A company has two sales divisions, Division X and Division Y. Division X has 12 representa… — GRE General Test

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

Cevap: 18500 dollars

Cevap

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 (

518,000

) and divide by the total number of remaining items (

28

), yielding

18,500

Adım Adım Çözüm

Find total monthly sales for Division X

12 \times 14,000 = 168,000

The total value of a group is the product of its count and its arithmetic mean.

Find total monthly sales for Division Y before representatives left

18 \times 24,000 = 432,000

Multiply the number of representatives in Division Y by their average sales volume.

Determine the remaining total sales in Division Y

432,000 - 82,000 = 350,000

Subtract the sales volume of the 2 departing representatives from Division Y's original total.

Calculate the total combined sales for both divisions

168,000 + 350,000 = 518,000

Add the total sales of Division X and the remaining sales of Division Y.

Calculate total number of remaining representatives across both divisions

12 + (18 - 2) = 28

Division X retains 12 representatives, while Division Y retains 16 representatives.

Compute the combined mean sales volume

\frac{518,000}{28} = 18,500

Divide the total combined sales volume by the total number of remaining representatives.

Anahtar Kavram

Weighted Mean and Combining Group Data

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