × 40 = 280, plus 44 + 45 + 46 = 135, gives 415 over 10 = 41.5.

💡 Two shift rules worth knowing cold

Add k to every value and the average rises by k. Multiply every value by k and the average is multiplied by k. Order matters: add 4 then double gives (A + 4) × 2, not 2A + 4.

How do you find an average fast without adding everything?

Big, close-together numbers eat time. Use the assumed-mean method, which is just the balance idea as a shortcut: guess a round number, average the small gaps, correct the guess.

1
Pick a round guess
For 4,980, 5,030, 5,110 and 4,920, guess 5,000.
2
Write the deviations
−20, +30, +110, −80.
3
Average them
Sum = +40; 40 ÷ 4 = +10.
4
Correct the guess
5,000 + 10 = 5,010. Deviations summing to zero means your guess was exact.

Options are your other shortcut. The average must sit between the smallest and largest value, and option × count must equal the total. One multiplication often kills two options.

🎛️ Try it yourself — change any number

Move the balance point

Days counted so far Average orders per day Orders on the extra day

Current total

1,500

Average if it joins

320

Average if it leaves

270

Total = 5 × 300 = 1,500; then add or remove 420 and divide by the new count

Defaults match the fest caselet below: 5 days averaging 300, then a 420-order Saturday lifts it to 320. Now try an extra day of exactly 300: nothing moves.

How does CLAT hide averages inside a caselet?

Since 2020, nobody asks "find the average of 4, 8 and 12". You get a paragraph or chart, and one of five questions wants an average buried in it. Here's a CLAT-style caselet.

📊 The data

Fest-week orders at a campus food stall

Mon

240

Tue

315

Wed

180

Thu

405

Fri

360

1,500 orders over five days: an average of 300 a day.

✍️ Worked example CLAT level ⏱ 75 sec

Three questions from one caselet

(i) Average orders per day? (ii) On how many days were orders above average? (iii) If Saturday is added and the six-day average becomes 320, how many orders came on Saturday?

1
(i) 240 + 315 + 180 + 405 + 360 = 1,500; 1,500 ÷ 5 = 300.
2
(ii) Above 300: Tue, Thu, Fri = 3 days.
3
(iii) 6 × 320 = 1,920; Saturday = 1,920 − 1,500 = 420.

Answer: (i) 300 (ii) 3 days (iii) 420

⚡ The exam-hall shortcut

For (iii): Saturday covers its own 320 and lifts 5 earlier days by 20 each: 320 + 5 × 20 = 420.

What are the traps in CLAT average questions?

⚠️ The average of averages is usually wrong

Section A averages 60, Section B 80. Combined is 70 only if the sections are the same size. With 40 in A and 10 in B it's 64; flip the sizes and it's 76. No sizes given? The answer is cannot be determined.

⚔️ Side by side

Can you actually find the average?

✅Determinable

Total and count both known

•Every value is given
•An average and its count are given
•Group averages and sizes are given

❓Cannot be determined

Total or count missing

•Group averages, no sizes
•Only the lowest and highest values
•A group the passage never describes

Ask: do I know the total and the count for exactly the group the question names?

✓Midpoint isn't the average. 20, 22, 25 and 80 average 36.75, not 50.
✓Count carefully. "3rd to 10th innings" is 8 innings, not 7.
✓Read the units. "In thousands" turns 20.6 into 20,600.

How has CLAT asked average questions?

📝 Asked in CLAT 2020 · Q137 Average after a ratio split

The following data presents the cases of Japanese Encephalitis in five states of India. No. of persons affected (in thousands): Odisha 57, West Bengal 45, Chhattisgarh 21, Jharkhand 29, Andhra Pradesh 13. Ratio of males to females: Odisha 12 : 7, West Bengal 6 : 3, Chhattisgarh 5 : 2, Jharkhand 15 : 14, Andhra Pradesh 7 : 6.

What is the average number of males affected by Japanese encephalitis in all the five states?

A9,000

B13,500

C18,400

D20,600

Reveal answer + reasoning

Answer: D

Males (thousands): Odisha 57 × 12/19 = 36; West Bengal 45 × 6/9 = 30; Chhattisgarh 21 × 5/7 = 15; Jharkhand 29 × 15/29 = 15; Andhra Pradesh 13 × 7/13 = 7.
Total = 103 thousand. Average = 103 ÷ 5 = 20.6 thousand = 20,600. About 60 seconds.

Why the others fail

A — × 5 = 45,000 males, but Odisha and West Bengal alone have 66,000.
B — × 5 = 67,500, leaving 1,500 for three states; Jharkhand alone has 15,000.
C — × 5 = 92,000 leaves 26,000 for the last three states, which actually total 37,000. A slip in one ratio split.

📝 Asked in CLAT 2024 · Q114 Average after % share and ratio

…Total number of cars for which data was collected was 8000. Of these, State 1 had 15% of the total cars in the ratio of 3:4:1 (diesel, petrol and electric); State 2 had 20% of the total cars in the ratio of 5:3:2…; State 3 had 30% of the total cars in the ratio of 4:5:3…, and; State 4 had 35% of the total cars in the ratio of 7:5:2 (diesel, petrol and electric)…

What is the average number of diesel cars in all the States?

A810

B862.5

C886

D912.5

Reveal answer + reasoning

Answer: B

Cars: 1,200, 1,600, 2,400, 2,800. Diesel: 1,200 × 3/8 = 450; 1,600 × 5/10 = 800; 2,400 × 4/12 = 800; 2,800 × 7/14 = 1,400.
Total = 3,450; ÷ 4 = 862.5. An average needn't be a whole number. About 70 seconds.

Why the others fail

A — × 4 = 3,240, which is 210 short of the real total.
C — × 4 = 3,544, which doesn't match 3,450.
D — × 4 = 3,650: taking State 4's diesel as 1,600 instead of 1,400 gives exactly this.

📝 Asked in CLAT 2023 · Q148 Cannot be determined

Players are selected for Judo based on their body weights from the following 10 weight groups: 1. (48 kg - 52 kg) … 10. (84 kg - 88 kg). The average weight of the players after selecting one player from each group is 68 kg. If one of the players (named S) leaves the team, their average weight comes down to 66.5 kg.

What is the average weight of all the players taken together?

A68 kg

B66 kg

C69 kg

DCannot be determined

Reveal answer + reasoning

Answer: D

Build what you can: 10 selected players total 680 kg; 9 after S leaves total 598.5 kg, so S weighs 81.5 kg. But "all the players" reaches beyond the selected team to everyone in the ten weight groups, whose number and weights are never given. No total, no count: the key says D.
It's arguable that 68 kg fits if only the ten selected were meant, but the passage already states that figure. Name the group first, then check you have its total and count. About 30 seconds.

Why the others fail

A — 68 kg is the average of the 10 selected only, a number the passage hands you.
B — 66 kg matches nothing; it is near 66.5 kg, the average after S leaves.
C — 69 kg has no basis in the data.

Ready to test your average basics?

💥 Myth vs fact

Myths that cost marks

🙅 Myth

The average is halfway between the smallest and largest value.

Tap to bust it →

✅ Fact

Only for evenly spaced data. 20, 22, 25 and 80 average 36.75.

🙅 Myth

To combine two groups, average their averages.

Tap to bust it →

✅ Fact

Only for equal sizes. Otherwise weight by size; no sizes means it can't be determined.

🙅 Myth

The average must be one of the values.

Tap to bust it →

✅ Fact

1, 2 and 6 average 3. Averages can even be decimals, like 862.5 cars.

🙅 Myth

Any new value changes the average.

Tap to bust it →

✅ Fact

A value equal to the current average leaves it unchanged.

🎯 Quick quiz

Average basics: 5 quick checks

0 / 5

Q1. What is the average of 12, 15, 18, 21, 24, 27 and 30?

Four friends get an average of ₹750 a month as pocket money. Three of them get ₹600, ₹820 and ₹700.

Q2. How much does the fourth friend get?

A test out of 50 has a class average of 31. The teacher adds 4 grace marks to everyone, then doubles every score to make it out of 100.

Q3. What is the new class average?

Class XII-A averages 72 in the pre-board. Class XII-B averages 64.

Q4. What is the average of both classes together?

Rohan's step counts over five days: 9,850, 10,120, 9,940, 10,210 and 9,880.

Q5. What is his average daily step count?

🎯 Average basics in a nutshell

An average is a fair share: pool the total, split it equally.
Sum = Average × Count: convert averages to totals at once.
Deviations above and below the average always cancel.
No total or no count means cannot be determined.

📎 Formula card

Average = Sum ÷ n · Sum = Average × n · n = Sum ÷ Average
Assumed mean: Average = Guess + (Sum of deviations ÷ n)
Evenly spaced: Average = (First + Last) ÷ 2 = middle term
First n natural numbers: (n + 1) ÷ 2
Add k to all: average + k · Multiply all by k: average × k
Balance: Σ(value − average) = 0, and min ≤ average ≤ max

Frequently asked questions

What is the formula for average?

Average equals the sum of all values divided by the number of values. If five scores add up to 350, the average is 350 ÷ 5 = 70. In CLAT you will more often use it backwards, total = average × count, because totals can be added and subtracted while averages cannot.

How do I calculate an average quickly in the CLAT exam?

Use the assumed-mean method. Pick a round number near the middle, add up each value's gap from it, divide by the count and add the result to your guess. For 4,980, 5,030, 5,110 and 4,920, guess 5,000; the gaps sum to 40, so the average is 5,010.

Can the average be greater than all the values?

No. The average always lies between the smallest and largest value, because the amounts above it must cancel the amounts below it. If your calculated average falls outside the range of the data, you have made a slip in the total or the count, so recheck both before moving on.

What is the average of the first n natural numbers?

It is (n + 1) ÷ 2, because 1, 2, 3 … n are evenly spaced and the average is the first plus the last, halved. The first 50 natural numbers average 25.5 and the first 20 average 10.5. The same rule works for consecutive odd or even numbers.

When is the answer 'cannot be determined' in average questions?

When you cannot fix both the total and the count for the exact group asked about. The classic case is two group averages with no group sizes: 60 and 80 could combine to anything between them. CLAT 2023 used this in a judo caselet about all the players.