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Median-Median Line

Median-Median Line. MM2D2b Examine the issues of curve fitting by finding good linear fits to data using simple methods such as median-median line and “eyeballing.”. Median-Median Line. Median-Median Line The line is fit only to summary points, Key points calculated using medians.

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Median-Median Line

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  1. Median-Median Line MM2D2b Examine the issues of curve fitting by finding good linear fits to data using simple methods such as median-median line and “eyeballing.”

  2. Median-Median Line • Median-Median Line The line is fit only to summary points, Key points calculated using medians.

  3. Median-Median Line • Step 1 • Organize the data so that x is from least to greatest. • Separate the coordinates into three equal sized groups. If the number of coordinates is not divisible by three, make sure the 1st and last group have an equal number of coordinates.

  4. Median-Median Line • Step 1 (1, 48), (2, 42), (2, 50), (4, 45), (5, 69), (6, 44), (7, 82), (7, 93), (8, 96)

  5. Median-Median Line • Step 2 • Find the median x-value and the median y-value for each group Groupx-valuesy-valuesMedian x-valueMedian y-value 1 1, 2, 2 42, 48, 50 2 48 2 4,5,6 44, 45, 69 5 45 3 7,7,8 82, 93, 96 7 93

  6. Median-Median Line • Step 3 • Create a summary point for each group by combining the median x-value and the median y-value into an ordered pair. Group 1: (2, 48) Group 2: (5, 45) Group 3: (7, 93)

  7. Median-Median Line • Step 4 • Determine the equation of the line between the two outer points by finding m and using point-slope form to write the equation. m= 93-48 = 9 y-48=9(x-2) y=9x+30 7-2

  8. Median-Median Line • Step 5 • Move the equation one-third of the way toward the middle summary point. Middle summary point: (5, 45) Predicted value at x=5; y=9(5)+30=75 One-third difference between y=45 and y=75 1/3(45-75)=-10 New equation y=9x+30-10=9x+20 The equation of the median-median line is y=9x+20.

  9. Median-Median Line • Example 1 Find the equation of the median-median line for the data: (1, 22) (2, 27) (2, 20) (3, 15) (4, 19) (5, 10) (5, 14) (6, 9) (8, 7) (8, 11) (8, 13) (9, 5)

  10. Median-Median Line • Group x-values y-values 1 1, 2, 2, 3 15, 20, 22, 27 2 4, 5, 5, 6 9, 10, 14, 19 3 8, 8, 8, 9 5, 7, 11, 13 Median x-value Median y-value 1 2 21 2 5 12.5 3 8 9 Summary point Group 1 (2, 21) Group 2 (5, 12.5) Group 3 (8, 9)

  11. Median-Median Line Group 1 (2, 21) Group 2 (5, 12.5) Group 3 (8, 9) m= 9-21/8-2=-2 y-9=-2 (x-8) Y = -2x+25 Move Middle Summary Point (5, 12.5) At x=5, y=-2(5)+25 y=15 One-third between 12.5 and 15=1/3(12.5-15)=-.8 New equation y=-2x+25-.8 or y= -2x +24.2

  12. Median-Median Line Page 251 (13) Page 253 (10)

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