Warm Up To qualify for security officers’ training, recruits are tested for stress tolerance. The scores are normally distributed, with a mean of 62 and a standard deviation of 8. If only the top 15% of recruits are selected, find the cutoff score.

Think/Pair/Share Ideal boyfriend or girlfriend.

Dr. Ballard’s Little Problem I am 5’2”. My husband is 6’7”. Is that weird? Do women typically date/marry men taller than themselves? Do tall women typically date taller men than do short women? How could I find out?

Chapter 4 Overview Chapter 3 dealt with descriptions of a single variable. Chapter 4 presents basic data analysis for relationships between two quantitative variables. The most common statistical tools discussed: scatterplots correlation least-squares regression

Today’s Essential Question: What is a scatterplot, how do I create one, and what does it tell me? S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Lesson 6: Scatterplot A scatter plot is a graph made by plotting ordered pairs in a coordinate plane to show the relationship between two sets of data. Scatter plots will easily show a relationship exists between two sets of data .

Examples The scatter plot shows the hours of study and test scores of 20 students. As the number of hours of study increases, the marks scored tend to increase.

Taller or Shorter? I wonder if tall women tend to date taller men than do short women. So I gathered data from teachers here at GMC! The data is on the handout. Construct a scatterplot to show the relationship between women’s and men’s heights.

Taller or Shorter?

Response vs. Explanatory In many studies more than one variable is recorded per case or individual. It is often the purpose of the study to determine if and/or how one or more variables affect another. Response Variable—A variable you would be interested in predicting. A result. Often called a dependent variable. Plotted on the y-axis. Explanatory Variable—Any variable that explains the response variable. A cause. Often called an independent variable. Plotted on the x-axis. What was women in my example? Men? Why?

Examples Determine which variable is the explanatory variable and which is the response variable. In cases with no relationship write none. Hair length and shoe size A family’s income and the years of education their child completes Price of a house and square footage Amount of time spent studying and grade on exam The weight of a person and the height of a person A student’s scores on the SAT Math test and the SAT Critical Reading test

How to Save a Life Studies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest. How is the survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered? The question is addressed in the paper “Improving Survival from Sudden Cardiac Arrest: The Role of Home Defibrillators.” The data below give the survival rate (percent) and mean call-to-shock time (minutes) for 5 different cardiac rehabilitation centers. Construct a scatterplot to show the relationship between survival rate and mean call-to-shock time. Call-to-shock time (min.) 2 6 7 9 12 Survival rate (%) 90 45 30 5

How to Save a Life

Want a Quicker Way? L1: Explanatory/independent/x L2: Response/dependent/y 2ndStatPlotPlot1 On1st type Xlist: L1 Ylist: L2 Zoom9:ZoomStat

Today’s Essential Question: What is a scatterplot, how do I create one, and what does it tell me?

Interpreting Scatterplots Look for an overall pattern. Form: Strength: Direction:

Form Examples

Strength Examples

Positive A scatter plot describes a positive association if, as (x variable) set of  values  increases, the other (y variable) values tends to increase. 

Negative A scatter plot describes a negative association if, as (x variable) set of values increases, the (y variable) set tends to decrease.

None A scatter plot shows no association if the ordered pairs show no trend.

Direction Examples

Examples, Revisited Determine whether the data would show a positive, negative, or no correlation. Hair length and shoe size A family’s income and the years of education their child completes Price of a house and square footage Amount of time spent studying and grade on exam The weight of a person and the height of a person A student’s scores on the SAT Math test and the SAT Critical Reading test

Let’s Tie the Knot! Materials: rope, measuring tape, paper, pencil What is the relationship between the length of a rope and the number of knots tied in it?

We’re Tying the Knot… Response variable: Explanatory variable: Demonstration Collect your data! Plot your data—by hand, please  Describe your data—direction, strength, form Save your data—I’ll collect to use on Wednesday

Today’s Essential Question: What is a scatterplot, how do I create one, and what does it tell me?

Scatterplot Worksheet Due Wednesday Homework Scatterplot Worksheet Due Wednesday

3-2-1 Ticket Out The Door 3 things you did today 2 things you learned 1 question you still have