Question

The average of first 'N' whole numbers is. X. If the first whole number is removed from them.then what is the average

Answer 1

Answer:

X + 1/2

Average increases by 1/2

Step-by-step explanation:

The average of first 'N' whole numbers is. X. If the first whole number is removed from them.then what is the average

Average of first N whole numbers = (n+1)/2

(n+1)/2 = X

=> n + 1 = 2X

=> n = 2X-1

Sum of n number = nX

now first number is reduced so value reduce by 1 & number also decrease by

new Sum = nX - 1

Numbers = n -1

new average = (nX - 1) / n-1

= ((2X-1)X - 1) / (2X -1 - 1)

= (2X² - X - 1)/(2X -2)

= (2X² -2X + X -1)/ (2(X-1))

= (2X(X-1) + 1(X-1))/ (2(X-1))

= (2X +1)(X-1) / (2(X-1))

= (2X + 1 )/2

= X + 1/2

Average increase by 1/2 = 0.5