Need some statistical help

[BNB]

I have a work scenario that I was hoping someone could help me with. I'm gonna change the actual details of what it has to do with so it can make more sense, but really, the numbers should work the same.

Say.... 1,000 people in one hour are calling to buy Bears tickets. There aren't enough people to handle to volume of customers. So the management team requests that some other people assist. Even with these extra people, 200 (20%) out of the 1,000 ultimately hang up because they don't want to wait anymore. These extra people handled a total of 100 customers.

If these extra people never would have handled the 100 customers, how many more (than 200) would have just hung up?

 

[Crystallas]

Unless this is a trick question...


The answer is

These extra people handled a total of 100 customers.

200 existing +100 ..... So 300 would have hung up.

 

[BNB]

Answer is



So 300 would have hung up.

My follow up question then would be.... why would these people be more or less likely to hang up than everyone else?

I understand that there isn't a sure way to know because there's a huge human component. Some of those people may have really wanted the Bears tickets, so they would have held as long as it took.

Why do we assume that 100% of them would have hung up?

 

[Warden of the Northeast]

Perhaps some of those customers called separately to order tickets but were actually part of a group looking to secure tickets. Once one got through the other dropped out as there was no need to stay on the line.

 

[BNB]

Perhaps some of those customers called separately to order tickets but were actually part of a group looking to secure tickets. Once one got through the other dropped out as there was no need to stay on the line.

This is assuming 1,000 people are calling for themselves.

 

[Warden of the Northeast]

This is assuming 1,000 people are calling for themselves.

Ok, sorry.

 

[BNB]

Ok, sorry.

hahahaha no need to apologize. I wasn't exactly detailed. I don't necessarily write math books for a living.

 

[Warden of the Northeast]

hahahaha no need to apologize. I wasn't exactly detailed. I don't necessarily write math books for a living.

So you're trying to figure why 300 people would hang up even if they really wanted the tickets?

 

[BNB]

So you're trying to figure why 300 people would hang up even if they really wanted the tickets?

No, I'm trying to figure out how much of an impact the "helpers" made.

 

[Crystallas]

Well here is an important detail missing from your problem.

How many regulars and how many extras? That would determine the rate of sale for each, and to another extent, rate of error.

 

[nc0gnet0]

No, I'm trying to figure out how much of an impact the "helpers" made.

Your servicing 800 calls an hour, but getting in 1,000 calls an hour. So for every 1 call you service, you get 1.2 calls in. Without the extra help this number would be 1.3. Even if these people where willing to wait the extra time, your call rate in doesn't change.


picture a graph with two plot points.......

or

Picture a line at McDonalds with the same problem, the line keeps getting bigger an bigger, until eventually they close, and those left in line are SOL.

 

[CODE_BLUE56]

300 would be the easy answer, but it's probably more complicated.

-There's data associated with how long a customer can wait for tickets before hanging up in this scenario. The average time a person waited before hanging up would be a crucial stat. As well as the average amount of callers the a worker handled in that hour, and how long it takes the average person to handle a call(these two would be directly related if we assume that the average worker was taking/handling calls the entire time).

Then go further. What was the average # of calls handled by each extra person? Is that number higher or lower than the non-extra people? How long had the 100 people that were handled by the extras been waiting before they were handled? Did they wait at all?

Based on those numbers, you should be able to reasonably estimate out of those 100 handled customers how many would hang up without the extra people.

ETA: This whole thing also assumes that after the 1 hour, no more calls come in, but the workers can address people still waiting.

 

[Crystallas]

lol

BNB has opened a can of worms. Users without components will create imaginary variables. Also, you need to decide whether you want to apply proportionality formulation or avoid it. Whatever is suitable, after all this is simply logistical analysis, so if you are building an efficiency model, you want the simple answer so you can tweak the macro with other variables to get something that is conclusive and repeatable. Applying proportionality tables like nc0gneto suggests is good though, but you don't seem like you're ready for that much work just yet.

 

[nc0gnet0]

lol

BNB has opened a can of worms. Users without components will create imaginary variables. Also, you need to decide whether you want to apply proportionality formulation or avoid it. Whatever is suitable, after all this is simply logistical analysis, so if you are building an efficiency model, you want the simple answer so you can tweak the macro with other variables to get something that is conclusive and repeatable. Applying proportionality tables like nc0gneto suggests is good though, but you don't seem like you're ready for that much work just yet.

Yeah, tons of variables could apply, assuming this is a call center scenario. Some people might be willing to wait 5 minutes, others 20, while others maybe 1 hour. Then you have to figure for peak call rate times, slow times etc (highly doubtful you will be receiving exactly the same amount of calls per hour every hour, regardless of time).

If we were given the overall number of workers, that would at least let you solve for 0 call loss. However, it is highly doubtful that would be the most profitable business model, as ultimately a good portion of those callers that hung up would call back, hopefully during non-peak times......

 

[Crystallas]

Gary Larson may draw a comic cell of this scenario.

Professor Frink from the Simpsons will portary the 'extra' and prime Tara Reid(for her voice) is the regular.

with a caption that says. "And they could never figure out why so many eager customers hung up when Frink came in to help"

 

[Warrior Spirit]

This cannot be figured without making assumptions and when you assume...

[video=youtube;LfvTwv5o1Qs]https://www.youtube.com/watch?v=LfvTwv5o1Qs[/video]

 

[Tater]

Trick question. Who the hell wants to pay to see the Bears?

 

[Raskolnikov]

the easy answer is 220. to be exact you need the average time before a customer hangs up with ncGnoeto's formula and come up with probably 222 or something, 225ish