Question

A collection of 8 backpacks has a mean weight of 14 pounds. A different collection of 12 backpacks has a mean weight of 9 pounds. What is the mean weight of the 20 backpacks? Explain how you found your answer.

Answer 1

Answer: 11

Explanation:

We know that mean of a number of observations is given by :-

`\text{Mean}=\frac{\text{Sum of all observations}}{\text{Number of observations}}\\\\\Rightarrow\ \text{Sum of all observations}=\text{Mean*Number of observations}`

Given: The mean weight of 8 backpacks = 14 pounds

`\Rightarrow\ \text{Sum of weight of 8 backpacks}=14*8=112`

The mean weight of different 12 backpacks =9 pounds

`\Rightarrow\ \text{Sum of weight of 12 backpacks}=12*9=108`

Now, Total sum of all observations = 112+108=220 pounds

Now, the mean weight of the 20 backpacks is given by :-

`\text{Mean}=(220)/(20)=11`

Answer 2

Total weight of the first 8 backpacks
8*14
112 pounds

Total weight of the second 12 backpacks
12*9
108

Total weight of the whole 20 backpacks
112+108
220

So the mean weight of the 20 backpacks
220 / 20
11