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Influence of a Single Observation
It is interesting to consider the influence of a single observation
on the median. On the one hand, we don't want our estimate of the typical observation to
be overwhelmed by a single data value. On the other hand, we want our estimate to make the
best use of all the information. In the graph below you can examine how much the median changes
as you alter the value of a single observation. As you do so, try to determine whether
the median can be overwhelmed by a single observation and whether the median is sensitive
to changes in the single observation.
These data are the speeds in
miles per hour of nine cars observed on a residential street with a posted speed limit of
25 mph. Change the speed of the last car to see what effect it has on the median.
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Use your mouse to drag the green data point up or
down to change its value. As you move the data point, the median is automatically
recalculated. The median is displayed numerically at the top of the graph and graphically
as the blue line. To avoid clutter, the red error lines included in previous graphs have been removed.
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Summary for the Median
- The median is a useful estimate of the value of a typical or center
observation.
- To find the median, order the data from smallest to largest and find
the middle observation; it is the median. If there are an even number of observations,
then there will be two observations in the middle; in that case, average those two middle
observations to find the median.
- The median is not influenced by extreme observations.
- The median is not sensitive to all the information available in the
data.
Next we will consider an alternative method for estimating the
typical observation.
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File:
© 1999, Duxbury Press.
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