Question

if the mean of a set of observations X1,X2,.....,.....,X10 IS 20 find the mean of x1+4,x2+8,x3+12,..... ......,x10+40

Answer 1

If the mean of this set is equal to 20, we can write down the below equation,

20 = (x1 + x2 +x3 + .... + x10)/10

x1 + x2 + x3 + ... x10 = 200

Then we can also write an equation for the mean of the given numbers as below,

Mean  = [(x1+4) + (x2+8) + (x3+12) + .... + (x10+40)]/10

           = (x1 + x2 + x3 + ... + x10 + 4 + 8 + 12 + ... + 40)/10

Then we can use above equation (1) to replace x1 + x2 + x3 + ... + x10 by 200

Mean = (200 + 4 + 8 +12 + 16 + 20 + 24 + 28 + 32 + 36 + 40)/10

         = 420/10

         = 42

If you remember Arithmetic Progressions you can simply add together the above number set.

If you closely look above, you can find that there is an Arithmetic Progression : 4, 8, 12, ... , 40

Here we want the addition of 10 terms. So we can use,

Sn = n/2(a+l)

S10 = 10/2(4+40)

       = 220

Then you can easily get the answer,

Mean = (200 + 220)/10

          = 42

Answer 2

Answer:

42

Step-by-step explanation:

MEAN = X1+X2+X3+....+X10/10

20= X1+X2+X3+....+X10/10

X1+X2+X3+....+X10=20 MULTIPLIED BY 10

X1+X2+X3+....+X10= 200 -- FIRST STEP

MEAN = [X1+4]+[X2+8]+[X3+12]+...+[X10+40]/10

          = [X1+X2+X3+....+X10]+[4+8+12+...+40]/10

          = 200+220/10

          = 420/10

NOW CANCEL THE ZEROS

MEAN= 42