Question

if the mean of five numbers is 16, if a number is added to the group then the mean of 6numbers becomes 21, then find the value of sixth number.

Answer 1

Answer:

Mean = Total Sum of terms / Total number of terms

Case 1: When 5 numbers are taken

=> Mean = 16

=> 16 = Sum / 5

=> Sum = 16 × 5 = 80

Therefore the sum of the five terms is 80.

Now a new term is added to the sum of 5 terms. Let us assume it to be x

=> New Sum = 80 + x

=> New Number of terms = 6

=> Mean = 21

Substituting we get,

=> 21 = 80 + x / 6

=> 21 × 6 = 80 + x

=> 126 = 80 + x

=> 126 - 80 = x

=> 46 = x

Hence the new number that was added was 46.

Hence the value of sixth term is 46.

Hope it helped !

Answer 2

$<b>$HEY MATE HERE IS YOUR ANSWER

We know that,

➡️ mean = total sum of terms / total number of terms

When 5 numbers are taken,

Mean ;- sum/5

16 = sum/5

Sum.= 16 × 5 = 80

Therefore , sum of 5 terms is 80

Now,

Let the number be x

Sum = 80 + x

New number of terms = 6

Mean :- 21

Now

Substitute,

= 21 = 80 + x / 6

=21 × 6 = 80 +x

➡️ 126 = 80 +x

➡️ 126 - 80 =x

➡️ x = 46

= Hence the 6 th number is 46.