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**What is an average?**

refer to the sum of given numbers divided by the total number of terms listed.

number of terms

Average is the estimation of the

middle number of any series of numbers.

**For example average**of

1,2,3,4, 5 is 3.

Average can be calculated by sum of all numbers divided by the total number of

numbers

Average of 1,2,3,4,5= (1+2+3+4+5)/5 = 15/5 = 3

Which is also the middle number of the series , from here we can also say that

in an A.P. i.e arithmetic progression the middle term is the average of the

series .

**Rule 1: In the Arithmetic**

Progression there are two cases when the number of terms is odd and second one

is when number of terms is even.

Progression there are two cases when the number of terms is odd and second one

is when number of terms is even

odd the average will be the middle term.

And when the number of terms is even then the average will be the average of

two middle terms.

**Examples 1**: what will be

the average of 13, 14, 15, 16, 17?

**Solution**: Average is the middle term when the number of terms is odd,

but before that letâ€™s checks whether it is in A.P or not, since the common

difference is same so the series is in A.P.

our average of the series.

**Letâ€™s check it in another way**.

In the first statement of the article we have written that the average of a set

of terms is equal to:

Sum of all terms / Number of terms

So the sum of all terms in this case is 75 and the number of terms is 5 so the

average is 15.

the number of terms are even

**Example 2**: What will be

the average of 13, 14, 15, 16, 17, 18?

Solution: We have discussed that when the number of terms are even then the

average will be the average of two middle terms.

and 16, but before that the average we must check that the series should be

A.P. Since the common difference is same for each of the term we can say

that the series is in A.P.

And the average is (16+15)/2 = 15.5

**Rule 2: The average of the**

series which is in A.P. can be calculated by Â½(first + last term)

series which is in A.P. can be calculated by Â½(first + last term)

**Example 1:**What will be the average of 216, 217 , 218?

Solution: So the answer would be = Â½ (216 + 218) = 217

(Which is also the middle term of the series)

**Example 2:**

What will be the average of first 10 natural numbers?

Solution: The first 10 natural numbers are 1,2,3,4,5,6,7,8,9,10

So the average will be Â½ (1 + 10 ) = Â½ (11) = 5.5

**Rule 3: If the average of n**

numbers is A and if we add x to each term then the new average will be = (A+

x).

numbers is A and if we add x to each term then the new average will be = (A+

x).

**For example:**The

average of 5 numbers is18. If 4 is added to each of the number then the average

would be equal to __?

**Solution**: Old average = 18

New average will be = 4 + old average = 22

This is because each term is increased by 4 so the average would also be

increased by 4 so the new average will be 22

**Rule 4: If the average of n**

numbers is A and if we multiply p with each term then the new average will be =

(A x p).

numbers is A and if we multiply p with each term then the new average will be =

(A x p).

**For Example**: The average of 5 numbers is 18. If 4 is multiplied to each

of the number then the average would be equal to __?

**Solution**: Old average = 18

New average will be = 4 x 18= 72

**There are two more**

operation which can also be applied on the same principle as the above, i.e.

subtraction and division.

operation which can also be applied on the same principle as the above, i.e.

subtraction and division.

**Rule 5 :**In some cases, if a

number is included in the series of numbers then the average will change and

the value of the newly added term will be = Given average + (number of new

terms x increase in average).

the New average + (number of previous terms x increase in average ) .

**For example:**The

average age of 12 students is 40. If the age of the teacher also included then

the average becomes 44. Then what will be the age of the teacher?

**Solution**: Average given =

40

Number of students = 12

Therefore the age of the teacher = 40 + (12 + 1) x 4 = 40 + 52 = 92

And this is also calculated as 44 + (12 x 4)= 92

Therefore the average age of the teacher is 92 yrs

**Alternatively**

The average of 12 = 40 that means the total number of units are 12 x 40 = 480

Now the new average is 44 and the number of terms are 13 so therefore the total

number of units are = 44 x 13 = 572

So the included units would be equal to 572 â€“ 480 = 92

**Rule 6:**In some cases

a number is excluded and one more number is added in the series of the number

then the average will change by q and the value of the newly added term will be

= Replaced Term + (increased in average x number of terms ).

**For example:**The

average age of 6 students is increased by 2years when one student whose age was

13 years replaced by a new boy then find the age of the new boy

**Solution**: The age of the

boy will be = Age of the replaced boy +increase in average x number of terms

i.e. the age of the newly added boy = 13 + 2 x 6 = 25

**Rule 7: There are two more**

cases when the series is divided into two parts and one of the terms is either

included or excluded, then the middle term can be calculated by following

methods.

cases when the series is divided into two parts and one of the terms is either

included or excluded, then the middle term can be calculated by following

methods.

**Case 1 : When the term is**

excluded.

excluded.

Average(total ) + number of terms in first part x {average (total) â€“ average

(first part)} + number of terms in second part x {average (total) â€“ average

(second part)}

**Case 2: When the term is**

included.

included.

Average (total) + number of terms in first part x {average (first part) â€“

average(total) }+ x number of terms in second part x {average (second part) â€“

average (total)}

**For Example:**The

average of 20 numbers is 12 .The averages of the first 12 is 11 and the average

of next 7 numbers is 10. The last number will be?

**Solution:**

Here in this case one number is excluded so the number would be =

Average(total ) + number of terms in first part x {average (total) â€“ average

(first part)} + number of terms in second part x {average (total) â€“ average

(second part)}

**i.e. = 12 + 12 x (12-11)+(12-10) x 7 = 38.**

how can block me main to kisi se baat bhi nai karti bus que puchti hu padhai karti hu bus

this unfair not good vary upset by this

sorry but i will never come in this site bus kuch nahi aata hai ti bo puchti thi kabhi koi galat baat to chodo baat bhi nahi ki and block kae diya

Hello Riya

you are not blocked by anyone. who say you this.

Very good post mam thanks for this

Maa saraswati se meri yahi prathna hai ki sabhi SSCADDA readers ki is year job lag Jaye

Happy vasantpanchmi to all my friends and specially to sandeep sir and ayushi mam

In SA no one ever blocked by anyone …..

Thanks bro

i was sir that time it was showing

well thanx i m not blocked

Hi riyaaaa……next exam….

I've seen all your comments and found that you've been a sincere reader and visitor of SA. It must be your misunderstanding that you were blocked. Keep visiting here as we want that students like you keep in touch with SA.

Good Evening sandeep sir ,Ayushi mam…!!

kindly post other TOPICS in DETAIL…..N thanks for this one..!! ðŸ™‚

may god bless all f us

Who is ayushi

thanks

same 2 prince bhaiiiii……

sir kindly post general science quiz for ib and ssc cgl exams

thanx

She is the mentor/teacher/guide……of SSC Adda….

We all call her Ma'am with respect…..

U too better call her Ayushi Ma'am………..

goood one …thanx to Sa

Please help me friends how can I get daily update about the regular SSC adda as of bankers adda

Thank you SA ðŸ™‚

Visit daily SSC Adda n take part in quizzes.