Statistical Thinking with Trend Charts

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