The mean of 7 number is 20. If onene more number is added to the list,

1.	The mean of 7 number is 20. If onene more number is added to the list, there means 21. Find the added number.
Answer» $\huge\boxed{\fcolorbox{purple}{yellow}{Example:-}}$ Let the 20 observations be X1 ,X2 ,X3 ,…., X20 Sum of n observations = MEAN × no. of observations Sum of 20 observations = 18 ×20 X1 + X2 +X3 + ….+X20 = 360 ….…(1) When 3 is added to first 10 NUMBERS, then sum of NEW observations will be (X1+3)+(X2+3)+(X3+3)+…+(X9+3)+(X10+3)+X11+…+X20 = (X1+X2+X3+….+X20)+3×10 =360 + 30 …….(from 1) =390 So , mean of new observations = 390÷20 = 19.5

The mean of 7 number is 20. If onene more number is added to the list, there means 21. Find the added number.

Answer»

Let the 20 observations be X1 ,X2 ,X3 ,…., X20

Sum of n observations = MEAN × no. of observations

Sum of 20 observations = 18 ×20

X1 + X2 +X3 + ….+X20 = 360 ….…(1)

When 3 is added to first 10 NUMBERS, then sum of NEW observations will be

(X1+3)+(X2+3)+(X3+3)+…+(X9+3)+(X10+3)+X11+…+X20 = (X1+X2+X3+….+X20)+3×10

=360 + 30 …….(from 1)

=390

So , mean of new observations = 390÷20 = 19.5