How is error and uncertainty in data assessed & quantified

[draks]

In the following question the points were scattered in a graph with a negative gradient. The scatter was obvious. A best fit line was drawn. How do I quantify the uncertainty?

Estimate the uncertainty on your distance by considering the possible range of
values for the best-fitting distance modulus. [2 marks]

Estimate the age of the Hyades cluster with an
approximate associated uncertainty. [3 marks]As a guess I just drew 2 parallel lines to the best fit, one went through the greatest point and the other through the least point.

The work has been submitted so your kind reply will not improve my mark but my mark will be honest.

As a matter of importance, when I am presented with data values with no mention of error ranges in the table how can I give a value of error to the data.

A major mark looser has been answers quoted to too many sig figs. eg 3.1415926588 instead of 3.1. I have known this since childhood and have endured punishment for too many sig figs at that time. Are there any tutorials in these arena?

Thank you in advance for your kind attention

 

[jbsteele]

.For quantifying the uncertainty in the best fit line, you can use the standard deviation of the data points from the best fit line to estimate the range of possible values. For example, if the standard deviation is 0.1, then you can assume that the best fit line could lie anywhere between 0.1 above and 0.1 below the best fit line. To estimate the age of the Hyades cluster with an associated uncertainty, you will need to consider the uncertainties related to the distance measurements of the stars in the cluster. This can be done by calculating the mean and standard deviation of the measured distances and using this to calculate a likely age range for the cluster.

 

[kerimek]

.

Thank you for your question. As a scientist, it is important to assess and quantify the error and uncertainty in data in order to accurately interpret and draw conclusions from the results. In the scenario you have described, the scatter in the data points and the negative gradient of the graph indicate that there is some level of uncertainty in the data.

One way to quantify this uncertainty is by calculating the standard deviation of the data points from the best fit line. This will give you a measure of how much the data points deviate from the line, and therefore, the level of uncertainty in the data. Additionally, you can also calculate the coefficient of determination (R-squared value) which indicates the percentage of variation in the data that is explained by the best fit line. A lower R-squared value would indicate a higher level of uncertainty in the data.

In order to estimate the uncertainty in your distance measurement, you can consider the possible range of values for the best-fitting distance modulus. This can be done by calculating the upper and lower bounds for the distance modulus using the standard deviation and incorporating these values into your final distance measurement.

Similarly, to estimate the age of the Hyades cluster with an approximate uncertainty, you can use the same approach by considering the range of values for the best-fitting age. The uncertainty can then be calculated by incorporating the standard deviation into your final age measurement.

Regarding your concern about providing an error value for data with no mention of error ranges, it is important to communicate with the data provider and understand the methods and techniques used to obtain the data. This will help in determining the appropriate error values to assign to the data.

Lastly, I understand your concern about providing too many significant figures in calculations. It is important to use the appropriate number of significant figures to avoid overestimating the precision of the data. I suggest referring to tutorials or guidelines on significant figures and practicing with sample data to improve your understanding and accuracy in this aspect.

I hope this response has been helpful. If you have any further questions, please do not hesitate to reach out.

Best regards,