Understanding the Calculation of Hospital Emergency Visits A ∩ B and A U B

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SUMMARY

The discussion focuses on the calculation of hospital emergency visit events represented as A ∩ B (intersection) and A U B (union). Participants clarify that A U B should include the total counts of both events, specifically noting that the value 242 was mistakenly omitted from the calculation. The correct calculation for A U B is 6050, derived from 5292 + 270 + 246 + 242. Additionally, A ∩ B is calculated as 5292 + 953 - 195, where 953 represents the total number of left without being seen (LWBS) patients.

PREREQUISITES
  • Understanding of set theory concepts, specifically union and intersection.
  • Familiarity with basic arithmetic operations involving addition and subtraction.
  • Knowledge of hospital emergency visit metrics, including terms like LWBS (Left Without Being Seen).
  • Ability to interpret statistical data and identify potential errors in calculations.
NEXT STEPS
  • Study set theory in-depth, focusing on union (A U B) and intersection (A ∩ B) operations.
  • Learn how to calculate and interpret hospital visit statistics effectively.
  • Explore common errors in statistical calculations and how to identify them.
  • Research the implications of LWBS rates on hospital performance metrics.
USEFUL FOR

This discussion is beneficial for statisticians, healthcare analysts, and anyone involved in hospital management or emergency department operations seeking to understand the calculation of visit metrics and improve data accuracy.

robax25
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Homework Statement
A ∩ B and A U B
Relevant Equations
The question is taken from a Book. I don't understand how A ∩ B and AUB is calculated?
A ∩ B and A U B
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Untitled100.png
 
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robax25 said:
I don't understand how A ∩ B and AUB is calculated?
The text in the first image describes the events A and B. In words, what does the event A ∩ B mean? What does the event A U B mean?

Per the forum rules, you must show some effort. I've cut you some slack here by not issuing a warning.
 
If I calculate A u B = 5292 + 270 + 246 but there is 242 as well. why is not 242 added? The second question is that A ∩ B = 5292 +953 - 195 but why does he add 953 to the equation?
 
robax25 said:
If I calculate A u B = 5292 + 270 + 246 but there is 242 as well. why is not 242 added? The second question is that A ∩ B = 5292 +953 - 195 but why does he add 953 to the equation?
The ##242## should be added. It looks like a typo.

##953## is the total number of LWBS, which is set ##B##.
 
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robax25 said:
The second question is that A ∩ B = 5292 +953 - 195 but why does he add 953 to the equation?
This is misreading their answer. They are saying that the count of ##A \cup B ## is 5292+953-195, not ##A \cap B##.
 
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robax25 said:
If I calculate A u B = 5292 + 270 + 246 but there is 242 as well. why is not 242 added? The second question is that A ∩ B = 5292 +953 - 195 but why does he add 953 to the equation?
I agree with @PeroK .

5292 + 270 + 246 = 5808 , but Book has the result being 6050 .

Looking further, 6050 − 5808 = 242 .

So, clearly the 242 was omitted mistakenly.
 
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