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Given an Ostrich egg with known density, what is its age?
Here is the data file: click here to see

Answer 1:

Here I added a linear regression to the data you plotted, giving an equation in the form
y = mx + b

We invert this equation (x = [y - b] / m) to find an equation for the year in terms of the egg density. We must be careful to restrict our analysis only to eggs which have ~0.3 > density > ~ 0.175 to fall within our interpolating limits.

To find an error associated with this interpolated year, we calculate the standard deviation in the residuals of the plot. To do this, we find estimated values for the age each known egg, and subtract the true age. Here we find that our curve is off by about 40 years (mean) for each egg.

We're looking for a confidence interval, such that we're 95% sure that our egg has an age within a certain range. Invoking the assumption that our errors are normally distributed (wikipedia 'normal distribution'), which seems to be appropriate in this case, a 95% confidence interval encompasses values up to 2 standard deviations away from the calculated value. In this case, +/- 41.2 years.

Therefore, given an egg of density 0.250, you could be 95% sure it came from sometime between 1720 and 1800.

Best,

Answer 2:

Eggs are egg-shaped. The calculations you did are not useful for eggs. Therefore, the graph you made is not useful. The only numbers that are useful for graphs are the numbers you measured directly. See the attached spread sheet and the extra pages with the graphs that can be made for your data.
Comparative- Analysis
Picture of Ostrich Egg 1
Picture of Ostrich Egg 2
The axes of the graphs are given in the names of the extra pages. These new graphs don't show any good correlations with time.

Other comments:
1. You call them ostrich eggs, but you measure the thickness of the shells, so they must be ostrich egg Shells?
2. You give weights, but if the weights are for ostrich egg shells of known thickness, the shells have a hole in them, so you don't know the weight of the entire shell?
3. If you want to do good science, you need to get a few fresh ostrich eggs and make your measurements on them. Then you can see how much the fresh ostrich eggs vary in the different measurements you are making. You need this baseline data, before you can say anything about the few old ostrich eggs you have.

Sincerely,


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