Question

Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if the observations, given above, be: multiplied by 3 and then divided by 2.

Answer 1

Mean of the given data = `[ 8 + 12 + 16 + 22 + 10 + 4 ]/6`
= `72/6` = 12

multiplied by 3 and then divided by 2
If `barx` is the mean of n number of observation x₁, x₂, x₃, ...., x_n,

then mean of `a/b x_1, a/b x_2, a/b x_3, ...., a/b x_n  "is" a/b barx`
Thus, when each of the given data is multiplied by `3/2`,
the mean is also multiplied by `3/2`.
The mean of the original data is 12.
Hence, the new mean = `3/2 xx 12 = 36/2` = 18.