Warm Up This data, from 2005, shows the scores of 8th graders on a standardized math test. Make a histogram of this data set and comment on the distribution. Would mean and standard deviation be an appropriate summary for this data? State Score State Score Alabama 225 New Hampshire 246 Arizona 235 New York 238 California 231 Nevada 221 Idaho 242 Oregon 238 Kansas 246 Texas 242 Mississippi 230 Vermont 244 Montana 241 Washington 242

Scatterplot Unlike one variable data, we will mainly use scatterplots to plot bivariate data.

Interpreting a Scatterplot Direction – As x-axis variables increase do y-axis variables increase (positive association), decrease (negative association) or neither (no association)? Form – Is the correlation between x-axis and y-axis variables linear or does it follow some other function? Strength – Is the correlation consistent or is there a lot of variation? Outlier – An individual point that is outside the overall pattern

Interpreting a Scatterplot Correlation between 2 variables does not mean there is a “cause and effect” relationship. Correlation may be due to a third variable, sometimes called a lurking variable. Correlation may be due to simple coincidence or chance.

Practice The horsepower ratings and expected gas mileage for several cars are shown below. Make a scatterplot of the data and interpret the plot. Can we say that horsepower affects the gas mileage of a car? Horsepower Gas Mileage Horsepower Gas Mileage 200 32 295 21 230 30 140 40 200 30 166 34 148 32 138 36 291 22 306 28 300 20 300 18

Interpreting a Scatterplot Which scatterplot shows a stronger association?

Correlation coefficient - r

Graphing Calculator Practice The horsepower ratings and expected gas mileage for several cars are shown below. Horsepower Gas Mileage Horsepower Gas Mileage 200 32 295 21 230 30 140 40 200 30 166 34 148 32 138 36 291 22 306 28 300 20 300 18 Enter horsepower into L1 and gas mileage into L2 on your calculator.

Activity Is there a correlation between the length of a person’s foot and the size of their hands? Work with your partner to measure the length of your foot and the “width” of your hand from thumb tip to pinky tip (in centimeters). Write your data as an ordered pair on the board (foot length, hand width)

Activity 1) Enter the data into your calculator – foot length in L1 and hand width in L2. 2) Make a scatterplot using your calculator and sketch it on to your paper. 3) Describe the Direction, Form, Strength and Outliers in your scatterplot. 4)Calculate the correlation coefficient for our data set. 5) What does this tell us about the relation between foot length and hand width?