A Tale of Two Medians

Determine the median of Oxford's crew (with coxswain), then determine the median without the coxswain.

# Data for all 18 crew members
oxfordWeights = [186, 184.5, 204, 184.5, 195.5, 202.5, 174, 183, 109.5]

# Sort the data, lowest value to highest value
oxfordWeights.sort()

# Display the sorted data
print oxfordWeights

# How to find the median:
print "Finding Median #1:"
print "The value in position", (len(oxfordWeights) + 1)/2.0, "of this list is the median."
print ""

# Data for just 16 crew members, without coxswains
oxfordWeightsNoCox = [186, 184.5, 204, 184.5, 195.5, 202.5, 174, 183]

# Sort the data
oxfordWeightsNoCox.sort()

# Display the sorted data
print oxfordWeightsNoCox

# How to find the median:
print "Finding Median #2:"
print "The value in position", (len(oxfordWeightsNoCox) + 1)/2.0, "of this list is the median."

Save the program as oxford-median.py.

What you should get

After clicking Run, you should get this:

[109.5, 174, 183, 184.5, 184.5, 186, 195.5, 202.5, 204]
Finding Median #1:
The value in position 5.0 of this list is the median.

[174, 183, 184.5, 184.5, 186, 195.5, 202.5, 204]
Finding Median #2:
The value in position 4.5 of this list is the median.

To find median #1, we have to count five items in, from the left or the right. What is the median? It is 184.5 pounds.

To find median #2, we have to count four and a half items in. Since there can't be a fourth-and-a-half item, just calculate the average between the item that is fourth from the left, 184.5, and the item that is fourth from the right, 186. So, what's the median? It is (186 − 184.5)/(2) = 185.25.

Notice how close in value median #1 (184.5) and #2 (185.25) are. The median tool is not affected much by outliers like a coxswain, so it is a robust estimator of data.

Study Drill

• Calculate the means for Oxford's crew with and without the coxswain. How different are the two means? Reflect on why the mean tool is not a robust estimator like median.