# Im new to statistics and need help with this data

#### jgh234

##### New member

[h=3][/h]
1. The problem statement, all variables and given/known data
Mass (g) +/- 0.01 grams Drop height (centimeters) +/- 3.00 Shell
53.47 45 No crack
56.78 45 Cracked
59.33 35 No crack
52.96 35 No crack
55.33 40 No crack
58.44 40 Cracked

My question is on how I should go about representing the value of an egg's maximum height before it cracks. I have 5 data tables like the one below. I need to show a point for which an egg is at its highest point without cracking. I was hoping you would know of a solution to my conundrum. I saw that 70% of the eggs broke at the top of the range (this being 5 centimeters above the central value). 20% of the eggs broke at and 5 centimeters below the middle value. I got the percentages from all five of my trials, which meant that ten eggs were dropped from each value range (Middle, Maximum or 5 cm above middle, and minimum 5 centimeters below middle). I was hoping you could shed some light on the situation.

If you need the other data tables, I can send them

Again, I'm looking for the best way to represent the possible value for the maximum height an egg can be dropped without breaking

#### Dr.Peterson

##### Elite Member
1. The problem statement, all variables and given/known data
Mass (g) +/- 0.01 grams Drop height (centimeters) +/- 3.00 Shell
53.47 45 No crack
56.78 45 Cracked
59.33 35 No crack
52.96 35 No crack
55.33 40 No crack
58.44 40 Cracked

My question is on how I should go about representing the value of an egg's maximum height before it cracks. I have 5 data tables like the one below. I need to show a point for which an egg is at its highest point without cracking. I was hoping you would know of a solution to my conundrum. I saw that 70% of the eggs broke at the top of the range (this being 5 centimeters above the central value). 20% of the eggs broke at and 5 centimeters below the middle value. I got the percentages from all five of my trials, which meant that ten eggs were dropped from each value range (Middle, Maximum or 5 cm above middle, and minimum 5 centimeters below middle). I was hoping you could shed some light on the situation.

If you need the other data tables, I can send them

Again, I'm looking for the best way to represent the possible value for the maximum height an egg can be dropped without breaking

Please show the exact wording of the assignment.

As you have stated it, you just want "the maximum height an egg can be dropped without breaking", which is hardly a statistical problem. Just find the greatest height from which an egg didn't break, and that's the best answer you can give. (Of course, you can never be sure whether another egg might have been safe at a greater drop height.) But maybe you really wanted "the maximum height from which an egg can be dropped to be sure that it will not break". (Again, you can't be certain that the next egg wouldn't break from a lower height.) Or maybe you want some given probability of breaking.

Another problem, besides clarifying the goal, is that you have only tested three different heights, so you have no data about other heights, which might be necessary to answer your question.

#### jgh234

##### New member
Please show the exact wording of the assignment.

As you have stated it, you just want "the maximum height an egg can be dropped without breaking", which is hardly a statistical problem. Just find the greatest height from which an egg didn't break, and that's the best answer you can give. (Of course, you can never be sure whether another egg might have been safe at a greater drop height.) But maybe you really wanted "the maximum height from which an egg can be dropped to be sure that it will not break". (Again, you can't be certain that the next egg wouldn't break from a lower height.) Or maybe you want some given probability of breaking.

Another problem, besides clarifying the goal, is that you have only tested three different heights, so you have no data about other heights, which might be necessary to answer your question.
________________________________________________________________________________________________________________________________________________________________

Really, I want to know two things, The maximum height an egg can be dropped without breaking, and the error bar values I should use.

Before making these trials, I tested from .4 meters to the height that was fouund to be the middle height in the data. Then I raised and lowered the egg .05 meters to make sure that the egg's drop range was reasonable. Below is a data table (Sadly many eggs were killed in the making) of an egg drop with 4 layers of bubble wrap. I found a maximum height of around 1.75 meters. Then I tested the range of 0.05 meters above and below. I did this for no layers of bubble wrap, 1 layer, 2 layers, 3 layers, and 4 layers.

I don't want the probability of the egg breaking, just the best value for it's maximum height before breaking. The error bars are also important. the uncertainty of the ruler used was +/- 0.025 meters and the uncertainty of the nail used to hold the egg in place (this was important because the egg would sit a little higher than on the measured value) was +/- 0.005 meters plus 0.01 meters. The combined uncertainty for the height would be 3 centimeters plus a 1 centimeter nail raising the egg. Or should the error bars be the range in values where the egg can fall without breaking. realistically, I can't measure to the nearest centimeter, these values get supper small. So 5 centimeter was the closest I could get to observable differences in height without getting obsessive over the small values.

I was able to look at all my data again, and just want conformation on what method to use.
Here is a list of all my data.

So Just to show you the process I went to find the values of heights where the eggs were assumed to be at their max point in terms of height (I mean this took way too long).

 Mass (g) +/- 0.01 grams Height (meters) +/- .03 Egg shell 53.18 0.50 No Crack 55.87 0.60 No Crack 60.12 0.70 No Crack 53.00 0.80 No Crack 54.21 0.90 No Crack 53.61 1.00 No Crack 53.05 1.10 No Crack 52.79 1.20 No Crack 59.87 1.30 No Crack 56.73 1.40 No Crack 57.94 1.50 No Crack 58.91 1.60 No Crack 59.03 1.70 No Crack 57.63 1.80 Crack 58.05 1.85 Crack 54.30 1.75 No Crack

this was just to find the range (and this was only for the one trial with 4 bubble wrap layers)

I then did that method of raising or lowering the egg and finding the max height 4 more times plus 1 more time to prove repeatability.

 Mass (g) +/- 0.01 grams Drop height (centimeters) +/- 3.00 Shell 54.92 180.00 Crack 57.63 180.00 Crack 57.83 180.00 Crack 55.58 175.00 No Crack 54.73 175.00 No Crack 54.30 175.00 No Crack 58.92 170.00 No Crack 53.37 170.00 Cracked 59.03 170.00 No Crack

I don't know if you want all the data, but this is what method I used for all of the trials.
So, I just want to know the maximum height value it can break and the error bars I should use.

Would it be reasonable to, as you said, use the maximum height it could go without breaking? And would it also be reasonable for the error bars to be the uncertainty in height (+/- 3 centimeters)?

If so, that would be supper less statistical and easier.
Thank you

Thank you so much for bearing with me and responding.

#### jgh234

##### New member
Sadly, I think my response didn't go through, but alas, here goes another one.

Looking back at all my data, there are clear points where the egg's height reached it's maximum height without breaking or came extremly close to it. By extremly close, I mean by 5 cm, It would be darn near impossible to get it to the nearest centimeter. Anyway here is some data for the egg's drop from the chute whe four ayers were used.

 Mass (g) +/- 0.01 grams Height (meters) +/- .03 Egg shell 53.18 0.50 No Crack 55.87 0.60 No Crack 60.12 0.70 No Crack 53.00 0.80 No Crack 54.21 0.90 No Crack 53.61 1.00 No Crack 53.05 1.10 No Crack 52.79 1.20 No Crack 59.87 1.30 No Crack 56.73 1.40 No Crack 57.94 1.50 No Crack 58.91 1.60 No Crack 59.03 1.70 No Crack 57.63 1.80 Crack 58.05 1.85 Crack 54.30 1.75 No Crack

As you will see, there are a lot of points (and a lot of eggs used). But, I found an area where the eggs started to crack and the value within 5 centimeters where the eggs didn't start to crack. This part I didn't count as a trial, it was just used to find the possible range.

For my trial, I made the range around the point of not breaking and on the verge of breaking found in the above data. The trial looked like this

 Mass (g) +/- 0.01 grams Drop height (centimeters) +/- 3.00 Shell 54.92 180.00 Crack 57.63 180.00 Crack 57.83 180.00 Crack 55.58 175.00 No Crack 54.73 175.00 No Crack 54.30 175.00 No Crack 58.92 170.00 No Crack 53.37 170.00 Cracked 59.03 170.00 No Crack

As you can see, all the eggs above my middle heights broke. So my maximum height was at or around 175 centimeters. But, one egg broke at 170 meters. Could I disregard this as a dat appoint, and if so, how could I justify it?

In addition, I need help finding what error bars are most appropriate to use.

I think I can use the uncertainties (3 centimeters). If not, what would be a better value to use for the error bars?

So the two questions

What should my error bars be?
and
How can I make prove my maximum value is, in this situation, 175 centimeters and not the lower value of 170 centimeters.

Thanks