WARM – UP Mean = Range = Median = Standard Dev. = IQR = 3 4 1.41 2 1.) Identify the Mean, Standard Deviation, Median, Range and IQR for each data set: Which values are Robust? a.) 1, 3, 3, 3, 5 b.) 1, 3, 3, 3, 5, 300 Mean = Range = Median = Standard Dev. = IQR = 3 4 1.41 2 Mean = Range = Median = Standard Dev. = IQR = 52.5 299 3 121.25 2 2.) Domestic house cats have an average weight of 10 lbs. σ = 3 lbs. What are you more likely to find, a cat weighting 6 lbs. or one weighing 15 lbs.?

2.) Domestic house cats have an average weight of 10 lbs. σ = 3 lbs. What are you more likely to find, a cat weighting 6 lbs. or one weighing 15 lbs.? Normalcdf(-E99, -1.333) = 0.091 Normalcdf(1.667,E99) = 0.048

CENTER, UNUSUAL, SPREAD, SHAPE WARM - UP What are the four characteristics that one comments on when asked to analyze a HISTOGRAM or BOXPLOT? CENTER, UNUSUAL, SPREAD, SHAPE Univariate data

Associations among Bivariate Data CHAPTER 7 Associations among Bivariate Data A Scatterplot shows the relationship between two quantitative variables.

Interpreting Scatterplots The Scatterplot reveals Form, Direction, and Strength. FORM: Linear Patterns Non-Linear = Curved Patterns Clusters DIRECTION: Positively Associated – Upward linear trend. Negatively Associated – Downward linear trend.

0.5 ≤ |r|< 0.9 = MODERATELY STRONG |r| ≥ 0.9 = VERY STRONG STRENGTH: The CORRELATION measures strength (how linear the data is) and direction of the linear relationship between two quantitative variables. Symbol = r -1 ≤ r ≤ 1 |r| < 0.5 = WEAK 0.5 ≤ |r|< 0.9 = MODERATELY STRONG |r| ≥ 0.9 = VERY STRONG

Different Correlation Strengths

Different Correlation Strengths

Describe the association’s Form, Direction, and Strength CORRELATION = r Is there a relationship between student quiz grades and their test grade? Quiz Avg. 75 86 92 95 80 Test Avg. 79 100 90 Describe the association’s Form, Direction, and Strength

Quiz Avg. 75 86 92 95 80 Test Avg. 79 100 90 r = ¼ [1.7449 + -0.0239 + 0.9577 + 0.7033 + 0] r = ¼ (3.382) = 0.8455

Quiz Avg. 75 86 92 95 80 Test Avg. 79 100 90 99 Quiz Avg. 75 86 92 95 80 Test Avg. 79 100 90 r = 0.8455 r = -0.287

Page 160: 5,6,11,12,17,20

Page 160: 5,6,11,12,17,20

FACTS ABOUT CORRELATION Positive r refers to positively associated variables while negative r refers to negatively associated variables. (The Pos./Neg. sign of ‘r’ matches the slope’s sign.) 2. Correlation is ALWAYS between -1 ≤ r ≤ 1. The correlation is strong when r is close to 1 or -1 but weak when r is close to zero. 3. r has NO UNITS. 4. Correlation is only valuable for LINEAR relationships. Like the Mean and Std. Dev., Correlation is non-resistant and is very influenced by outliers.

NEGATIVELY ASSOCIATED, and STRONG EXAMPLE: A new antibacterial cleaner is introduced to a Petri dish. SECONDS: 1 3 4 6 8 9 BACTERIA POP.: 22 17 15 9 5 1 Construct a Scatterplot and describe the form, direction, and strength. LINEAR, NEGATIVELY ASSOCIATED, and STRONG with r = -0.998 5 10 15 20 25 BACTERIA 2 4 6 8 10 SECONDS