Question

Consider the following data and corresponding weights. xi Weight (wi) 3.2 6 3.0 3 2.5 2 4.0 8 (a) Compute the weighted mean. (Round your answer to three decimal places.) (b) Compute the sample mean of the four data values without weighting. Note the difference in the results provided by the two computations.

Answer 1

Answer:

(a) 3.432

(b) 3.175

Step-by-step explanation:

The given data and corresponding weights is:

                                                  $\begin{array}{cc}x_i&w_i\\3.2&6\\3.0&3\\2.5&2\\4.0&8\\\end{array}$

(a) The weighted mean is determined by the following expression:

$M_W=\sum\frac{x_i*w_i}{w_i}\\M_W=\frac{3.2*6+3.0*3+2.5*2+4.0*8}{6+3+2+8}\\M_W=3.432$

(b) The simple mean of the given data is determined by adding up the four values dividing the result by 4:

$M_S = \frac{3.2+3.0+2.5+4.0}{4}\\ M_S=3.175$

The value is lower than the weighted mean.