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.
Let us say numbers are be
3, 4, 5
Therefore, Mean =
=
=
= 4
(i) = 2 on each term
New numbers are = 5, 6, 7
New mean =
=
= 6
Therefore new mean will be 2 more than the original mean.
(ii) Subtracting constant terms ‘k’ = 2 in each term
New numbers are = 1, 2, 3
Therefore, new mean =
=
= 2
Therefore, new mean will be 2 less than the original mean.
(iii) = 2 in each term
New numbers are = 6, 7, 8
Therefore, new mean =
=
= 8
Therefore, new mean will be 2 times of the original mean.
(iv) Divide by constant term ‘k’ = 2 in each term
New numbers are = 1.5, 2, 2.5
Therefore, new mean =
=
= 2
Therefore, new mean will be half of the original mean.