Video summary

Rajasthan Computer Anudeshak Bharti 2026 | Maths Class – औसत (Average) | By SS Bainsla Sir

Main summary

Key takeaways

Educational

Main Ideas & Lessons: Average (Mean/Median)

  • Average is also known as the mean (English: “average”).
    • In Hindi, it is called मध्यम (madhyaman).

  • A common wrong belief is confusing average with the middle value:

    • People think: average = (sum of numbers) / (number of numbers) but interpret it as if it always means the middle term after arranging.

    • The clarification: the “middle value” idea works only in some ordered cases; otherwise you must use the correct method.

Correct simple concept/definition

  • Average = the middle value (mean)
  • More practical view: Average is the value that makes all numbers “effectively equal”—i.e., it balances increases and decreases around it.

Core formula

[ \text{Average}=\frac{\text{Sum of observations}}{\text{Number of observations}} ]

Equivalent rearranged form: [ \text{Average}\times \text{Number of observations}=\text{Sum} ]

Step-by-Step Methodology (Exam Usage)

1) If you know the numbers and want the average

  1. Identify the number of observations: (n).
  2. Add all numbers to get the total sum.
  3. Divide the sum by (n).

Use the formula when the numbers are not arranged in a simple consecutive/middle way.

2) If the average is given and you need a missing value

  1. Use: [ \text{Average}\times n=\text{Sum of all numbers} ]

  2. Subtract the known numbers’ sum from the total sum.

  3. The remainder is the missing number.

3) Speed trick for totaling (digit-based approximation)

For two-digit integers:

  • Add tens digits first (track place value).
  • Then add unit digits separately.
  • Combine totals to save time.

4) When numbers are in Arithmetic Progression (A.P.)

  • In A.P., the difference between consecutive terms is constant.
  • Average can be found quickly using: [ \text{Average}=\frac{\text{First term}+\text{Last term}}{2} ]

This works regardless of whether terms are natural/even/odd/multiples—as long as they form an A.P.

5) Careful wording caution: “first (n) odds/evens”

Read the question carefully because endpoints matter:

  • Average of first (n) odd numbers = (n)
  • Average of first (n) even numbers = (n+1)

For consecutive odds/evens over a symmetric span, the average aligns with the midpoint (often like A.P.: half of first + last).

6) Averages of multiples (pattern-based)

For the first (n) multiples of (k):

  • The terms form an A.P.
  • So the average becomes: [ \frac{\text{First multiple}+\text{Last multiple}}{2} ]

Example:

  • First 5 multiples of 3: (3, 6, 9, 12, 15)
    • Average (=\frac{3+15}{2}=9)

Examples / Problems Demonstrated

  • Example: 9 students average

    • Marks: 27, 79, 62, 57, 40, 84, 29, 71, 80
    • Since the numbers are not in order, you cannot directly choose the “middle value.”
    • Use: [ \text{Average}=\frac{\text{sum}}{9} ]

  • Example: average of 76, 48, 84, 66, 70, 64

    • Demonstrates fast digit-wise addition:
      • add tens first, then units.

  • Example: find (x) from average

    • If average of 3 numbers is 40:
      • total sum (=3\times 40=120)
    • Subtract known numbers’ sum to get the missing (x).

  • Example: average in A.P.

    • Average of numbers from 1 to 100 (A.P.): [ \frac{1+100}{2}=50.5 ]

    • Average of first even numbers up to 80: [ \frac{2+80}{2}=41 ]

    • For odd numbers from 1 to 100:

      • correctly treated as first odd terms, ending at 99 (not 100).

  • Prime-number fact used

    • “Average of the first nine prime numbers” stated as: [ \frac{100}{9}=11\frac{1}{9} ]

    • (As given in the speaker’s stated result.)

Speakers / Sources Featured

  • SS Bainsla Sir (main instructor; often referred to as “Sir”)
  • Manisha ji (listener/participant name in greetings/addressed remarks)
  • Praveen ji (listener/participant)
  • Kabra ji (listener/participant)
  • Priyanka (listener/participant)
  • Pratham (listener/participant)
  • Rachana (listener/participant)
  • Dhanraj / Dhanraj son (used as an addressed-name example in a commentary)
  • Mentions of “Sanatani Sir” (contextual reference, not a separate primary speaker)

Original video