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Difficulty: MediumWeighted Average and Combined Sets

A regional healthcare provider operates two outpatient facilities, Facility X and Facility Y. Facility X manages 6060 patient appointments per day with an average consultation time of 1515 minutes per patient. Facility Y manages 4040 patient appointments per day with an average consultation time of 2525 minutes per patient. What is the overall average consultation time, in minutes per patient, for all 100100 appointments combined across both facilities?

Answer: 19 minutes

Answer

The overall average consultation time across both facilities is 1919 minutes per patient.
The total consultation time across both facilities is 60×15+40×25=900+1000=190060 \times 15 + 40 \times 25 = 900 + 1000 = 1900 minutes. Dividing this by the total number of appointments (60+40=10060 + 40 = 100) gives a weighted average of 1900100=19\frac{1900}{100} = 19 minutes.

Step-by-Step Solution

1
Calculate the total consultation minutes contributed by Facility X.
60×15=90060 \times 15 = 900 minutes
Total time for a set is the number of items multiplied by the mean of that set.
2
Calculate the total consultation minutes contributed by Facility Y.
40×25=100040 \times 25 = 1000 minutes
Total time for the second set is the number of items multiplied by its mean.
3
Find the grand total consultation time and total number of patients.
Total minutes = 900+1000=1900900 + 1000 = 1900; Total patients = 60+40=10060 + 40 = 100
Combined sets require aggregating both total values and total counts.
4
Compute the combined weighted average.
1900100=19\frac{1900}{100} = 19 minutes
The weighted average is total accumulated value divided by total count.

Key Concept

Weighted Average of Combined Sets
Estimated Time:1m 30s
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Topics

Weighted Average and Combined Sets

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