LEARNING ASTRONOMY BY DOING ASTRONOMY ACTIVITY 1 MATHEMATICAL

LEARNING ASTRONOMY BY DOING ASTRONOMY ACTIVITY 1 – MATHEMATICAL AND SCIENTIFIC METHODS STEP 5 – SIMPLE STATISTICS Let’s get started!

There are lots of web sites available that cover graphing linear relationships. We investigate here a simple example of a linear relationship and its corresponding graph, and then decide what to do when the data points do NOT lie in a perfectly straight line.

Linear relationships are completely defined by their: Independent variable x Slope of the data m y-intercept of the line b and the Dependent variable y

If we know the equation of the linear relationship (function), then we can produce a table of x values and calculate the corresponding y values and make a graph.

This graph shows all of the data in a perfectly linear relationship. We recalculated the slope of the data just to make sure we didn’t make any graphing errors.

But, rarely in nature – and certainly in astronomy – do we ever find a perfect linear relationship in our measurements. There is always an uncertainty in every measurement, and this fact results in data that are “scattered. ” What can we do about it?

Unless we use a graphing calculator or a computer software program, we find a ruler or a straight edge and draw a “best fit line” – by eye. We try to put as many data points above our line as there are below. We can then calculate the slope and the y-intercept. Easiest way to find the y and x values is to locate values that cross a grid point.

Your turn: 16. For the car with no engine problems, what is the slope of the line? _____ 
 17. What are the units of the slope? _____ (HINT: label of the y-axis over the label of the x-axis. )
 18. How fast would this car be going after 3. 5 seconds? _____ mph