Explain, by taking a suitable example, how the arithmetic mean alters by (i) adding a constant  to each term, (ii) subtracting a constant  from each them, (iii) multiplying each term by a constant  and (iv) dividing each term by a non-zero constant

Explanation

Let the numbers be `3,4,5`
`therefore` Mean=`(3+4+5)/3`
`=12`/`3=4`
(i)Adding a constant `K=2` to each term
New Numbers are `5,6,7`
New Mean`=(5+6+7)/3`
`=18`/`3`
`=6=4+2`
`therefore` New mean will be increased by `2`
(ii)Subtracting a constant `K=2` from each term
New Numbers are `1,2,3`
New Mean`=(1+2+3)/3`
`=6/3`
`=2=4-2`
`therefore` New mean will be decreased by `2`
(iii)Multiplying each term by a constant `K=2`
New Numbers are `6,8,10`
New Mean=`(6+8+10)/3`
`=24/3`
`=8=4xx2`
`therefore` New mean will be `2` times the original mean
(iv)Dividing each term by
a constant `K=2`
New Numbers are `1.5,2,2.5`
New Mean=`(1.5+2+2.5)/3`
`=6/3`
`=2=4/2`
`therefore` New mean will be half of the original mean