411 REFERENCE · Wikibooks
Linear Algebra/Topic: Line of Best Fit/Solutions
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
Solutions
Problem 1
Use least-squares to judge if the coin in this experiment is fair.
<TR>
<TD style="border-right:2px black solid; border-bottom:2px black solid;">flips
<TD style="border-bottom:2px black solid;"> 8
<TD style="border-bottom:2px black solid;"> 16
<TD style="border-bottom:2px black solid;"> 24
<TD style="border-bottom:2px black solid;"> 32
<TD style="border-bottom:2px black solid;"> 40
<TR>
<TD style="border-right:2px black solid;"> heads
<TD> 4
<TD> 9
<TD> 13
<TD> 17
<TD> 20
Answer
As with the first example discussed above, we are trying to find a
best to "solve" this system.
Projecting into the linear subspace gives this
so the slope of the line of best fit is approximately .
x200px
Problem 2
For the men's mile record, rather than give each of the many
records and its exact date, we've "smoothed" the data somewhat by
taking a periodic sample.
Do the longer calculation and compare the conclusions.
Answer
With this input
(the dates have been rounded to months, e.g., for a September record,
the decimal was used), Maple responded
with an intercept of and a slope of
.
x200px
Problem 3
Find the line of best fit for the men's meter run.
How does the slope compare with that for the men's mile?
(The distances are close; a mile is about meters.)
Answer
With this input (the years are zeroed at )
(the dates have been rounded to months, e.g., for a September record,
the decimal was used),
Maple gives an intercept of and a slope of
.
The slope given in the body of this Topic for the men's mile is
quite close to this.
x200px
Problem 4 Find the line of best fit for the records for women's mile.
Answer
With this input (the years are zeroed at )
(the dates have been rounded to months, e.g., for a September record,
the decimal was used),
MAPLE gave an intercept of and a slope of
.
x200px
Problem 5
Do the lines of best fit for the men's and women's miles cross?
Answer
These are the equations of the lines for men's and women's mile
(the vertical intercept term of the equation
for the women's mile has been adjusted from the answer above,
to zero it at the year ,
because that's how the men's mile equation was done).
Obviously the lines cross.
A computer program is the easiest way to do the
arithmetic: MuPAD gives and
( seconds is minutes and seconds).
Remark.
Of course all of this projection is highly dubious — for one thing,
the equation for the women is influenced by the quite slow early
times — but it is nonetheless fun.
x200px
Problem 6
When the space shuttle Challenger exploded in 1986, one of the
criticisms made of NASA's decision to launch was in the way the
analysis of number of O-ring failures versus temperature was made
(of course, O-ring failure caused the explosion).
Four O-ring failures will cause the rocket to explode.
NASA had data from 24 previous flights.
<TR>
<TD style="border-right:2px black solid; border-bottom:2px black solid;">temp °F
<TD style="border-bottom:2px black solid;"> 53
<TD style="border-bottom:2px black solid;"> 75
<TD style="border-bottom:2px black solid;"> 57
<TD style="border-bottom:2px black solid;"> 58
<TD style="border-bottom:2px black solid;"> 63
<TD style="border-bottom:2px black solid;"> 70
<TD style="border-bottom:2px black solid;"> 70
<TD style="border-bottom:2px black solid;"> 66
<TD style="border-bottom:2px black solid;"> 67
<TD style="border-bottom:2px black solid;"> 67
<TD style="border-bottom:2px black solid;"> 67
<TR>
<TD style="border-right:2px black solid;">failures
<TD> 3
<TD> 2
<TD> 1
<TD> 1
<TD> 1
<TD> 1
<TD> 1
<TD> 0
<TD> 0
<TD> 0
<TD> 0
<TR style="height:20px">
<TR>
<TD style="border-right:2px black solid; border-bottom:2px black solid;">temp °F
<TD style="border-bottom:2px black solid;"> 68
<TD style="border-bottom:2px black solid;"> 69
<TD style="border-bottom:2px black solid;"> 70
<TD style="border-bottom:2px black solid;"> 70
<TD style="border-bottom:2px black solid;"> 72
<TD style="border-bottom:2px black solid;"> 73
<TD style="border-bottom:2px black solid;"> 75
<TD style="border-bottom:2px black solid;"> 76
<TD style="border-bottom:2px black solid;"> 76
<TD style="border-bottom:2px black solid;"> 78
<TD style="border-bottom:2px black solid;"> 79
<TD style="border-bottom:2px black solid;"> 80
<TD style="border-bottom:2px black solid;"> 81
<TR>
<TD style="border-right:2px black solid;">failures
<TD> 0
<TD> 0
<TD> 0
<TD> 0
<TD> 0
<TD> 0
<TD> 0
<TD> 0
<TD> 0
<TD> 0
<TD> 0
<TD> 0
<TD> 0
The temperature that day was forecast to be .
<li> NASA based the decision to launch partially on a chart showing
only the flights that had at least one O-ring failure.
Find the line that best fits these seven flights.
On the basis of this data,
predict the number of O-ring failures when the temperature is , and
when the number of failures will exceed four.
<li> Find the line that best fits all 24 flights.
On the basis of this extra data,
predict the number of O-ring failures when the temperature is , and
when the number of failures will exceed four.
Which do you think is the more accurate method of predicting?
(An excellent discussion appears in Dalal Folkes Hoadley 1989.)
Answer
<li> A computer algebra system like MAPLE or MuPAD will give
an intercept of
and a slope of
Plugging into the equation yields a predicted number of
O-ring failures of (rounded to two places).
Plugging in and solving gives a temperature of
F.
<li> On the basis of this information
MAPLE gives the intercept and the
slope .
Here, plugging into the equation predicts
O-ring failures (rounded to two places).
Plugging in failures gives a temperature of
F.
x200px
Problem 7
This table lists the average distance from the sun to
each of the first seven planets, using earth's average as a unit.
<TR>
<TD style="border-bottom:2px black solid">Mercury
<TD style="border-bottom:2px black solid"> Venus
<TD style="border-bottom:2px black solid"> Earth
<TD style="border-bottom:2px black solid"> Mars
<TD style="border-bottom:2px black solid"> Jupiter
<TD style="border-bottom:2px black solid"> Saturn
<TD style="border-bottom:2px black solid"> Uranus
<TR>
<TD> 0.39
<TD> 0.72
<TD> 1.00
<TD> 1.52
<TD> 5.20
<TD> 9.54
<TD> 19.2
<li> Plot the number of the planet
(Mercury is , etc.) versus the distance.
Note that it does not look like a line, and so finding the
line of best fit is not fruitful.
<li> It does, however look like an exponential curve.
Therefore, plot the number of the planet versus the
logarithm of the distance.
Does this look like a line?
<li> The asteroid belt between Mars and
Jupiter is thought
to be what is left of a planet that broke apart.
Renumber so that Jupiter is , Saturn is , and Uranus is
, and plot against the log again.
Does this look better?
<li> Use least squares on that data to predict the
location of Neptune.
<li> Repeat to predict where Pluto is.
<li> Is the formula accurate for Neptune and Pluto?
This method was used to help discover Neptune (although the second item is
misleading about the history; actually, the discovery of Neptune
in position
prompted people to look for the "missing planet" in position ).
See Gardner 1970
Answer
<li> The plot is nonlinear.
x200px
<li> Here is the plot.
x200px
There is perhaps a jog up between planet and planet .
<li> This plot seems even more linear.
x200px
<li>
With this input
MuPAD gives that the intercept is and
the slope is .
<li> Plugging into the equation
from the prior item gives
that the log of the distance is , so the expected
distance is .
The actual distance is about .
<li> Plugging into the same equation
gives that the log of the distance is , so the expected
distance is .
The actual distance is about .
Problem 8
William Bennett has proposed an Index of Leading Cultural Indicators
for the US Bennett 1993.
Among the statistics cited are the average daily hours spent watching TV,
and the average combined SAT scores.
<TR>
<TD style="border-right:2px black solid;border-bottom:2px black solid;">
<TD style="border-bottom:2px black solid;"> 1960
<TD style="border-bottom:2px black solid;"> 1965
<TD style="border-bottom:2px black solid;"> 1970
<TD style="border-bottom:2px black solid;"> 1975
<TD style="border-bottom:2px black solid;"> 1980
<TD style="border-bottom:2px black solid;"> 1985
<TD style="border-bottom:2px black solid;"> 1990
<TD style="border-bottom:2px black solid;"> 1992
<TR>
<TD style="border-right:2px black solid;">TV
<TD> 5:06
<TD> 5:29
<TD> 5:56
<TD> 6:07
<TD> 6:36
<TD> 7:07
<TD> 6:55
<TD> 7:04
<TR>
<TD style="border-right:2px black solid;">SAT
<TD> 975
<TD> 969
<TD> 948
<TD> 910
<TD> 890
<TD> 906
<TD> 900
<TD> 899
Suppose that a cause and effect relationship is proposed between
the time spent watching TV and the decline in SAT scores (in this article,
Mr. Bennett does not argue that there is a direct connection).
<li> Find the line of best fit relating the independent variable
of average daily TV hours to the dependent variable of SAT scores.
<li> Find the most recent estimate of the average daily TV hours
(Bennett's cites Neilsen Media Research as the source of these
estimates).
Estimate the associated SAT score.
How close is your estimate to the actual average?
(Warning: a change has been made recently in the SAT,
so you should investigate whether some adjustment needs to be made to
the reported average to make a valid comparison.)
Answer
<li> With this input
MAPLE gives the intercept
and the slope
.
x200px
Additional Data
Data on the progression of the world's records (taken from the Runner's World web site) is below.
<TR>
<TD colspan="3" style="border-left:2px black solid;border-right:2px black solid;border-top:2px black solid; border-bottom:2px black solid; text-align:center;">
Progression of Men's Mile Record
<TR>
<TD style="border-left:2px black solid;border-bottom:2px black solid;"> time <TD style="border-bottom:2px black solid;"> name <TD style="border-right:2px black solid; border-bottom:2px black solid;"> date
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:52.0 <TD> Cadet Marshall (GBR) <TD style="border-right:2px black solid;"> 02Sep52
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:45.0 <TD> Thomas Finch (GBR) <TD style="border-right:2px black solid;"> 03Nov58
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:40.0 <TD> Gerald Surman (GBR) <TD style="border-right:2px black solid;"> 24Nov59
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:33.0 <TD> George Farran (IRL) <TD style="border-right:2px black solid;"> 23May62
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:29 3/5 <TD> Walter Chinnery (GBR) <TD style="border-right:2px black solid;"> 10Mar68
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:28 4/5 <TD> William Gibbs (GBR) <TD style="border-right:2px black solid;"> 03Apr68
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:28 3/5 <TD> Charles Gunton (GBR) <TD style="border-right:2px black solid;"> 31Mar73
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:26.0 <TD> Walter Slade (GBR) <TD style="border-right:2px black solid;"> 30May74
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:24 1/2 <TD> Walter Slade (GBR) <TD style="border-right:2px black solid;"> 19Jun75
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:23 1/5 <TD> Walter George (GBR) <TD style="border-right:2px black solid;"> 16Aug80
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:19 2/5 <TD> Walter George (GBR) <TD style="border-right:2px black solid;"> 03Jun82
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:18 2/5 <TD> Walter George (GBR) <TD style="border-right:2px black solid;"> 21Jun84
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:17 4/5 <TD> Thomas Conneff (USA) <TD style="border-right:2px black solid;"> 26Aug93
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:17.0 <TD> Fred Bacon (GBR) <TD style="border-right:2px black solid;"> 06Jul95
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:15 3/5 <TD> Thomas Conneff (USA) <TD style="border-right:2px black solid;"> 28Aug95
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:15 2/5 <TD> John Paul Jones (USA) <TD style="border-right:2px black solid;"> 27May11
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:14.4 <TD> John Paul Jones (USA) <TD style="border-right:2px black solid;"> 31May13
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:12.6 <TD> Norman Taber (USA) <TD style="border-right:2px black solid;"> 16Jul15
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:10.4 <TD> Paavo Nurmi (FIN) <TD style="border-right:2px black solid;"> 23Aug23
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:09 1/5 <TD> Jules Ladoumegue (FRA) <TD style="border-right:2px black solid;"> 04Oct31
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:07.6 <TD> Jack Lovelock (NZL) <TD style="border-right:2px black solid;"> 15Jul33
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:06.8 <TD> Glenn Cunningham (USA) <TD style="border-right:2px black solid;"> 16Jun34
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:06.4 <TD> Sydney Wooderson (GBR) <TD style="border-right:2px black solid;"> 28Aug37
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:06.2 <TD> Gunder Hagg (SWE) <TD style="border-right:2px black solid;"> 01Jul42
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:04.6 <TD> Gunder Hagg (SWE) <TD style="border-right:2px black solid;"> 04Sep42
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:02.6 <TD> Arne Andersson (SWE) <TD style="border-right:2px black solid;"> 01Jul43
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:01.6 <TD> Arne Andersson (SWE) <TD style="border-right:2px black solid;"> 18Jul44
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:01.4 <TD> Gunder Hagg (SWE) <TD style="border-right:2px black solid;"> 17Jul45
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:59.4 <TD> Roger Bannister (GBR) <TD style="border-right:2px black solid;"> 06May54
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:58.0 <TD> John Landy (AUS) <TD style="border-right:2px black solid;"> 21Jun54
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:57.2 <TD> Derek Ibbotson (GBR) <TD style="border-right:2px black solid;"> 19Jul57
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:54.5 <TD> Herb Elliott (AUS) <TD style="border-right:2px black solid;"> 06Aug58
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:54.4 <TD> Peter Snell (NZL) <TD style="border-right:2px black solid;"> 27Jan62
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:54.1 <TD> Peter Snell (NZL) <TD style="border-right:2px black solid;"> 17Nov64
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:53.6 <TD> Michel Jazy (FRA) <TD style="border-right:2px black solid;"> 09Jun65
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:51.3 <TD> Jim Ryun (USA) <TD style="border-right:2px black solid;"> 17Jul66
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:51.1 <TD> Jim Ryun (USA) <TD style="border-right:2px black solid;"> 23Jun67
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:51.0 <TD> Filbert Bayi (TAN) <TD style="border-right:2px black solid;"> 17May75
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:49.4 <TD> John Walker (NZL) <TD style="border-right:2px black solid;"> 12Aug75
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:49.0 <TD> Sebastian Coe (GBR) <TD style="border-right:2px black solid;"> 17Jul79
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:48.8 <TD> Steve Ovett (GBR) <TD style="border-right:2px black solid;"> 01Jul80
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:48.53 <TD> Sebastian Coe (GBR) <TD style="border-right:2px black solid;"> 19Aug81
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:48.40 <TD> Steve Ovett (GBR) <TD style="border-right:2px black solid;"> 26Aug81
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:47.33 <TD> Sebastian Coe (GBR) <TD style="border-right:2px black solid;"> 28Aug81
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:46.32 <TD> Steve Cram (GBR) <TD style="border-right:2px black solid;"> 27Jul85
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:44.39 <TD> Noureddine Morceli (ALG) <TD style="border-right:2px black solid;"> 05Sep93
<TR>
<TD style="border-left:2px black solid; border-bottom:2px black solid; border-right:2px black solid;"> 3:43.13 <TD style="border-bottom:2px black solid;"> Hicham el Guerrouj (MOR) <TD style="border-bottom:2px black solid; border-right:2px solid black;"> 07Jul99
<TR>
<TD colspan="3" style="border-left:2px black solid;border-right:2px black solid;border-top:2px black solid; border-bottom:2px black solid; text-align:center;">
Progression of Men's 1500 Meter Record
<TR>
<TD style="border-left:2px black solid;border-bottom:2px black solid;"> time <TD style="border-bottom:2px black solid;"> name <TD style="border-right:2px black solid; border-bottom:2px black solid;"> date
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:09.0 <TD> John Bray (USA) <TD style="border-right:2px black solid;"> 30May00
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:06.2 <TD> Charles Bennett (GBR) <TD style="border-right:2px black solid;"> 15Jul00
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:05.4 <TD> James Lightbody (USA) <TD style="border-right:2px black solid;"> 03Sep04
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:59.8 <TD> Harold Wilson (GBR) <TD style="border-right:2px black solid;"> 30May08
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:59.2 <TD> Abel Kiviat (USA) <TD style="border-right:2px black solid;"> 26May12
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:56.8 <TD> Abel Kiviat (USA) <TD style="border-right:2px black solid;"> 02Jun12
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:55.8 <TD> Abel Kiviat (USA) <TD style="border-right:2px black solid;"> 08Jun12
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:55.0 <TD> Norman Taber (USA) <TD style="border-right:2px black solid;"> 16Jul15
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:54.7 <TD> John Zander (SWE) <TD style="border-right:2px black solid;"> 05Aug17
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:53.0 <TD> Paavo Nurmi (FIN) <TD style="border-right:2px black solid;"> 23Aug23
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:52.6 <TD> Paavo Nurmi (FIN) <TD style="border-right:2px black solid;"> 19Jun24
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:51.0 <TD> Otto Peltzer (GER) <TD style="border-right:2px black solid;"> 11Sep26
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:49.2 <TD> Jules Ladoumegue (FRA) <TD style="border-right:2px black solid;"> 05Oct30
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:49.0 <TD> Luigi Beccali (ITA) <TD style="border-right:2px black solid;"> 17Sep33
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:48.8 <TD> William Bonthron (USA) <TD style="border-right:2px black solid;"> 30Jun34
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:47.8 <TD> Jack Lovelock (NZL) <TD style="border-right:2px black solid;"> 06Aug36
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:47.6 <TD> Gunder Hagg (SWE) <TD style="border-right:2px black solid;"> 10Aug41
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:45.8 <TD> Gunder Hagg (SWE) <TD style="border-right:2px black solid;"> 17Jul42
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:45.0 <TD> Arne Andersson (SWE) <TD style="border-right:2px black solid;"> 17Aug43
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:43.0 <TD> Gunder Hagg (SWE) <TD style="border-right:2px black solid;"> 07Jul44
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:42.8 <TD> Wes Santee (USA) <TD style="border-right:2px black solid;"> 04Jun54
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:41.8 <TD> John Landy (AUS) <TD style="border-right:2px black solid;"> 21Jun54
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:40.8 <TD> Sandor Iharos (HUN) <TD style="border-right:2px black solid;"> 28Jul55
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:40.6 <TD> Istvan Rozsavolgyi (HUN) <TD style="border-right:2px black solid;"> 03Aug56
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:40.2 <TD> Olavi Salsola (FIN) <TD style="border-right:2px black solid;"> 11Jul57
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:38.1 <TD> Stanislav Jungwirth (CZE) <TD style="border-right:2px black solid;"> 12Jul57
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:36.0 <TD> Herb Elliott (AUS) <TD style="border-right:2px black solid;"> 28Aug58
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:35.6 <TD> Herb Elliott (AUS) <TD style="border-right:2px black solid;"> 06Sep60
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:33.1 <TD> Jim Ryun (USA) <TD style="border-right:2px black solid;"> 08Jul67
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:32.2 <TD> Filbert Bayi (TAN) <TD style="border-right:2px black solid;"> 02Feb74
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:32.1 <TD> Sebastian Coe (GBR) <TD style="border-right:2px black solid;"> 15Aug79
<TR>
<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:31.36 <TD> Steve Ovett (GBR) <TD style="border-right:2px black solid;"> 27Aug80
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:31.24 <TD> Sydney Maree (usa) <TD style="border-right:2px black solid;"> 28Aug83
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:30.77 <TD> Steve Ovett (GBR) <TD style="border-right:2px black solid;"> 04Sep83
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:29.67 <TD> Steve Cram (GBR) <TD style="border-right:2px black solid;"> 16Jul85
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:29.46 <TD> Said Aouita (MOR) <TD style="border-right:2px black solid;"> 23Aug85
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:28.86 <TD> Noureddine Morceli (ALG) <TD style="border-right:2px black solid;"> 06Sep92
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 3:27.37 <TD> Noureddine Morceli (ALG) <TD style="border-right:2px black solid;"> 12Jul95
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<TD style="border-left:2px black solid; border-right:2px black solid; border-bottom:2px black solid;"> 3:26.00 <TD style="border-bottom:2px black solid;"> Hicham el Guerrouj (MOR) <TD style="border-right:2px black solid; border-bottom:2px black solid;"> 14Jul98
<TD colspan="3" style="border-left:2px black solid;border-right:2px black solid;border-top:2px black solid; border-bottom:2px black solid; text-align:center;">
Progression of Women's Mile Record
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<TD style="border-left:2px black solid;border-bottom:2px black solid;"> time <TD style="border-bottom:2px black solid;"> name <TD style="border-right:2px black solid; border-bottom:2px black solid;"> date
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 6:13.2 <TD> Elizabeth Atkinson (GBR) <TD style="border-right:2px black solid;"> 24Jun21
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:27.5 <TD> Ruth Christmas (GBR) <TD style="border-right:2px black solid;"> 20Aug32
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:24.0 <TD> Gladys Lunn (GBR) <TD style="border-right:2px black solid;"> 01Jun36
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:23.0 <TD> Gladys Lunn (GBR) <TD style="border-right:2px black solid;"> 18Jul36
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:20.8 <TD> Gladys Lunn (GBR) <TD style="border-right:2px black solid;"> 08May37
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:17.0 <TD> Gladys Lunn (GBR) <TD style="border-right:2px black solid;"> 07Aug37
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:15.3 <TD> Evelyne Forster (GBR) <TD style="border-right:2px black solid;"> 22Jul39
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:11.0 <TD> Anne Oliver (GBR) <TD style="border-right:2px black solid;"> 14Jun52
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:09.8 <TD> Enid Harding (GBR) <TD style="border-right:2px black solid;"> 04Jul53
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:08.0 <TD> Anne Oliver (GBR) <TD style="border-right:2px black solid;"> 12Sep53
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:02.6 <TD> Diane Leather (GBR) <TD style="border-right:2px black solid;"> 30Sep53
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:00.3 <TD> Edith Treybal (ROM) <TD style="border-right:2px black solid;"> 01Nov53
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 5:00.2 <TD> Diane Leather (GBR) <TD style="border-right:2px black solid;"> 26May54
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:59.6 <TD> Diane Leather (GBR) <TD style="border-right:2px black solid;"> 29May54
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:50.8 <TD> Diane Leather (GBR) <TD style="border-right:2px black solid;"> 24May55
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:45.0 <TD> Diane Leather (GBR) <TD style="border-right:2px black solid;"> 21Sep55
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:41.4 <TD> Marise Chamberlain (NZL) <TD style="border-right:2px black solid;"> 08Dec62
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:39.2 <TD> Anne Smith (GBR) <TD style="border-right:2px black solid;"> 13May67
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:37.0 <TD> Anne Smith (GBR) <TD style="border-right:2px black solid;"> 03Jun67
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:36.8 <TD> Maria Gommers (HOL) <TD style="border-right:2px black solid;"> 14Jun69
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:35.3 <TD> Ellen Tittel (FRG) <TD style="border-right:2px black solid;"> 20Aug71
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:34.9 <TD> Glenda Reiser (CAN) <TD style="border-right:2px black solid;"> 07Jul73
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:29.5 <TD> Paola Pigni-Cacchi (ITA) <TD style="border-right:2px black solid;"> 08Aug73
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:23.8 <TD> Natalia Marasescu (ROM) <TD style="border-right:2px black solid;"> 21May77
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:22.1 <TD> Natalia Marasescu (ROM) <TD style="border-right:2px black solid;"> 27Jan79
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:21.7 <TD> Mary Decker (USA) <TD style="border-right:2px black solid;"> 26Jan80
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:20.89 <TD> Lyudmila Veselkova (SOV) <TD style="border-right:2px black solid;"> 12Sep81
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:18.08 <TD> Mary Decker-Tabb (USA) <TD style="border-right:2px black solid;"> 09Jul82
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:17.44 <TD> Maricica Puica (ROM) <TD style="border-right:2px black solid;"> 16Sep82
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:15.8 <TD> Natalya Artyomova (SOV) <TD style="border-right:2px black solid;"> 05Aug84
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:16.71 <TD> Mary Decker-Slaney (USA) <TD style="border-right:2px black solid;"> 21Aug85
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<TD style="border-left:2px black solid; border-right:2px black solid;"> 4:15.61 <TD> Paula Ivan (ROM) <TD style="border-right:2px black solid;"> 10Jul89
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<TD style="border-left:2px black solid; border-right:2px black solid; border-bottom:2px black solid;"> 4:12.56 <TD style=" border-bottom:2px black solid;"> Svetlana Masterkova (RUS) <TD style="border-right:2px black solid; border-bottom:2px black solid;"> 14Aug96
References
Bennett William Quantifying America's Decline Wall Street Journal March 15, 1993 1993
Dalal Siddhartha Folkes Edward Hoadley Bruce Lessons Learned from Challenger: A Statistical Perspective Stats: the Magazine for Students of Statistics Fall 1989 1989 14-18
Gardner Martin Mathematical Games, Some mathematical curiosities embedded in the solar system Scientific American April 1970 1970 108-112