Problem Solving and Data Analysis Lessons 4 5

Problem Solving and Data Analysis Lessons 4 -5 Linear and Exponential Functions Two-Way Frequency Tables Two-Way Relative Frequency Tables Association and Independence

Linear Functions: y = mx + b • Watch for positive (uphill) and negative (downhill) slope • A linear function adds a constant over and over – that constant is the slope • The y-intercept (b value) is next to the Zero in your table. If there is no 0 in the table then add it and find b using the pattern

Exponential Functions: y = a▪bx • Exponential decay appears downhill and Growth appears uphill • Decay has a b < 1, Growth has a b > 1 • In a table, exponential functions have a pattern of multiplication • “b” is the number that is continually multiplied • In the table “a” is next to Zero (provided there is no shifting)

Two-Way Frequency Tables • Joint frequencies are entries in the body of the table (not borders) • Marginal frequencies are entries along the borders (totals) • Total frequency is the entry in the lower right-hand corner Relative Frequency = joint frequency total frequency Relative Marginal Frequency = marginal frequency total frequency Conditional Relative Frequency = joint frequency (conditional probability) marginal frequency

Association and Independence • Variables are said to be Independent is the conditional relative frequencies are roughly the same • If they are the same then one did not effect the value of the other • Variables are said to be Associated if the conditional relative frequencies are different • If they are different, then one is effecting the other