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

$\bf\large\underline\pink{Answer:-}$

Let us say numbers are be 3, 4,5 (i) Adding constant term k = 2 in each term New numbers are = 5,6,7. New mean = 5+6+7/2 = 18/3 = 6 = 4+2 New mean will be 2 more than the original mean (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 = 2 in each term New numbers are = 6, 8, 10 New mean = 6+8+10/3 = 24/3 = 8 = 4 x 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.

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Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

Let us say numbers are be 3, 4,5 (i) Adding constant term k = 2 in each term New numbers are = 5,6,7. New mean = 5+6+7/2 = 18/3 = 6 = 4+2 New mean will be 2 more than the original mean (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 = 2 in each term New numbers are = 6, 8, 10 New mean = 6+8+10/3 = 24/3 = 8 = 4 x 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.