How many significant figures should I report?

The importance and validity of significant figures is not what you probably think it is.

First, as you are doing calculations you should always retain more digits (at least 2 or 3) than the number of significant figures you wish to report at the end of your calculations. If you round at each step, the results become very prone to compounding errors and even if you do everything right you can be off by a lot. Only round off at the very end when reporting the final value. This applies to subsequent calculations too. If you use a previous answer to perform more calculations, use the value before rounding when you continue to avoid rounding error. Answers to assignment and exam questions will be graded with a narrow window for credit and too much intermediate rounding may result in points being lost even if the steps performed are correct.

In the real world of biological research and measurement we rarely actually know anything to great precision and we report our means with standard errors (you learn about this in this course) to provide a range within which we think the true value is. For example, a scientist should never say, "the mean body temperature of the set of patients is 98.6 degrees" even if that is the mean they get from their measurements. They should instead say something like, "the men body temperature of the patients is 98.6 with a 95% confidence interval of plus or minus 0.3 degrees." The first erroneously claims to have perfect precision whereas the second conveys the degree of uncertainty in a quantitative manner.

Why should I take this course?

A few semesters ago a student in Bio 260 was having trouble and considering dropping. She shared these thoughts with a friend who sent her the following email message from a third person. I didn't write this, but find it useful to share. I have censored the names, but left everything else the same (including grammar errors).
Link to copy of the email: why-study-biostats1.pdf

I also received this card from a student recently. I have censored their name, but their words will hopefully motivate you.
Link to picture of the card: why-study-biostats2.jpg

What is the deal with "i" and "j" in the subscripts of summations?

The index subscripts representing rows and columns in a data set are arbitrary, the "i" and "j" are meaningless, what matters is which is first or second. In this class we always use the first to reference the row and the second to reference the column.

For example, X_2,i would reference the value in the second row and i^th column, the use of an "i" is arbitrary, only the position matters.

Similarly if I asked you to find X_c,d and c=3, d=7 this would reference the value in the 3^rd row and 7^th column.