Question

The average of 7 numbers is 52. If 5 new numbers with sum of deviation 17 from average are included and 3 numbers 56 57 51 are excluded then find the average

Answer 1

What is the 6th number if the average of the first five is 54, and the last three is 52.? The average of all nine numbers is 50.

How does DuckDuckGo know where I am?

Average of first 5 numbers =54 , Then sum of this 5 numbers = 54*5 =270.

The average of last 3 numbers = 52 . Sum of last 3 numbers = 52*3 = 156

The average of all 9 numbers =50 . The sum of all 9 numbers = 50*9 =450.

The required 6th number = sum of all 9 numbers -(sum of first 5 numbers + sum of last 3 numbers)

= 450 -(270+156)

= 450 - 426

=24

Answer 2

Answer:

The new average is 53

Step-by-step explanation:

Average of 7 numbers = 52

The total value of the 7 numbers $=52\times 7=364$

Total value of the 5 new numbers added will be

= $5\times 52+\text{ sum of deviations}$

= $260+17$

= $277$

The sum of the value of the three numbers removed

= $56+57+51$

= $164$

Now the total numbers $=7+5-3=9$

Total value $=364+277-164=477$

New Average $=\frac{477}{9}=53$

Hope this helps.