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REET Level 1+2 . Maths

Average - REET Maths Notes

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Average is a practical topic in REET Maths that extends to consecutive numbers, squares-cubes and average speed. This page brings together every formula, key precautions, and REET 2024's solved questions.

  • 2 questions in REET 2024
  • Class 6-7 level
  • 6 min read
Verified 17 September 2026 · Source: NCERT Class 6-8 Maths textbooks (official)

How REET asks this topic

REET 2024 had one question giving the average of four consecutive even numbers and asking for the largest one, and another asking for the average of the cubes of the first five natural numbers. In other words, rather than a plain 'find the average' question, the concept is tested by combining the average formula with consecutive numbers or special series (squares, cubes).

Key formulas for average

SituationFormula
General averageAverage = sum of all observations / number of observations
Average of n consecutive numbers(first number + last number) / 2
Average of the first n natural numbers(n+1)/2
Average of the first n even numbersn+1
Average of the squares of the first n natural numbers(n+1)(2n+1)/6
Average of the cubes of the first n natural numbersn(n+1)^2/4
Average speed (equal distance, two speeds x and y)2xy/(x+y)

Using the simple average (x+y)/2 for average speed is wrong when the distance is equal and the speeds are different.

Worked examples (based on REET 2024)

The average of four consecutive even numbers is 23 - find the largest number. Let the numbers be x, x+2, x+4, x+6. Average = (4x+12)/4 = x+3 = 23, so x=20. The numbers are 20, 22, 24, 26 - the largest is 26.

Average of the cubes of the first five natural numbers: the cubes are 1, 8, 27, 64, 125, which sum to 225 (using the formula [n(n+1)/2]^2 for n=5: (15)^2=225). Average = 225/5 = 45.

Average speed - one important caution

When someone covers an equal distance at two different speeds, the average speed is not the simple (arithmetic) average of the two speeds, but the harmonic mean - formula: 2xy/(x+y). For example, if someone travels at 20 km/h and returns the same distance at 30 km/h, average speed = (2x20x30)/(20+30) = 1200/50 = 24 km/h, not (20+30)/2=25 km/h. This misconception is very common in exams like REET.

Weighted average

When two or more groups have different averages and different numbers of members, the combined average is found using a weighted average: weighted average = (sum of every group's total) / (total number of members).

Example: in a class, 30 boys have an average weight of 40 kg, and 20 girls have an average weight of 35 kg. The average weight of the whole class (50 students) = (30x40 + 20x35) / 50 = (1200+700) / 50 = 1900 / 50 = 38 kg. Note that this answer is not equal to the simple average of the two averages (40 and 35), which would be 37.5, because the two groups have different numbers of members.

Rules for how the average changes

Adding the same value to every number
New average = old average + that value. Example: the average of 5 numbers is 30; adding 4 to every number makes the new average = 34.
Multiplying every number by the same value
New average = old average x that value. Example: the average is 30; multiplying every number by 2 makes the new average = 60.

Average, median and mode - a brief distinction

The average (mean) is the 'central representative' value of a dataset, calculated by taking every number into account. The median, on the other hand, is the middle number of ordered data, and the mode is the number that appears most often - all three are covered in detail in the next topic, 'Mean, Median, Mode'. It's important to distinguish between them for REET, because similar-looking questions can ask for different measures.

How to teach this to children

Classroom activity

In Classes 6-7, distribute marbles or pencils unequally among students and ask them to make the amounts 'equal' among themselves - this 'levelling' process gives a physical understanding of the concept of average.

Teaching aids

Show towers of blocks of different heights and ask what height each tower would be if they were all made equal - this is also a visual demonstration of 'average'.

Common misconception

Children often think the average must always be one of the given numbers, or assume average speed is the simple average of two speeds - clear up both misconceptions with examples.

Assessment idea

Have students calculate the average marks from a real class test and check whether they're applying the formula correctly.

Cross-curricular link

In a sports class, have students calculate the average of their running times or long-jump distances, connecting maths to physical education - this makes the concept engaging and memorable.

Trick to remember / exam tip

The average of consecutive numbers (an AP) can always be found the fastest way - (first + last) / 2 - there's no need to add up the whole series. And wherever you see 'equal distance, different speeds', apply the formula 2xy/(x+y) directly instead of the simple average.

Questions asked in REET 2024 (with solutions)

Question 116

The average of four consecutive even numbers is 23. The largest number among them is

  1. A26
  2. B24
  3. C20
  4. D18

Explanation

चार क्रमागत सम संख्याएँ x, x+2, x+4, x+6 मानें। औसत = (4x + 12)/4 = x + 3 = 23 ⇒ x = 20। संख्याएँ 20, 22, 24, 26 हैं, अतः सबसे बड़ी संख्या 26 है।

Question 120

The average of the cubes of the first five natural numbers is

  1. A40
  2. B64
  3. C45
  4. D50

Explanation

प्रथम पाँच प्राकृतिक संख्याओं के घन: 1, 8, 27, 64, 125; योग = 225 (सूत्र [n(n+1)/2]² = 15² = 225)। औसत = 225/5 = 45।

Practice Questions

Question 1

What is the average of 10, 20, 30, 40?

  1. A20
  2. B25
  3. C30
  4. D35

Explanation

Sum=100, average=100/4=25.

Question 2

What is the average of the first 10 natural numbers?

  1. A5
  2. B5.5
  3. C6
  4. D10

Explanation

Using the formula (n+1)/2 for n=10: 11/2=5.5.

Question 3

The average of five consecutive natural numbers is 18. What is the smallest number?

  1. A14
  2. B15
  3. C16
  4. D17

Explanation

In 5 consecutive natural numbers, the middle number is the average, so the middle number=18. The numbers are 16,17,18,19,20; the smallest is 16.

Question 4

The average of 5 numbers is 20. On removing one number, the average of the remaining 4 becomes 18. What is the removed number?

  1. A22
  2. B24
  3. C26
  4. D28

Explanation

Sum of 5 numbers=100, sum of remaining 4=72. The removed number=100-72=28.

Question 5

What is the average of the first 6 even numbers (2,4,6,8,10,12)?

  1. A6
  2. B7
  3. C8
  4. D9

Explanation

Using the formula n+1 for n=6: average=7. Check: sum=42/6=7.

Question 6

A person travels 60 km at 20 km/h and returns the same distance at 30 km/h. What is his average speed?

  1. A25 किमी/घंटा
  2. B24 किमी/घंटा
  3. C26 किमी/घंटा
  4. D22 किमी/घंटा

Explanation

Average speed = 2xy/(x+y) = 2x20x30/50 = 1200/50 = 24 km/h - the simple average of 25 is wrong.

Question 7

The average weight of a group of 20 students is 45 kg. If a new student weighing 66 kg joins, what will the new average be?

  1. A45 किग्रा
  2. B45.5 किग्रा
  3. C46 किग्रा
  4. D47 किग्रा

Explanation

Old total weight=20x45=900; new total=900+66=966; new count=21; new average=966/21=46.

Question 8

The average of 3 numbers is 24. The first number is 20 and the second is 22. What is the third number?

  1. A26
  2. B28
  3. C30
  4. D32

Explanation

Sum of all three=24x3=72; third number=72-20-22=30.

Question 9

What is the average of the squares of the first 5 natural numbers?

  1. A9
  2. B10
  3. C11
  4. D12

Explanation

Sum of squares=1+4+9+16+25=55; average=55/5=11 [using the formula (n+1)(2n+1)/6 for n=5: 6x11/6=11].

Question 10

Which is the most suitable activity to practically explain the concept of 'average' to Class 6-7 students?

  1. Aविद्यार्थियों के बीच कंचे/पेंसिलें बराबर-बराबर बाँटकर 'बराबरीकरण' के रूप में दिखाना
  2. Bकेवल सूत्र लिखकर समझाना
  3. Cबिना उदाहरण परिभाषा रटवाना
  4. Dकोई गतिविधि न कराना

Explanation

The 'levelling' activity lets children physically see that averaging means bringing unequal quantities to an equal level, giving far more lasting understanding than an abstract formula.

Frequently Asked Questions

How many questions come from Average in REET?+

REET 2024 had 1-2 questions from this topic in the Maths section, based on the average of consecutive numbers and of cubes.

What is the basic formula for average?+

Average = sum of all observations (numbers) / total number of observations.

What is the formula for average speed?+

When an equal distance is covered at two different speeds x and y, average speed = 2xy/(x+y), not the simple average (x+y)/2.

What's the quick way to find the average of consecutive numbers?+

Add the first and last numbers and divide by 2 - this is much faster than adding up the entire series.

How is weighted average different from a simple average?+

In a simple average, every value carries equal weight, while in a weighted average, each value is weighted by the size of its group, so the results can differ.

If the same value is added to every number, what happens to the average?+

The new average also increases by that same value - that is, new average = old average + the value added.

What's the biggest thing to watch out for when finding average speed?+

When the distance is equal but the speeds are different, you must use the harmonic mean formula 2xy/(x+y) instead of the simple average [(x+y)/2], otherwise the answer will be wrong.

Does the average always fall among the given numbers?+

Yes, the average always lies between the smallest and largest number, whether or not it happens to be one of the given numbers itself.

How many numbers are needed at minimum to calculate an average?+

At least one number is enough to calculate an average (in which case the average is that number itself), but practically it's a useful concept for two or more numbers.

Read next

Unitary Method

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Time and Work

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REET Syllabus

See the complete REET Level 1 and Level 2 syllabus in one place.

REET 2024 Solved Paper

Read all REET 2024 questions with solutions and explanations.

Official Sources

  1. NCERT Class 6-8 Maths textbooks (official)
  2. Rajasthan Board of Secondary Education (BSER) - official REET information

Change Log

  • 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked