Question

On Monday, a person mailed $8$ packages weighing an average (arithmetic mean) of $12\frac{3}{8}$ pounds, and on Tuesday, $4$ packages weighing an average of $15\frac{1}{4}$ pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

• A. $13\frac{1}{3}$
• B. $13\frac{13}{16}$
• C. $15\frac{1}{2}$
• D. $15\frac{15}{16}$
• E. $16\frac{1}{2}$

Answer 1

Answer: (A)

$13\frac{1}{3}$

Mean is the sum of the values divided by the total number of values in the data set.

Given that mean of $8$ packages is $12\frac{3}{8}=\frac{99}{8}$

$⟹\frac{\text{sum of 8 packages}}{8}=\frac{99}{8}$

$⟹\text{sum of 8 packages}=99$ -------(1)

Given that mean of $4$ packages is $15\frac{1}{4}=\frac{61}{4}$

$⟹\frac{\text{sum of 4 packages}}{4}=\frac{61}{4}$

$⟹\text{sum of 4 packages}=61$ --------(2)

Total mean is $⟹\frac{\text{sum of 8 packages}+\text{sum of 4 packages}}{8+4}$

$=\frac{99+61}{12}=\frac{160}{12}=13\frac{1}{3}$