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Difficulty: MediumMeasures of Central Tendency (Mean, Median, Mode)

A company has two sales divisions, Division X and Division Y. Division X has 12 representatives with an average monthly sales volume of $14,000\$14,000. Division Y has 18 representatives with an average monthly sales volume of $24,000\$24,000. If 2 representatives leave Division Y who together accounted for $82,000\$82,000 in monthly sales, what is the new combined average monthly sales volume, in dollars, for all remaining representatives in both divisions?

Answer: 18500 dollars

Answer

The new combined average monthly sales volume for all remaining representatives is $18,500.
To find the combined mean, calculate the sum of all remaining values across both groups (518,000518,000) and divide by the total number of remaining items (2828), yielding 18,50018,500.

Step-by-Step Solution

1
Find total monthly sales for Division X
12×14,000=168,00012 \times 14,000 = 168,000
The total value of a group is the product of its count and its arithmetic mean.
2
Find total monthly sales for Division Y before representatives left
18×24,000=432,00018 \times 24,000 = 432,000
Multiply the number of representatives in Division Y by their average sales volume.
3
Determine the remaining total sales in Division Y
432,000−82,000=350,000432,000 - 82,000 = 350,000
Subtract the sales volume of the 2 departing representatives from Division Y's original total.
4
Calculate the total combined sales for both divisions
168,000+350,000=518,000168,000 + 350,000 = 518,000
Add the total sales of Division X and the remaining sales of Division Y.
5
Calculate total number of remaining representatives across both divisions
12 + (18 - 2) = 28
Division X retains 12 representatives, while Division Y retains 16 representatives.
6
Compute the combined mean sales volume
518,00028=18,500\frac{518,000}{28} = 18,500
Divide the total combined sales volume by the total number of remaining representatives.

Key Concept

Weighted Mean and Combining Group Data
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Topics

Measures of Central Tendency (Mean, Median, Mode)

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