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Standard Deviation?
In my statistical analysis of mile splits and
times, I calculate two different standard deviations: an individual standard
deviation among your mile splits and a team standard deviation within the
different individual times from the race.
Standard
Deviation is a “measure of central tendency.” The standard deviation among your
mile splits measures on average how spread apart your mile splits was from your
average pace. In other words, it measures how consistent you ran.
Example: At
Cincinnati I ran 26:41. My mile splits were 5:17, 5:19, 5:24, 5:17, and 5:24. My
pace for the race was 5:20.2.
So with my race
at Cincinnati, first we subtract the mile splits from my pace. These are the
deviations from the average.
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(x- µ) |
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Mile 1 |
(5:17 – 5:20.2) = -3.2 |
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Mile 2 |
(5:19 – 5:20.2) = -1.2 |
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Mile 3 |
(5:24 – 5:20.2) = 3.8 |
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Mile 4 |
(5:17 – 5:20.2) = -3.2 |
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Mile 5 |
(5:24 – 5:20.2) = 3.8 |
If you add up those differences it will equal zero. That should make sense,
because we adding the time the splits are from the average pace. That is why we
square these differences. These are the squared deviations from the average.
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(x- µ)2 |
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Mile 1 |
(-3.2)2 =
10.24 |
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Mile 2 |
(-1.2)2 =
1.44 |
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Mile 3 |
(3.8)2 =
14.44 |
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Mile 4 |
(-3.2)2 =
10.24 |
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Mile 5 |
(3.8)2 =
14.44 |
The next step is to add up these squared deviations.
10.24 + 1.44 + 14.44 + 10.24 + 14.44 = 50.8
Next we take the average of these, so we divide by 5 in this case (since we have
5 mile splits). 50.8/5 = 10.16. This number is called the variance. The standard
deviation is the square root of this number. Sqr(10.16) = 3.19 (rounded to the
nearest hundredth).
So my standard deviation among my mile splits was 3.19 seconds. That means “on
average my mile splits were 3.19 seconds away from my pace.” If you go back to
see my mile splits, you will see this to be about right. That means I ran a
fairly consistent race. Usually we try to keep this number less than 10 seconds.
Generally, you don’t want you splits to vary more than ten seconds from your
pace. (Note: With the girls splits, for the third mile split, I use your pace
instead of your time for the last 1800 meters.)
The standard deviation for the team is calculated the same as it is for the
standard deviation in the mile splits, but the interpretation is a little
different. In this case we are using the average time for the team for a
particular race, and seeing “on average how far apart each runner is from this
the team average time.”
At Cincinnati the guys’ average time was 27:57. Their standard deviation was
12.67 seconds. This was for the first 5 runners. That means, on average their
times were 12.67 seconds off 27:57 (either faster or slower). Our guys’ standard
deviation was excellent. However, really good teams have a fast average time as
well as a small standard deviation.
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