Question

Explain, by taking a suitable example, how the arithmetic mean alters by

(i) adding a constant k to each term

(ii) subtracting a constant k from each them

(iii) multiplying each term by a constant k and

(iv) dividing each term by a non-zero constant k.

Answer 1

Let us say numbers are be 3, 4, 5

      ∴ Mean = `"Sum of number "/"Total number"`

       = `(3+ 4 + 5 )/ 3`

       = `12 / 3`

       =  4

(i) Adding constant term K=2 in each term
     New numbers are 5, 6, 7.

     ∴ New mean =` (5+ 6+ 7)/ 3`

                     =  ` 18 / 3 = 6 = 4 + 2`

    ∴ New mean will be 2 more than the  

(ii) Subtracting constant term K = 2 in each        term New number are 1, 2, 3.

     ∴ New mean =`(1+ 2 + 3)/3 =6/3` = 2 = 4 - 2.

    ∴ New mean will be 2 less than the original mean

(iii)  Multiplying by constant term k = 2in each term
        New numbers are = 6, 8, 10
        New mean  = `(6+8+10)/3`
 `                      = 24 / 3 `

                         = 8

                         = `4 xx 2`

   ∴  New mean will be 2 times of the original mean.

 

(iv)Divide by constant term k = 2 in each term
     New number are  = 1.5, 2, 2.5

            ∴  New mean = `(1.5 + 2 + 2.5)/3`

                                = `6/3 = 2 = 4/2`

∴ New mean will be half of the original mean.