Statistical Thinking
with Trend Charts
SAT Mean Scores of College-Bound Seniors (1995-2012)
YEAR WRITING SCORE ALL MALE FEMALE
2005-06 497 491 5022006-07 494 489 5002007-08 494 488 5012008-09 493 486 4992009-10 492 486 4982010-11 489 482 4962011-12 488 481 494
SAT Mean Writing Score of College-Bound Seniors (2006-2012)
2012201120102009200820072006
497496495494493492491490489488
Year
Scor
es
SAT Mean Writing Score of College-Bound Seniors (2006-2012)
TREND LINE CONSTRUCTION Prediction
ALL Predictions Error2006 497 Half-Average 496.25 0.752007 494 (2007, 495) 495 -12008 494 493.75 0.25
Slope m = -1.252009 493 Intercept b = 3003.75 492.5 0.5
2010 492 Half-Average 491.25 0.752011 489 (2011, 490) 490 -12012 488 488.75 -0.75
TREND PREDICTION LINE
Score = -1.25*Year + 3003.75
Time Series Plot with Trend Line Predictions for Writing Scores
2012201120102009200820072006
497496495494493492491490489488
Year
Scor
esCombinedPredictions
Time Series Plot with Predictions for Writing Scores
Moving Ranges and Margin of Error Prediction
Error Moving Range0.75 -1 0.75 1.75-1 0.25 -1 1.25
0.25 0.5 0.25 0.250.5 0.75 0.5 0.25
0.75 -1 0.75 1.75-1 -0.75 -1 0.25
-0.75
Average Moving Range = AMR = 0.9167
Moving Range Margin of Error = 3.27*AMR = 3.27*0.9167 = 2.9976
654321
3.0
2.5
2.0
1.5
1.0
0.5
0.0
Index
Mov
ing
Rang
esUMRLMRCenterlineLMRL
Moving Range Chart
2012201120102009200820072006
500.0
497.5
495.0
492.5
490.0
487.5
485.0
Year
UTLALLPredictionsLTL
Trend Chart with Statistical Margin of Error
SAT Mean Male Writing Score of College-Bound Seniors (2006-2012)
2012201120102009200820072006
492
490
488
486
484
482
480
Year
Mal
e Sc
ore
SAT Mean Male Writing Score of College-Bound Seniors (2006-2012)
SAT Mean Female Writing Score of College-Bound Seniors (2006-2012)
2012201120102009200820072006
502501500499498497496495494493
Year
Fem
ale
SAT Mean Female Writing Score of College-Bound Seniors (2006-2012)
YEAR CRITICAL READING SCORE
MATHEMATICS SCORE
ALL MALE FEMALE * ALL MALE FEMALE1995-96 505 507 503 * 508 527 4921996-97 505 507 503 * 511 530 4941997-98 505 509 502 * 512 531 4961998-99 505 509 502 * 511 531 495
1999-2000 505 507 504 * 514 533 4982000-01 506 509 502 * 514 533 4982001-02 504 507 502 * 516 534 5002002-03 507 512 503 * 519 537 503
SAT Mean Scores of College-Bound Seniors (1995-2012)
SAT Mean Scores of College-Bound Seniors (1995-2012)
2003-04 508 512 504 * 518 537 5012004-05 508 513 505 * 520 538 5042005-06 503 505 502 * 518 536 5022006-07 502 504 502 * 515 533 4992007-08 502 504 500 * 515 533 5002008-09 501 503 498 * 515 534 4992009-10 501 503 498 * 516 534 5002010-11 497 500 495 * 514 531 5002011-12 496 498 493 * 514 532 499
YEAR CRITICAL READING SCORE MATHEMATICS SCORE
530
525
520
515
510
505
YEAR
Scor
es
ALLPredictionLTLUTL
Variable
COMBINED SCORES, Centerline Predictions, LTL, UTL
545
540
535
530
525
YEAR
Scor
es
MALEPredictionLPLUPL
Variable
MALE MATH SCORES, Centerline Predictions, LTL, UTL
515
510
505
500
495
490
YEAR
Scor
es
FEMALEPredictionLTLUTL
Variable
FEMALE MATH SCORES, Centerline Predictions, LTL, UTL