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? The mean weight is pounds.

Answer 1

Answer:

11

Step-by-step explanation:

Given:

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

Question asked:

What is the mean weight of the 20 backpacks ?

Solution:

For first collection of  backpacks.

As we know:

$Mean = \frac{Sum\ of \ observations}{Total \ observations}$

$14=\frac{sum\ of \ observation}{8} \\14\times 8= Sum\ of \ observation\\112=Sum\ of \ observation$

For Second collection of  backpacks.

$Mean = \frac{Sum\ of \ observations}{Total \ observations}$

$9=\frac{Sum \ of\ observations}{12} \\9\times12=Sum \ of\ observations\\108 = Sum \ of\ observations$

Now, we will find the mean weight of the 20 backpacks altogether.

Mean weight of the 20 backpacks = Total sum of observations divided by total number of observations

Combined Mean = $\frac{112+108}{8+12}$

                            =$\frac{220}{20} =11$

Therefore, the mean weight of the 20 backpacks is 11.