The Median-Median Line

8/10/2019 The Median-Median Line

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You then order the y-values within

each of the groups. The

representative point for each

group has the coordinates of themedian x-value of that group and

the median y-value of that group.

Because a good line of fit divides

the data evenly, the median-

median line should pass betweenM1, M2, and M3, but be closer to

M1and M3because they represent

two-thirds of the data.

To accomplish this, you can findthe y-intercept of the line through

M1and M3, and the y-intercept of

the line through M2that has the

same slope.

The mean of the three y-intercepts


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Example

Find the median-median

line for these data.


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1 3

60 295.08211.9 5.8

m mslope

1 3

1 3

29 5.082( 5.8)

0.475 5.082

m m

m m

y x

y x


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1 3

60 295.082

11.9 5.8m m

slope

2

2

44.5 5.082( 8.6)0.795 5.082

M

M

y xy x


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The Median-Median Line

The median-median line is parallel to both ofthese lines, so it will also have a slope of 5.082.

To find the y-intercept of the median-median line,

you find the mean of the y-intercepts of the lines

through M1, M2, and M3.

Since there is one line that passes through M1

and M2,the y-intercept for these lines are both -0.475. The y-intercept of the line through M

3is

0.795.

The mean of the y-intercepts is

So the equation of the median-median line is

20.795 5.082

My x

1 30.475 5.082

m my x

-0.475 + (-0.475) + 0.7950.052

3

0.052 5.082median median

y x


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Finding a Median-Median Line

1.Order your data by domain value first. Then, divide thedata into three sets equal in size. If the number of pointsdoes not divide evenly into three groups, make sure thatthe first and last groups are the same size. Find themedian x-value and the median y-value in each group. Callthese points M1, M2, and M3.

2.Find the slope of the line through M1and M3. This is theslope of the median-median line.

3.Find the equation of the line through M1with the slope youfound in Step 2. The equation of the line through M3willbe the same.

4.Find the equation of the line through M2with the slope youfound in Step 2.

5.Find the y-intercept of the median-median line by takingthe mean of the y-intercepts of the lines through M1, M2,

and M3. The y-intercepts of the lines through M1and M3


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Airline Schedules In this investigation you

will use data aboutairline flights to find amedian-median line tomodel the relationshipbetween the distance of

a flight and the flighttime. You will use thelinear model to makepredictions about flight

times and distances thatarent in the table.

The flights listed hereare morning departuresfrom Detroit, Michigan.Write a complete


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Graph the data

on graph paper.

Show the stepsto calculate the

median-median

line through the

data. Write theequation of this

line. Use your

calculator to

check your

work.

1

2

3

(67,306)

(168.1033.5)

(288,1979)

M

M

M


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On your graph,

mark the three

representativepoints used in

the median-

median process.

Add the line to

this graph.


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Answer these questions about your data and model.

a. Use your median-median line to interpolate two

points for which you did not collect data. What is the

real-world meaning of each of these points?

b. Which two points differ the most from the value

predicted by your equation? Explain why.

c. What is the real-world meaning of your slope?d. Find the y-intercept of your median-median line.

What is its real-world meaning?

e. What are the domain and range for your data?

Why?f. Compare the median-median line method to the

method you used in Lesson 3.3 to find the line of fit.

What are the advantages and disadvantages of

each? In your opinion, which method produces a

The Median-Median Line

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