Formula for missing person's weight from team of 5

[20GT]

Our company is holding a weight loss contest consisting of 5 people teams. If one of the people weigh in but can't weigh out is there a fair formula to find out what that team lost?

 

[20GT]

The teams weighed in on a bulk scale at one time. Individuals weight not recorded.

 

[20GT]

Corporate says they are going to use a formula. How can the formulate whether a person will be successful in losing weight and not gain weight? We have one team member that has gained 2lbs.

 

[disregardthat]

If one of the people weigh in but can't weigh out is there a fair formula to find out what that team lost?

What do you mean by a person weighing in, and weighing out?

What do you mean by finding out what a team lost?

 

[mfb]

You can compare the averages, but you have no way to tell if that missing person gained or lost weight, of course.

 

[20GT]

the contest is based on weight loss. All teams stepped on the the bulk scale as a team one at a time. The one weight total was recorded as the way in. Next Thursday we have to repeat the process. The team weight total will be recorded as the weight out. The team that lost the most weight percentage will win.

One person has quit their job and they will not be available for the team weigh out. That team will have four out of five people. Corporate says they will use a Formula to estimate the missing person's weight.

is there a formula that can correctly estimate this? I don't think so but I'm not a mathematician.

 

[20GT]

if there are no individual weight how they can they compare averages?
we feel it is unfortunate but the team with 4 people must be disqualified

 

[20GT]

there is a $1000 grand prize split between the 5 people on the team.

 

[mfb]

if there are no individual weight how they can they compare averages?

You can just divide the weight by the number of persons getting weighted.

This would be easy to exploit - let the heaviest person be missing for the second weighting, and the average goes down just due to this.
A disqualification would be the most reasonable choice, I think.

 

[cpscdave]

there is a $1000 grand prize split between the 5 people on the team.

4 people on a team loose 10lbs each. person 5 gains 50 lbs. I'd suggest that the fifth person not weigh out :)

Do something like
Weight loss = Start_Weight - (End_Weight + Start_Weight/5*People_Missing)
For example my team of 5 people weight 1000lbs at the start
When weighing out only 4 people show up weighing 780lbs. Their weight loss would be:
1000 - (780 + 1000/5*1) = 20lbs

 

[larrybud]

I think the only fair way to do this would be average weight loss PERCENTAGE per person.

Much easier to drop 20 lbs when you weigh 300 rather than 200.

 

[disregardthat]

The formula they are thinking about is probably given by assuming that the missing individual lost the average of all percentages of weight loss. So each person lost some X% of his weight. Taking the average of all these percentages and substituting it into the predicted percentage wise weight loss for your missing teammate is reasonable.

 

[disregardthat]

Given the health oriented aspect of this contest I wouldn't hold it against the heavier ones that they lost relatively less weight than their skinnier counterparts in any way, especially not by saying it's easier for them...

 

[mfb]

The formula they are thinking about is probably given by assuming that the missing individual lost the average of all percentages of weight loss. So each person lost some X% of his weight. Taking the average of all these percentages and substituting it into the predicted percentage wise weight loss for your missing teammate is reasonable.

We cannot do this, as we don't know the individual starting weights. We would have to add the additional assumption that the missing person ("X") has the average weight, or some other assumption about X's weight. Otherwise we can't do anything.

 

[20GT]

we have been told, corporate has a formula that will make the fifth person look like they didn't lose or gain any weight.

But as mathematicians, you guys are saying, with just the starting team weight, and the ending team (minus one persons) weight alone it is impossible to do that.

can you explain to me how this is theoretically impossible so that I can put it into an e-mail to corporate ?

 

[mfb]

we have been told, corporate has a formula that will make the fifth person look like they didn't lose or gain any weight.

But as mathematicians, you guys are saying, with just the starting team weight, and the ending team (minus one persons) weight alone it is impossible to do that.

can you explain to me how this is theoretically impossible so that I can put it into an e-mail to corporate ?

It is impossible if they just have the summed weight.

Just consider two different cases that look the same for the scale, but different for the claimed calculation:

100kg, 100kg, 100kg, 100kg, 100kg -> 80kg, 80kg, 80kg, 80kg, missing
Weight goes down form 500kg to 320kg, weight loss within the 4 active participants is 80kg.

90kg, 90kg, 90kg, 90kg, 140kg -> 80kg, 80kg, 80kg, 80kg, missing
Weight goes down form 500kg to 320kg, weight loss within the 4 active participants is 40kg.

 

[20GT]

I will try to get them to reveal their "magic formula" and post it here so you guys can get a kick out of it.

in the meantime, what formula did you think, they will try to use. They will undoubtedly have to use an estimated variable.

Using an estimate variable what do you think their formula will look like?

 

[disregardthat]

From what I gather from your posts 20GT, that they want to make it seem like he haven't lost any weight at all, it seems to me that they want to simply plug in the average of the initial weights of the missing persons group as his final weight.

 

[mfb]

@20GT: They could assume that the weight of X at the start is the same as the average of the others, then
(summed weight loss) = 4/5 * (starting weight of 5) - (final weight of 4)

I don't see reasonable other assumptions.@disregardthat: I don't think it is reasonable. If X is heavier than average, you get a lot of imaginary weight loss (formula gives a large result without actual weight loss of anyone).

 

[disregardthat]

It is more likely he he closer to the average of his group than the average of everyone since he participated in his groups initial weigh in.

 

[mfb]

That makes it 20% less bad (as 20% of the weight* in the average comes from him), but still problematic.

*the mathematical weight, not the one in kg.

 

[20GT]

Thanks everyone

 

[20GT]

He was taller and fatter than the rest.
2 normal looking weights
1 short fat person
1 short stocky person