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प्रश्न
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.
उत्तर
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.
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