Question

The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean?

Answer 1

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.