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The Median-Median Line

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Process zSort the collected data by the independent variable (x). “SORT” zDivide the sorted data into three equal sized groups. If the number of coordinates is not divisible by 3, make sure the first and last group have the same number of coordinates. “SEPARATE” zOrder the dependent variable (y) within each group. The original x and y-values may be no longer be together. “SORT”

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Process zFind the median x and the median y of each group and write as an ordered pair called a summary point (median x, median y). zFind the slope of the line that passes through the first and last summary points (x 1, y 1 ) and (x 3, y 3 ). “SLOPE” zSince the median-median line is parallel to the line through these points, it will have the same slope.

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Process zThere are many ways to determine the y- intercept. One method is to use the formula: “Substitute” zWhen the slope and y-intercept have been determined, write the equation of the line in y = mx + b form.

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Write the Median-Median Line for this Wave Data

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Organize the Data Order the data by the x-values. Separate into 3 equal-sized groups, then order the y- values within each group. Find the median x and median y of each group.

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Find the slope of the line through (x 1, y 1 ) and (x 3, y 3 ). zSince the median-median line is parallel to this line, it will have the same slope.

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Find the y-Intercept

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Write the Equation y = 1.3x – 1.3 The red line is the median-median line. Is this a good representation of the data?

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Find the median-median line 294 179 040.580 385 5100 1.570 2.586 The following data set compares each student’s study time (in hours) to their grade on an exam (out of 100). Study time Grade 040.58079 1 80 1.570 294 2.58685 3 86 5100 Grade Study time Rearranged Grades Median Points (.5, 79) (1.75, 82) (3,86)

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Study time vs. Grade Cont’d z(x 1, y 1 ) = (.5,79) z(x 2, y 2 ) = (1.75,82) z(x 3, y 3 ) = (3,86) Slope between (x 1, y 1 ) and (x 3, y 3 ) Slope

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Almost there! zNow, we have the slope of the median- median line. To find the y-intercept, use the formula…

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Put it together… zThe slope is 2.8 zThe y-intercept is 77.43 zPutting the parts into y = mx + b, zMedian-median line: y = 2.8x + 77.43

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What do you think? z If you needed to get a 82 on the exam to pass the class, what is a good prediction for the number of hours you need to study? zIf you still have not taken the exam, what grade would you expect to get if you study for ¼ of an hour?

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Point slope form of an equation Y - y₁ = m(X- x₁) (x₁, y₁) An ordered pair on the line m slope.

Point slope form of an equation Y - y₁ = m(X- x₁) (x₁, y₁) An ordered pair on the line m slope.

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