Warm UpTo 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 OverviewChapter 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

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.

Today’s Essential Question:

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.

Examples

As the number of hours of study increases, the marks scored tend to increase.

The scatter plot shows the hours of study and test scores of 20 students.

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. ExplanatoryIn 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.

ExamplesDetermine which variable is the explanatory variable and which is the response variable. In cases with no relationship write none.1. Hair length and shoe size2. A family’s income and the years of education their child

completes3. Price of a house and square footage4. Amount of time spent studying and grade on exam5. The weight of a person and the height of a person6. A student’s scores on the SAT Math test and the SAT

Critical Reading test

How to Save a LifeStudies 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 12Survival rate (%) 90 45 30 5 2

How to Save a Life

Want a Quicker Way?

• L1: Explanatory/independent/x• L2: Response/dependent/y• 2ndStatPlotPlot1• On1st type• Xlist: L1• Ylist: L2• Zoom9:ZoomStat

What is a scatterplot, how do I create one, and what does it tell me?

Today’s Essential Question:

Interpreting Scatterplots

Look for an overall pattern.

1. Form:

2. Strength:

3. Direction:

Form Examples

Strength Examples

PositiveA 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, RevisitedDetermine whether the data would show a positive, negative, or no correlation.1. Hair length and shoe size2. A family’s income and the years of education their child

completes3. Price of a house and square footage4. Amount of time spent studying and grade on exam5. The weight of a person and the height of a person6. 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

What is a scatterplot, how do I create one, and what does it tell me?

Today’s Essential Question:

Homework

Scatterplot WorksheetDue Wednesday

3-2-1 Ticket Out The Door

• 3 things you did today• 2 things you learned• 1 question you still have