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Question
The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean?
Solution
Let x1, x2, x3,..., x16 be 16 numbers with their mean equal to 8. Then
`bar"X" = (1)/"n" (sum_(i = 1)^16 x_i)`
⇒ 8 = `(x_1 + x_2 + ... + x_16)/(16)`
⇒ x1 + x2 + ... + x16 = 16 x 8 = 128 ...(i)
New numbers are x1 + x2 + 2, x3 + 2,..., x16 + 2.
Let `bar"X"` be the mean of new numbers. Then,
`bar"X" = ((x_1 + 2) + (x_2 + 2) + ... (x_16 + 2))/(16)`
= `((x_1 + x_2 + ... + x_16) + 2 xx 16)/(16)`
= `(128 + 32)/(16)`, ...[Using (i)]
= `(160)/(16)`
= 10.
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