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Three median lines are sometimes used
instead of a least squares regression line to
describe a linear relationship
Three median lines are more appropriate than
least squares lines when outliers are involved
This is because outliers affect the mean, but
NOT the median
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In some cases, either line can be used. This is
when the pattern is linear and there are no
outliers
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In some cases, we must use the three median
line. This is when the pattern is linear but
there is an outlier
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If the relationship is not linear, we cannot use
either line
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To draw a three median line, first the
scatterplot needs to be split up into three
sections.
If the number of dots is a multiple of 3, divide
them up evenly (eg 9 dots = 3, 3, 3)
If there is one extra, put the extra dot in the
middle group (eg 10 dots = 3, 4, 3)
If there are two extra, put one dot extra in
each of the outside groups (eg 11 dots = 4,
3, 4)
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In each of the three sections of the
scatterplot, find the median in the x-direction
and the median in the y-direction. Put a dot
or an X where they meet
Remember, median is the middle NOT the
average
You should end up with three dots or X’s on
your scatterplot
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Connect a line between the first and last X
Keeping the slope unchanged, move the line
one-third of the way toward the middle X
This is difficult to judge so it will require
PRACTICE. You will get better at it after a few
attempts. We will now look at some worked
examples.
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Draw the three median line for the following
scatterplot (9 data points):
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Draw the three median line for the following
scatterplot (10 data points):
y
10
9
8
7
6
5
4
3
2
1
x
0
0
1
2
3
4
5
6
7
8
9
10
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Draw the three median line for the following
scatterplot (8 data points):
18
16
14
12
10
8
6
4
2
0
0
2
4
6
8
10
12
14
16
Using the arithmetic approach, you will
proceed as follows:
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Calculate the gradient (b) of the line. Use the
rule Gradient (b) = yU – yL

_______________
xU – xL
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Calculate the y-intercept (a) of the line. Use
the rule:
a = 1/3 [ (yL + yM + yU) – b(xL + xM + xU) ]
Thus, the equation of the regression line is:
y = a + bx
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Exercise 5D Q 1, 2, 3, 4, 5
For Q 3-5, use pencil to draw the three
median line in your textbook rather than
copying into your workbooks.