Have you got your workbook with you Have you got your workbook with you? Learning Astronomy by Doing astronomy Activity 1 – Mathematical and Scientific Methods step 5 – Simple Statistics Let’s get started!

The mean of a data set is the average, while the standard deviation gives a measure as to how spread out the data are. If we have enough data, we often make a graph to see if there is a relationship between variables. The slope of a line in a linear graph (of the kind 𝑦=𝑚𝑥+𝑏) is calculated by dividing the change in y by the corresponding change in x. We read these changes off of the axes labels by selecting two values of y and the corresponding values of x. The formula is: slope = (y2 – y1) / (x2 – x1). 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.

Graphing a linear relationship 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

Graphing a linear relationship 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.

Graphing a linear relationship 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.

Graphing a linear relationship 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?

Graphing a linear relationship 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