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NAEP Analysis and Scaling → Scale Linking and Transformation to the Reporting Metric → NAEP Variance Estimation During Transition to Digitally Based Assessment → Transformation Coefficients Used for Variance Calculation, Mathematics National Assessment: 2019
NAEP Technical Documentation Transformation Coefficients Used for Variance Calculation, Mathematics National Assessment: 2019
| Subscale | Index | A | B |
|---|---|---|---|
| Number properties and operations | 1 | 1.0082010225 | -1.4783152251 |
| Number properties and operations | 2 | 1.0108786517 | -1.8474086942 |
| Number properties and operations | 3 | 1.0084298625 | -1.4454894273 |
| Number properties and operations | 4 | 1.0081820747 | -1.4543302436 |
| Number properties and operations | 5 | 1.0062503336 | -1.1252993027 |
| Number properties and operations | 6 | 1.0088719581 | -1.6572979070 |
| Number properties and operations | 7 | 1.0083263904 | -1.4038446690 |
| Number properties and operations | 8 | 1.0109521388 | -1.9033329667 |
| Number properties and operations | 9 | 1.0065884944 | -1.2706992649 |
| Number properties and operations | 10 | 1.0085494498 | -1.6747072321 |
| Number properties and operations | 11 | 1.0067912642 | -1.3098162943 |
| Number properties and operations | 12 | 1.0114968821 | -2.0062028074 |
| Number properties and operations | 13 | 1.0098322855 | -1.6478161751 |
| Number properties and operations | 14 | 1.0074059911 | -1.3314043280 |
| Number properties and operations | 15 | 1.0077797038 | -1.3280952812 |
| Number properties and operations | 16 | 1.0077645825 | -1.4263022389 |
| Number properties and operations | 17 | 1.0095111235 | -1.6946500281 |
| Number properties and operations | 18 | 1.0101410900 | -1.7107806653 |
| Number properties and operations | 19 | 1.0095497315 | -1.5612621200 |
| Number properties and operations | 20 | 1.0093805880 | -1.6408899143 |
| Number properties and operations | 21 | 1.0080283756 | -1.4113540583 |
| Number properties and operations | 22 | 1.0131664092 | -2.2675701865 |
| Number properties and operations | 23 | 1.0086245544 | -1.5541897562 |
| Number properties and operations | 24 | 1.0069171977 | -1.2837536525 |
| Number properties and operations | 25 | 1.0088458764 | -1.5235422326 |
| Number properties and operations | 26 | 1.0100684549 | -1.7763476910 |
| Number properties and operations | 27 | 1.0085874670 | -1.5539281506 |
| Number properties and operations | 28 | 1.0086672309 | -1.3734578734 |
| Number properties and operations | 29 | 1.0082481320 | -1.5756625716 |
| Number properties and operations | 30 | 1.0089156015 | -1.5168422781 |
| Number properties and operations | 31 | 1.0085814897 | -1.4675208540 |
| Number properties and operations | 32 | 1.0115457761 | -1.9095441830 |
| Number properties and operations | 33 | 1.0105074279 | -1.7552099394 |
| Number properties and operations | 34 | 1.0085116616 | -1.4913782029 |
| Number properties and operations | 35 | 1.0061658645 | -1.1235118860 |
| Number properties and operations | 36 | 1.0101938392 | -1.7736230611 |
| Number properties and operations | 37 | 1.0081808987 | -1.6159655914 |
| Number properties and operations | 38 | 1.0081624835 | -1.5023202851 |
| Number properties and operations | 39 | 1.0100049887 | -1.8281976417 |
| Number properties and operations | 40 | 1.0084372241 | -1.5118840791 |
| Number properties and operations | 41 | 1.0093362354 | -1.6125257406 |
| Number properties and operations | 42 | 1.0089814430 | -1.6744355060 |
| Number properties and operations | 43 | 1.0067098557 | -1.2919133863 |
| Number properties and operations | 44 | 1.0084342239 | -1.4895088093 |
| Number properties and operations | 45 | 1.0075832533 | -1.4498632898 |
| Number properties and operations | 46 | 1.0085297591 | -1.5520138104 |
| Number properties and operations | 47 | 1.0075561662 | -1.4616403559 |
| Number properties and operations | 48 | 1.0101055116 | -1.6984616149 |
| Number properties and operations | 49 | 1.0103083518 | -1.8876718478 |
| Number properties and operations | 50 | 1.0089996866 | -1.5281488790 |
| Number properties and operations | 51 | 1.0072780411 | -1.4058595787 |
| Number properties and operations | 52 | 1.0083112275 | -1.4183649564 |
| Number properties and operations | 53 | 1.0094706982 | -1.6822013682 |
| Number properties and operations | 54 | 1.0083808855 | -1.5307537516 |
| Number properties and operations | 55 | 1.0096889225 | -1.7911336300 |
| Number properties and operations | 56 | 1.0104410357 | -1.8150333384 |
| Number properties and operations | 57 | 1.0098671756 | -1.6411089293 |
| Number properties and operations | 58 | 1.0105895143 | -1.7756125202 |
| Number properties and operations | 59 | 1.0095303043 | -1.6768938580 |
| Number properties and operations | 60 | 1.0072640905 | -1.3961892398 |
| Number properties and operations | 61 | 1.0091675691 | -1.6195365575 |
| Number properties and operations | 62 | 1.0087981482 | -1.6419989933 |
| Measurement and geometry | 1 | 0.9834741039 | 3.1022305727 |
| Measurement and geometry | 2 | 0.9844423761 | 2.9337672565 |
| Measurement and geometry | 3 | 0.9855847657 | 2.7838081443 |
| Measurement and geometry | 4 | 0.9834144820 | 3.0714359203 |
| Measurement and geometry | 5 | 0.9828575106 | 3.1496578538 |
| Measurement and geometry | 6 | 0.9849719663 | 2.7449247375 |
| Measurement and geometry | 7 | 0.9852077501 | 2.8804734008 |
| Measurement and geometry | 8 | 0.9874310449 | 2.5142063546 |
| Measurement and geometry | 9 | 0.9832880715 | 3.1420932581 |
| Measurement and geometry | 10 | 0.9835161785 | 2.9951012837 |
| Measurement and geometry | 11 | 0.9808151157 | 3.3861146373 |
| Measurement and geometry | 12 | 0.9855700302 | 2.7483920925 |
| Measurement and geometry | 13 | 0.9849005632 | 2.9085093220 |
| Measurement and geometry | 14 | 0.9825359193 | 3.2711352748 |
| Measurement and geometry | 15 | 0.9848361304 | 2.9649599551 |
| Measurement and geometry | 16 | 0.9844211812 | 2.9073185965 |
| Measurement and geometry | 17 | 0.9841047564 | 2.9464826626 |
| Measurement and geometry | 18 | 0.9847042922 | 2.9124039046 |
| Measurement and geometry | 19 | 0.9848320047 | 2.9404669395 |
| Measurement and geometry | 20 | 0.9842634686 | 2.9213170108 |
| Measurement and geometry | 21 | 0.9851660429 | 2.8039090809 |
| Measurement and geometry | 22 | 0.9862156246 | 2.6347361912 |
| Measurement and geometry | 23 | 0.9837629497 | 3.0025714231 |
| Measurement and geometry | 24 | 0.9823334722 | 3.1893503965 |
| Measurement and geometry | 25 | 0.9845078917 | 2.9735699570 |
| Measurement and geometry | 26 | 0.9847220253 | 2.8766813058 |
| Measurement and geometry | 27 | 0.9831820139 | 3.0226779877 |
| Measurement and geometry | 28 | 0.9844148548 | 3.0479657072 |
| Measurement and geometry | 29 | 0.9831374556 | 3.0497310037 |
| Measurement and geometry | 30 | 0.9856147768 | 2.7549757288 |
| Measurement and geometry | 31 | 0.9845041927 | 2.9345426874 |
| Measurement and geometry | 32 | 0.9834382637 | 3.0840584500 |
| Measurement and geometry | 33 | 0.9872996780 | 2.4322042417 |
| Measurement and geometry | 34 | 0.9854650571 | 2.7060884730 |
| Measurement and geometry | 35 | 0.9813850987 | 3.4459274780 |
| Measurement and geometry | 36 | 0.9844452356 | 2.8525447320 |
| Measurement and geometry | 37 | 0.9828619199 | 3.0305995542 |
| Measurement and geometry | 38 | 0.9838705860 | 2.9404112152 |
| Measurement and geometry | 39 | 0.9853940439 | 2.7102425243 |
| Measurement and geometry | 40 | 0.9830717847 | 3.1163207003 |
| Measurement and geometry | 41 | 0.9851079325 | 2.8007164800 |
| Measurement and geometry | 42 | 0.9838928055 | 2.9301312083 |
| Measurement and geometry | 43 | 0.9825535843 | 3.1580905121 |
| Measurement and geometry | 44 | 0.9835196674 | 3.0813174542 |
| Measurement and geometry | 45 | 0.9834384767 | 2.9616407074 |
| Measurement and geometry | 46 | 0.9828412148 | 3.0865188543 |
| Measurement and geometry | 47 | 0.9829388442 | 3.0910622809 |
| Measurement and geometry | 48 | 0.9858391319 | 2.7655813164 |
| Measurement and geometry | 49 | 0.9861142189 | 2.5997788275 |
| Measurement and geometry | 50 | 0.9849851511 | 2.8425593369 |
| Measurement and geometry | 51 | 0.9841350668 | 2.9314369252 |
| Measurement and geometry | 52 | 0.9842791297 | 3.0514641212 |
| Measurement and geometry | 53 | 0.9834597937 | 3.0447150544 |
| Measurement and geometry | 54 | 0.9843450769 | 2.8709361084 |
| Measurement and geometry | 55 | 0.9842217089 | 2.9080383794 |
| Measurement and geometry | 56 | 0.9863995170 | 2.5405251024 |
| Measurement and geometry | 57 | 0.9857202368 | 2.8254098738 |
| Measurement and geometry | 58 | 0.9877851154 | 2.4342750394 |
| Measurement and geometry | 59 | 0.9848706276 | 2.8760010684 |
| Measurement and geometry | 60 | 0.9839328486 | 2.9605470022 |
| Measurement and geometry | 61 | 0.9832070109 | 3.0876441371 |
| Measurement and geometry | 62 | 0.9860640442 | 2.6523036364 |
| Data analysis, statistics, and probability | 1 | 0.9925110286 | 1.4210506090 |
| Data analysis, statistics, and probability | 2 | 0.9929946531 | 1.3528462230 |
| Data analysis, statistics, and probability | 3 | 0.9930327003 | 1.2978754746 |
| Data analysis, statistics, and probability | 4 | 0.9930539994 | 1.2838779175 |
| Data analysis, statistics, and probability | 5 | 0.9920529511 | 1.4419760212 |
| Data analysis, statistics, and probability | 6 | 0.9934850267 | 1.1101845121 |
| Data analysis, statistics, and probability | 7 | 0.9941764167 | 1.2121263126 |
| Data analysis, statistics, and probability | 8 | 0.9964938870 | 0.8496555174 |
| Data analysis, statistics, and probability | 9 | 0.9925813018 | 1.3706599311 |
| Data analysis, statistics, and probability | 10 | 0.9926342728 | 1.1554398398 |
| Data analysis, statistics, and probability | 11 | 0.9913356053 | 1.4828404092 |
| Data analysis, statistics, and probability | 12 | 0.9956271173 | 0.9161438438 |
| Data analysis, statistics, and probability | 13 | 0.9948748464 | 1.0722163071 |
| Data analysis, statistics, and probability | 14 | 0.9929440970 | 1.3823707590 |
| Data analysis, statistics, and probability | 15 | 0.9935211509 | 1.2950466589 |
| Data analysis, statistics, and probability | 16 | 0.9929344367 | 1.2710773226 |
| Data analysis, statistics, and probability | 17 | 0.9934913029 | 1.2130498065 |
| Data analysis, statistics, and probability | 18 | 0.9939157460 | 1.1407571510 |
| Data analysis, statistics, and probability | 19 | 0.9928616754 | 1.4959828350 |
| Data analysis, statistics, and probability | 20 | 0.9926440335 | 1.3943850533 |
| Data analysis, statistics, and probability | 21 | 0.9941126201 | 1.1490285362 |
| Data analysis, statistics, and probability | 22 | 0.9942213746 | 1.1599336407 |
| Data analysis, statistics, and probability | 23 | 0.9940932684 | 1.1545744821 |
| Data analysis, statistics, and probability | 24 | 0.9918694014 | 1.3892854904 |
| Data analysis, statistics, and probability | 25 | 0.9934778866 | 1.2338153837 |
| Data analysis, statistics, and probability | 26 | 0.9946862397 | 1.0879670504 |
| Data analysis, statistics, and probability | 27 | 0.9925493131 | 1.2831933343 |
| Data analysis, statistics, and probability | 28 | 0.9939487148 | 1.3063706691 |
| Data analysis, statistics, and probability | 29 | 0.9925275432 | 1.2019659278 |
| Data analysis, statistics, and probability | 30 | 0.9943109426 | 1.0905614157 |
| Data analysis, statistics, and probability | 31 | 0.9933812532 | 1.2488135743 |
| Data analysis, statistics, and probability | 32 | 0.9966268614 | 0.7927846026 |
| Data analysis, statistics, and probability | 33 | 0.9969674070 | 0.7000326332 |
| Data analysis, statistics, and probability | 34 | 0.9934012065 | 1.2471725482 |
| Data analysis, statistics, and probability | 35 | 0.9914120712 | 1.6313196678 |
| Data analysis, statistics, and probability | 36 | 0.9937543069 | 1.1585027123 |
| Data analysis, statistics, and probability | 37 | 0.9920168262 | 1.2722911580 |
| Data analysis, statistics, and probability | 38 | 0.9925255261 | 1.3909846969 |
| Data analysis, statistics, and probability | 39 | 0.9937476091 | 1.0943807433 |
| Data analysis, statistics, and probability | 40 | 0.9920230289 | 1.3858495522 |
| Data analysis, statistics, and probability | 41 | 0.9940151250 | 1.1843730312 |
| Data analysis, statistics, and probability | 42 | 0.9937878255 | 1.1094488908 |
| Data analysis, statistics, and probability | 43 | 0.9913774002 | 1.5810331191 |
| Data analysis, statistics, and probability | 44 | 0.9932981991 | 1.3093847904 |
| Data analysis, statistics, and probability | 45 | 0.9927609305 | 1.2719900613 |
| Data analysis, statistics, and probability | 46 | 0.9924846174 | 1.3317387856 |
| Data analysis, statistics, and probability | 47 | 0.9936755819 | 1.2059802242 |
| Data analysis, statistics, and probability | 48 | 0.9959287754 | 0.9491091753 |
| Data analysis, statistics, and probability | 49 | 0.9953181794 | 0.8311126202 |
| Data analysis, statistics, and probability | 50 | 0.9939843456 | 1.1938544052 |
| Data analysis, statistics, and probability | 51 | 0.9909765346 | 1.5651351104 |
| Data analysis, statistics, and probability | 52 | 0.9924031975 | 1.4996887645 |
| Data analysis, statistics, and probability | 53 | 0.9926789686 | 1.3055258727 |
| Data analysis, statistics, and probability | 54 | 0.9936662783 | 1.1612505198 |
| Data analysis, statistics, and probability | 55 | 0.9938823747 | 1.0789820172 |
| Data analysis, statistics, and probability | 56 | 0.9950706745 | 0.9739840014 |
| Data analysis, statistics, and probability | 57 | 0.9956061250 | 1.0337800105 |
| Data analysis, statistics, and probability | 58 | 0.9972462970 | 0.7112281127 |
| Data analysis, statistics, and probability | 59 | 0.9950862381 | 1.0661684617 |
| Data analysis, statistics, and probability | 60 | 0.9920049013 | 1.3819147635 |
| Data analysis, statistics, and probability | 61 | 0.9921605033 | 1.4223608171 |
| Data analysis, statistics, and probability | 62 | 0.9940502568 | 1.1543804933 |
| Algebra | 1 | 1.0062561837 | -0.7346117859 |
| Algebra | 2 | 1.0050898601 | -0.5341930842 |
| Algebra | 3 | 1.0059586123 | -0.6619738317 |
| Algebra | 4 | 1.0059417125 | -0.6695282729 |
| Algebra | 5 | 1.0052971052 | -0.5920073257 |
| Algebra | 6 | 1.0060079334 | -0.7802855221 |
| Algebra | 7 | 1.0062971875 | -0.6978075657 |
| Algebra | 8 | 1.0081429060 | -1.0498956228 |
| Algebra | 9 | 1.0058480312 | -0.6907462181 |
| Algebra | 10 | 1.0044086223 | -0.5437395501 |
| Algebra | 11 | 1.0029740867 | -0.3190755543 |
| Algebra | 12 | 1.0076638597 | -0.9521713161 |
| Algebra | 13 | 1.0062026877 | -0.6530262193 |
| Algebra | 14 | 1.0039561338 | -0.3873578875 |
| Algebra | 15 | 1.0061721310 | -0.6489939870 |
| Algebra | 16 | 1.0054908122 | -0.6603267698 |
| Algebra | 17 | 1.0057521348 | -0.6780767701 |
| Algebra | 18 | 1.0066404172 | -0.8185278978 |
| Algebra | 19 | 1.0061362151 | -0.6211962862 |
| Algebra | 20 | 1.0055089689 | -0.6403666559 |
| Algebra | 21 | 1.0057645648 | -0.6652926263 |
| Algebra | 22 | 1.0068790277 | -0.7901459434 |
| Algebra | 23 | 1.0055558951 | -0.6553837966 |
| Algebra | 24 | 1.0039181078 | -0.4332480501 |
| Algebra | 25 | 1.0049738000 | -0.4944996665 |
| Algebra | 26 | 1.0065698331 | -0.7920729633 |
| Algebra | 27 | 1.0044383457 | -0.5471296857 |
| Algebra | 28 | 1.0066072923 | -0.6734332607 |
| Algebra | 29 | 1.0044384897 | -0.5709016555 |
| Algebra | 30 | 1.0068723437 | -0.8273704565 |
| Algebra | 31 | 1.0063366312 | -0.7642457826 |
| Algebra | 32 | 1.0058377927 | -0.6979611540 |
| Algebra | 33 | 1.0074850758 | -0.9843734768 |
| Algebra | 34 | 1.0049161703 | -0.5596158227 |
| Algebra | 35 | 1.0034291288 | -0.2594900045 |
| Algebra | 36 | 1.0073714266 | -0.9112202474 |
| Algebra | 37 | 1.0042228700 | -0.6005559476 |
| Algebra | 38 | 1.0053185826 | -0.6232924359 |
| Algebra | 39 | 1.0078417077 | -1.0825084045 |
| Algebra | 40 | 1.0058744066 | -0.7212625248 |
| Algebra | 41 | 1.0065283683 | -0.7750867670 |
| Algebra | 42 | 1.0054749296 | -0.7461171793 |
| Algebra | 43 | 1.0045211903 | -0.4980255669 |
| Algebra | 44 | 1.0052170817 | -0.5910664381 |
| Algebra | 45 | 1.0048981785 | -0.6277819289 |
| Algebra | 46 | 1.0049113472 | -0.6273695978 |
| Algebra | 47 | 1.0050695724 | -0.6134810156 |
| Algebra | 48 | 1.0071784125 | -0.8838673377 |
| Algebra | 49 | 1.0068459042 | -0.9022607194 |
| Algebra | 50 | 1.0068715192 | -0.8166406998 |
| Algebra | 51 | 1.0048999997 | -0.5901964786 |
| Algebra | 52 | 1.0054142481 | -0.4692513930 |
| Algebra | 53 | 1.0057607700 | -0.7437543363 |
| Algebra | 54 | 1.0058294322 | -0.7150355790 |
| Algebra | 55 | 1.0057111124 | -0.7344126776 |
| Algebra | 56 | 1.0083622233 | -1.1151519254 |
| Algebra | 57 | 1.0059683098 | -0.5950257760 |
| Algebra | 58 | 1.0092524116 | -1.2112932874 |
| Algebra | 59 | 1.0058385039 | -0.6316533572 |
| Algebra | 60 | 1.0048623984 | -0.5281048364 |
| Algebra | 61 | 1.0050591540 | -0.6208223062 |
| Algebra | 62 | 1.0064519219 | -0.8214477973 |
| NOTE: Since 2005, the measurement and geometry scales are combined at grade 12. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment. | |||
| Replicate | Subscale | DBA plausible value | Bridge PBA plausible value | A | B |
|---|---|---|---|---|---|
| 1 | Number properties and operations | 1 | 1 | 1.0087950165 | -1.5669687726 |
| 1 | Number properties and operations | 2 | 2 | 0.9965000038 | 0.5448570416 |
| 1 | Number properties and operations | 3 | 3 | 1.0054608050 | -0.3901117782 |
| 1 | Number properties and operations | 4 | 4 | 0.9952360533 | 0.3466513399 |
| 1 | Number properties and operations | 5 | 5 | 1.0046136325 | 0.3403223882 |
| 1 | Number properties and operations | 6 | 6 | 0.9833835604 | 2.5347280949 |
| 1 | Number properties and operations | 7 | 7 | 1.0079605809 | -0.6573459995 |
| 1 | Number properties and operations | 8 | 8 | 1.0030207258 | -0.6278313743 |
| 1 | Number properties and operations | 9 | 9 | 0.9787912001 | 2.8375693170 |
| 1 | Number properties and operations | 10 | 10 | 1.0037394259 | -1.3438440941 |
| 1 | Number properties and operations | 11 | 11 | 0.9906471687 | 0.7942443891 |
| 1 | Number properties and operations | 12 | 12 | 0.9957746387 | 0.3416351415 |
| 1 | Number properties and operations | 13 | 13 | 1.0231521182 | -3.9400001518 |
| 1 | Number properties and operations | 14 | 14 | 0.9759789920 | 4.3281946634 |
| 1 | Number properties and operations | 15 | 15 | 1.0073068762 | -0.2622628253 |
| 1 | Number properties and operations | 16 | 16 | 1.0031540981 | 0.3393081334 |
| 1 | Number properties and operations | 17 | 17 | 1.0068746451 | -1.3106221138 |
| 1 | Number properties and operations | 18 | 18 | 0.9894152796 | 0.5866607799 |
| 1 | Number properties and operations | 19 | 19 | 0.9898404911 | 1.3002618476 |
| 1 | Number properties and operations | 20 | 20 | 1.0316484715 | -4.3853907848 |
| 1 | Measurement and geometry | 1 | 1 | 0.9843453777 | 2.9181430002 |
| 1 | Measurement and geometry | 2 | 2 | 1.0121190522 | -2.0812498384 |
| 1 | Measurement and geometry | 3 | 3 | 1.0200601167 | -2.9932113917 |
| 1 | Measurement and geometry | 4 | 4 | 1.0060759684 | -1.2676886357 |
| 1 | Measurement and geometry | 5 | 5 | 0.9913924256 | 1.2300739250 |
| 1 | Measurement and geometry | 6 | 6 | 1.0066916633 | -1.0726284236 |
| 1 | Measurement and geometry | 7 | 7 | 0.9966926693 | 0.2509687098 |
| 1 | Measurement and geometry | 8 | 8 | 0.9937710517 | 1.1381245105 |
| 1 | Measurement and geometry | 9 | 9 | 0.9884997037 | 2.1442890318 |
| 1 | Measurement and geometry | 10 | 10 | 1.0157936061 | -2.3095867599 |
| 1 | Measurement and geometry | 11 | 11 | 0.9942833756 | 0.8449005952 |
| 1 | Measurement and geometry | 12 | 12 | 0.9911773864 | 1.9111290402 |
| 1 | Measurement and geometry | 13 | 13 | 0.9924599864 | 1.1353585999 |
| 1 | Measurement and geometry | 14 | 14 | 1.0049965215 | -0.4971152259 |
| 1 | Measurement and geometry | 15 | 15 | 0.9982411974 | 0.3945620381 |
| 1 | Measurement and geometry | 16 | 16 | 1.0036882835 | -0.5337006736 |
| 1 | Measurement and geometry | 17 | 17 | 0.9970294079 | -0.1665351139 |
| 1 | Measurement and geometry | 18 | 18 | 1.0007702161 | -0.2473497547 |
| 1 | Measurement and geometry | 19 | 19 | 0.9925874615 | 0.8952549344 |
| 1 | Measurement and geometry | 20 | 20 | 1.0102316057 | -1.8421679427 |
| 1 | Data analysis, statistics, and probability | 1 | 1 | 0.9934938428 | 1.2181980136 |
| 1 | Data analysis, statistics, and probability | 2 | 2 | 1.0033026001 | -0.2089769698 |
| 1 | Data analysis, statistics, and probability | 3 | 3 | 1.0066712970 | -1.3750854749 |
| 1 | Data analysis, statistics, and probability | 4 | 4 | 1.0002118593 | 0.4731237698 |
| 1 | Data analysis, statistics, and probability | 5 | 5 | 0.9955521475 | 1.1035766893 |
| 1 | Data analysis, statistics, and probability | 6 | 6 | 1.0196231481 | -2.9638543630 |
| 1 | Data analysis, statistics, and probability | 7 | 7 | 1.0014938333 | 0.0149507116 |
| 1 | Data analysis, statistics, and probability | 8 | 8 | 1.0015432515 | -0.2858119498 |
| 1 | Data analysis, statistics, and probability | 9 | 9 | 0.9935451135 | 0.8193136586 |
| 1 | Data analysis, statistics, and probability | 10 | 10 | 0.9944312455 | 0.5338853723 |
| 1 | Data analysis, statistics, and probability | 11 | 11 | 0.9877749719 | 2.0243986982 |
| 1 | Data analysis, statistics, and probability | 12 | 12 | 1.0066096879 | -1.2422725342 |
| 1 | Data analysis, statistics, and probability | 13 | 13 | 1.0110312122 | -1.1088723202 |
| 1 | Data analysis, statistics, and probability | 14 | 14 | 0.9871919266 | 0.9056264299 |
| 1 | Data analysis, statistics, and probability | 15 | 15 | 0.9912358867 | 0.9400862187 |
| 1 | Data analysis, statistics, and probability | 16 | 16 | 1.0021035069 | -0.1710894591 |
| 1 | Data analysis, statistics, and probability | 17 | 17 | 1.0034224902 | -1.1820532066 |
| 1 | Data analysis, statistics, and probability | 18 | 18 | 1.0010482869 | -0.3942645878 |
| 1 | Data analysis, statistics, and probability | 19 | 19 | 0.9945673903 | 1.5110941507 |
| 1 | Data analysis, statistics, and probability | 20 | 20 | 1.0056153101 | -0.6846636999 |
| 1 | Algebra | 1 | 1 | 1.0058694146 | -0.7047963185 |
| 1 | Algebra | 2 | 2 | 1.0103464361 | -2.0318753539 |
| 1 | Algebra | 3 | 3 | 1.0018132072 | -0.3836438695 |
| 1 | Algebra | 4 | 4 | 0.9963825645 | 0.5302027868 |
| 1 | Algebra | 5 | 5 | 0.9945323847 | 0.7054150126 |
| 1 | Algebra | 6 | 6 | 0.9950082131 | 0.6603065794 |
| 1 | Algebra | 7 | 7 | 0.9918939677 | 1.2256236331 |
| 1 | Algebra | 8 | 8 | 0.9980284449 | 0.5739791948 |
| 1 | Algebra | 9 | 9 | 1.0051099570 | -0.4106239190 |
| 1 | Algebra | 10 | 10 | 1.0052486903 | -1.0712569043 |
| 1 | Algebra | 11 | 11 | 1.0046734243 | -0.4043614332 |
| 1 | Algebra | 12 | 12 | 1.0015464907 | -0.4857419479 |
| 1 | Algebra | 13 | 13 | 0.9989587027 | 0.5279625282 |
| 1 | Algebra | 14 | 14 | 1.0138830753 | -2.0989221913 |
| 1 | Algebra | 15 | 15 | 0.9871744574 | 1.7605703024 |
| 1 | Algebra | 16 | 16 | 1.0008152444 | -0.0754389068 |
| 1 | Algebra | 17 | 17 | 1.0002961472 | 0.1887664913 |
| 1 | Algebra | 18 | 18 | 0.9831702560 | 2.3523575653 |
| 1 | Algebra | 19 | 19 | 1.0017306242 | -0.2332792547 |
| 1 | Algebra | 20 | 20 | 1.0041931895 | -0.7296231154 |
| 2 | Number properties and operations | 1 | 14 | 0.9917163492 | 1.0398003828 |
| 2 | Number properties and operations | 2 | 11 | 0.9879614988 | 1.4607812723 |
| 2 | Number properties and operations | 3 | 18 | 0.9910917265 | 0.9347975375 |
| 2 | Number properties and operations | 4 | 15 | 1.0125783426 | -1.6480624142 |
| 2 | Number properties and operations | 5 | 20 | 1.0269478263 | -4.0444628009 |
| 2 | Number properties and operations | 6 | 17 | 0.9885967690 | 1.2307243571 |
| 2 | Number properties and operations | 7 | 3 | 1.0188017188 | -2.6479824299 |
| 2 | Number properties and operations | 8 | 16 | 1.0073901476 | -0.5191030093 |
| 2 | Number properties and operations | 9 | 12 | 0.9951953203 | 0.0342018929 |
| 2 | Number properties and operations | 10 | 6 | 1.0043958835 | -0.4799628557 |
| 2 | Number properties and operations | 11 | 19 | 0.9955540502 | -0.0790863154 |
| 2 | Number properties and operations | 12 | 2 | 0.9919503698 | 1.4166351663 |
| 2 | Number properties and operations | 13 | 1 | 1.0201016739 | -3.1642481429 |
| 2 | Number properties and operations | 14 | 13 | 0.9957554044 | 1.0170831362 |
| 2 | Number properties and operations | 15 | 5 | 0.9901319802 | 2.8337998174 |
| 2 | Number properties and operations | 16 | 7 | 1.0003153358 | 0.7962754104 |
| 2 | Number properties and operations | 17 | 4 | 1.0005805421 | -0.0035910370 |
| 2 | Number properties and operations | 18 | 9 | 0.9730132013 | 3.6128631174 |
| 2 | Number properties and operations | 19 | 8 | 0.9995798534 | 0.0144063934 |
| 2 | Number properties and operations | 20 | 10 | 1.0094661732 | -1.9722469437 |
| 2 | Measurement and geometry | 1 | 14 | 0.9952873195 | 0.8939054272 |
| 2 | Measurement and geometry | 2 | 11 | 1.0067776110 | -0.8982564341 |
| 2 | Measurement and geometry | 3 | 18 | 1.0176541186 | -3.1805646187 |
| 2 | Measurement and geometry | 4 | 15 | 1.0001462591 | -0.3347088985 |
| 2 | Measurement and geometry | 5 | 20 | 1.0010637453 | -0.5433645810 |
| 2 | Measurement and geometry | 6 | 17 | 1.0036513451 | -0.9091342097 |
| 2 | Measurement and geometry | 7 | 3 | 1.0131614490 | -1.8629510899 |
| 2 | Measurement and geometry | 8 | 16 | 1.0063718329 | -0.9291021226 |
| 2 | Measurement and geometry | 9 | 12 | 0.9787279902 | 3.9641043100 |
| 2 | Measurement and geometry | 10 | 6 | 1.0082948626 | -1.3088710311 |
| 2 | Measurement and geometry | 11 | 19 | 0.9893286347 | 1.4175677627 |
| 2 | Measurement and geometry | 12 | 2 | 1.0073791297 | -1.1606155815 |
| 2 | Measurement and geometry | 13 | 1 | 0.9866599450 | 2.3748595132 |
| 2 | Measurement and geometry | 14 | 13 | 0.9997907221 | 0.2980204767 |
| 2 | Measurement and geometry | 15 | 5 | 0.9909033020 | 1.5187594238 |
| 2 | Measurement and geometry | 16 | 7 | 0.9901726365 | 1.2767487842 |
| 2 | Measurement and geometry | 17 | 4 | 1.0069136232 | -1.3469868213 |
| 2 | Measurement and geometry | 18 | 9 | 0.9948856493 | 0.9727121293 |
| 2 | Measurement and geometry | 19 | 8 | 0.9894516889 | 1.6885326335 |
| 2 | Measurement and geometry | 20 | 10 | 1.0144334519 | -2.1047628944 |
| 2 | Data analysis, statistics, and probability | 1 | 14 | 0.9843071640 | 2.1103232269 |
| 2 | Data analysis, statistics, and probability | 2 | 11 | 0.9937901921 | 0.8393426446 |
| 2 | Data analysis, statistics, and probability | 3 | 18 | 0.9968368350 | -0.0684528924 |
| 2 | Data analysis, statistics, and probability | 4 | 15 | 0.9973228518 | 0.1569841066 |
| 2 | Data analysis, statistics, and probability | 5 | 20 | 1.0051376289 | -0.2654227189 |
| 2 | Data analysis, statistics, and probability | 6 | 17 | 1.0049446167 | -0.7282026838 |
| 2 | Data analysis, statistics, and probability | 7 | 3 | 1.0070513527 | -0.8099613587 |
| 2 | Data analysis, statistics, and probability | 8 | 16 | 1.0038204995 | -0.6666972505 |
| 2 | Data analysis, statistics, and probability | 9 | 12 | 0.9948577696 | 0.6652635777 |
| 2 | Data analysis, statistics, and probability | 10 | 6 | 1.0105490265 | -1.4378342825 |
| 2 | Data analysis, statistics, and probability | 11 | 19 | 0.9914263197 | 2.0772716751 |
| 2 | Data analysis, statistics, and probability | 12 | 2 | 1.0084533698 | -0.9888228487 |
| 2 | Data analysis, statistics, and probability | 13 | 1 | 1.0087115121 | -1.3996628702 |
| 2 | Data analysis, statistics, and probability | 14 | 13 | 0.9986969298 | 0.2962721097 |
| 2 | Data analysis, statistics, and probability | 15 | 5 | 0.9905891353 | 1.4881984116 |
| 2 | Data analysis, statistics, and probability | 16 | 7 | 0.9960781158 | 0.6499128577 |
| 2 | Data analysis, statistics, and probability | 17 | 4 | 1.0044522960 | -0.6127660116 |
| 2 | Data analysis, statistics, and probability | 18 | 9 | 1.0047514736 | -0.8824846020 |
| 2 | Data analysis, statistics, and probability | 19 | 8 | 1.0015909187 | -0.1169115212 |
| 2 | Data analysis, statistics, and probability | 20 | 10 | 0.9969640341 | -0.3551536385 |
| 2 | Algebra | 1 | 14 | 1.0139555478 | -1.8215721494 |
| 2 | Algebra | 2 | 11 | 1.0114543731 | -2.0759797198 |
| 2 | Algebra | 3 | 18 | 0.9938228634 | 0.6837602877 |
| 2 | Algebra | 4 | 15 | 0.9952880972 | 0.5512174679 |
| 2 | Algebra | 5 | 20 | 1.0002118367 | -0.1497232879 |
| 2 | Algebra | 6 | 17 | 0.9944349337 | 0.8057821970 |
| 2 | Algebra | 7 | 3 | 0.9962616908 | 0.6687469161 |
| 2 | Algebra | 8 | 16 | 1.0114333182 | -1.5664531492 |
| 2 | Algebra | 9 | 12 | 1.0060551448 | -1.2190772847 |
| 2 | Algebra | 10 | 6 | 1.0004064599 | 0.0136729676 |
| 2 | Algebra | 11 | 19 | 1.0057767055 | -0.5737575799 |
| 2 | Algebra | 12 | 2 | 1.0019228715 | -0.4619877071 |
| 2 | Algebra | 13 | 1 | 1.0025829434 | -0.2045201459 |
| 2 | Algebra | 14 | 13 | 1.0021616589 | -0.2446488158 |
| 2 | Algebra | 15 | 5 | 0.9893345826 | 1.5883782913 |
| 2 | Algebra | 16 | 7 | 0.9932384853 | 0.6864232561 |
| 2 | Algebra | 17 | 4 | 1.0043076838 | -0.5480209489 |
| 2 | Algebra | 18 | 9 | 0.9892636307 | 2.0785651939 |
| 2 | Algebra | 19 | 8 | 0.9899636176 | 1.8980277316 |
| 2 | Algebra | 20 | 10 | 0.9988065282 | -0.2097653361 |
| 3 | Number properties and operations | 1 | 6 | 1.0018185641 | -0.5902295694 |
| 3 | Number properties and operations | 2 | 4 | 0.9978522791 | 0.1698407648 |
| 3 | Number properties and operations | 3 | 3 | 1.0054608050 | -0.3901117782 |
| 3 | Number properties and operations | 4 | 9 | 0.9812733400 | 2.4535511503 |
| 3 | Number properties and operations | 5 | 11 | 0.9945783711 | 0.5158339491 |
| 3 | Number properties and operations | 6 | 10 | 0.9827408361 | 1.6688765009 |
| 3 | Number properties and operations | 7 | 2 | 1.0002893511 | 0.0255656028 |
| 3 | Number properties and operations | 8 | 17 | 1.0045264400 | -1.0617347669 |
| 3 | Number properties and operations | 9 | 19 | 0.9877471024 | 1.1542090973 |
| 3 | Number properties and operations | 10 | 13 | 1.0144146782 | -2.2265777650 |
| 3 | Number properties and operations | 11 | 7 | 1.0068718283 | -0.8115254258 |
| 3 | Number properties and operations | 12 | 8 | 0.9980465071 | 0.1750512427 |
| 3 | Number properties and operations | 13 | 15 | 1.0296865324 | -4.2235138865 |
| 3 | Number properties and operations | 14 | 18 | 0.9875037257 | 1.7859103146 |
| 3 | Number properties and operations | 15 | 20 | 1.0121442234 | -1.4955513158 |
| 3 | Number properties and operations | 16 | 12 | 0.9965294591 | 0.3933224970 |
| 3 | Number properties and operations | 17 | 5 | 1.0006584715 | 1.1213588878 |
| 3 | Number properties and operations | 18 | 16 | 0.9958972006 | 0.7713278974 |
| 3 | Number properties and operations | 19 | 14 | 0.9857598249 | 2.5092294206 |
| 3 | Number properties and operations | 20 | 1 | 1.0171606825 | -2.0891269438 |
| 3 | Measurement and geometry | 1 | 6 | 0.9932864572 | 1.2098511927 |
| 3 | Measurement and geometry | 2 | 4 | 1.0098538800 | -1.4489527459 |
| 3 | Measurement and geometry | 3 | 3 | 1.0200601167 | -2.9932113917 |
| 3 | Measurement and geometry | 4 | 9 | 1.0020209640 | -0.6635213228 |
| 3 | Measurement and geometry | 5 | 11 | 1.0015948463 | -0.2778409067 |
| 3 | Measurement and geometry | 6 | 10 | 1.0141784836 | -2.0715872033 |
| 3 | Measurement and geometry | 7 | 2 | 1.0111577327 | -2.0593491461 |
| 3 | Measurement and geometry | 8 | 17 | 0.9951094994 | 0.3913060980 |
| 3 | Measurement and geometry | 9 | 19 | 0.9845457977 | 2.6594880646 |
| 3 | Measurement and geometry | 10 | 13 | 1.0050925523 | -0.8288870900 |
| 3 | Measurement and geometry | 11 | 7 | 0.9852593972 | 1.9567176939 |
| 3 | Measurement and geometry | 12 | 8 | 0.9939192650 | 1.3885378323 |
| 3 | Measurement and geometry | 13 | 15 | 0.9965472442 | 0.5767924337 |
| 3 | Measurement and geometry | 14 | 18 | 1.0117389902 | -1.8219948385 |
| 3 | Measurement and geometry | 15 | 20 | 1.0005698501 | -0.2518628717 |
| 3 | Measurement and geometry | 16 | 12 | 0.9883869435 | 2.0507800317 |
| 3 | Measurement and geometry | 17 | 5 | 0.9936209564 | 0.7165978908 |
| 3 | Measurement and geometry | 18 | 16 | 1.0003005010 | 0.2312905841 |
| 3 | Measurement and geometry | 19 | 14 | 0.9957875277 | 0.4677678136 |
| 3 | Measurement and geometry | 20 | 1 | 0.9978807245 | 0.6235747942 |
| 3 | Data analysis, statistics, and probability | 1 | 6 | 1.0085648324 | -1.1346437059 |
| 3 | Data analysis, statistics, and probability | 2 | 4 | 0.9980549849 | 0.8723940366 |
| 3 | Data analysis, statistics, and probability | 3 | 3 | 1.0066712970 | -1.3750854749 |
| 3 | Data analysis, statistics, and probability | 4 | 9 | 1.0023083520 | -0.7084196648 |
| 3 | Data analysis, statistics, and probability | 5 | 11 | 0.9948186938 | 0.8394547443 |
| 3 | Data analysis, statistics, and probability | 6 | 10 | 1.0033606392 | -0.9677954068 |
| 3 | Data analysis, statistics, and probability | 7 | 2 | 1.0040602037 | 0.1065336728 |
| 3 | Data analysis, statistics, and probability | 8 | 17 | 0.9940892947 | 0.7569299802 |
| 3 | Data analysis, statistics, and probability | 9 | 19 | 0.9908796436 | 2.0124360025 |
| 3 | Data analysis, statistics, and probability | 10 | 13 | 0.9977375864 | 1.2156619542 |
| 3 | Data analysis, statistics, and probability | 11 | 7 | 0.9946808911 | 0.8935877535 |
| 3 | Data analysis, statistics, and probability | 12 | 8 | 1.0096647145 | -1.5253546669 |
| 3 | Data analysis, statistics, and probability | 13 | 15 | 1.0073892574 | -1.2876796446 |
| 3 | Data analysis, statistics, and probability | 14 | 18 | 0.9963878449 | -0.2654798778 |
| 3 | Data analysis, statistics, and probability | 15 | 20 | 1.0001268313 | 0.1229022594 |
| 3 | Data analysis, statistics, and probability | 16 | 12 | 0.9968048846 | 0.4865068604 |
| 3 | Data analysis, statistics, and probability | 17 | 5 | 1.0008975587 | -0.3764395885 |
| 3 | Data analysis, statistics, and probability | 18 | 16 | 1.0114268548 | -1.7044872320 |
| 3 | Data analysis, statistics, and probability | 19 | 14 | 0.9843973817 | 1.9616924997 |
| 3 | Data analysis, statistics, and probability | 20 | 1 | 0.9979837662 | 0.0295896622 |
| 3 | Algebra | 1 | 6 | 0.9979971708 | 0.5980153287 |
| 3 | Algebra | 2 | 4 | 1.0061044608 | -1.1651256404 |
| 3 | Algebra | 3 | 3 | 1.0018132072 | -0.3836438695 |
| 3 | Algebra | 4 | 9 | 0.9992679782 | 0.4544368094 |
| 3 | Algebra | 5 | 11 | 0.9987347934 | -0.0412102704 |
| 3 | Algebra | 6 | 10 | 0.9998243145 | -0.4214934158 |
| 3 | Algebra | 7 | 2 | 0.9957501061 | 0.6675688741 |
| 3 | Algebra | 8 | 17 | 0.9994396307 | 0.2412954950 |
| 3 | Algebra | 9 | 19 | 1.0086432915 | -1.4090984125 |
| 3 | Algebra | 10 | 13 | 1.0046528092 | -0.5573278689 |
| 3 | Algebra | 11 | 7 | 0.9996864821 | 0.1999540640 |
| 3 | Algebra | 12 | 8 | 0.9923279291 | 1.4626060205 |
| 3 | Algebra | 13 | 15 | 0.9970538305 | 0.5280686242 |
| 3 | Algebra | 14 | 18 | 0.9980647183 | -0.0543180743 |
| 3 | Algebra | 15 | 20 | 0.9949843515 | 0.7382823077 |
| 3 | Algebra | 16 | 12 | 0.9967252817 | 0.1022970481 |
| 3 | Algebra | 17 | 5 | 1.0053997132 | -0.7030169743 |
| 3 | Algebra | 18 | 16 | 0.9942570788 | 1.0995182799 |
| 3 | Algebra | 19 | 14 | 1.0077963477 | -0.9842292192 |
| 3 | Algebra | 20 | 1 | 1.0018360065 | -0.4296434401 |
| 4 | Number properties and operations | 1 | 2 | 0.9994774901 | -0.2239571962 |
| 4 | Number properties and operations | 2 | 14 | 0.9887619836 | 1.8026446257 |
| 4 | Number properties and operations | 3 | 7 | 0.9947616287 | 1.5764984982 |
| 4 | Number properties and operations | 4 | 9 | 0.9812733400 | 2.4535511503 |
| 4 | Number properties and operations | 5 | 20 | 1.0269478263 | -4.0444628009 |
| 4 | Number properties and operations | 6 | 13 | 0.9931927583 | 0.8181845647 |
| 4 | Number properties and operations | 7 | 16 | 1.0108210394 | -1.1184384613 |
| 4 | Number properties and operations | 8 | 8 | 1.0030207258 | -0.6278313743 |
| 4 | Number properties and operations | 9 | 4 | 0.9927185946 | 0.7361337695 |
| 4 | Number properties and operations | 10 | 11 | 0.9934627371 | 0.8076210431 |
| 4 | Number properties and operations | 11 | 19 | 0.9955540502 | -0.0790863154 |
| 4 | Number properties and operations | 12 | 1 | 1.0011977254 | 0.0889178440 |
| 4 | Number properties and operations | 13 | 18 | 1.0146734070 | -3.1300943528 |
| 4 | Number properties and operations | 14 | 10 | 0.9852765140 | 1.8656819516 |
| 4 | Number properties and operations | 15 | 6 | 0.9910290228 | 1.7207753842 |
| 4 | Number properties and operations | 16 | 12 | 0.9965294591 | 0.3933224970 |
| 4 | Number properties and operations | 17 | 15 | 1.0180159607 | -2.0044078705 |
| 4 | Number properties and operations | 18 | 3 | 1.0037600526 | -0.7432959035 |
| 4 | Number properties and operations | 19 | 5 | 0.9949000007 | 2.0079405974 |
| 4 | Number properties and operations | 20 | 17 | 1.0154813565 | -2.4320957283 |
| 4 | Measurement and geometry | 1 | 2 | 1.0023472964 | -0.4273978066 |
| 4 | Measurement and geometry | 2 | 14 | 1.0049902486 | -0.7482977908 |
| 4 | Measurement and geometry | 3 | 7 | 1.0034792002 | -0.8609193889 |
| 4 | Measurement and geometry | 4 | 9 | 1.0020209640 | -0.6635213228 |
| 4 | Measurement and geometry | 5 | 20 | 1.0010637453 | -0.5433645810 |
| 4 | Measurement and geometry | 6 | 13 | 1.0034944446 | -0.5933947810 |
| 4 | Measurement and geometry | 7 | 16 | 1.0102973134 | -1.5734824291 |
| 4 | Measurement and geometry | 8 | 8 | 0.9937710517 | 1.1381245105 |
| 4 | Measurement and geometry | 9 | 4 | 0.9924999899 | 1.5514844386 |
| 4 | Measurement and geometry | 10 | 11 | 1.0121228096 | -1.7814170199 |
| 4 | Measurement and geometry | 11 | 19 | 0.9893286347 | 1.4175677627 |
| 4 | Measurement and geometry | 12 | 1 | 0.9892868405 | 2.1980936418 |
| 4 | Measurement and geometry | 13 | 18 | 1.0043206465 | -0.9746498808 |
| 4 | Measurement and geometry | 14 | 10 | 1.0104353283 | -1.1706811951 |
| 4 | Measurement and geometry | 15 | 6 | 0.9973144289 | 0.4795716999 |
| 4 | Measurement and geometry | 16 | 12 | 0.9883869435 | 2.0507800317 |
| 4 | Measurement and geometry | 17 | 15 | 1.0009789768 | -0.4135397087 |
| 4 | Measurement and geometry | 18 | 3 | 1.0031362962 | -0.0530616476 |
| 4 | Measurement and geometry | 19 | 5 | 0.9873972172 | 1.8217973330 |
| 4 | Measurement and geometry | 20 | 17 | 1.0039036668 | -0.9419655383 |
| 4 | Data analysis, statistics, and probability | 1 | 2 | 1.0002975772 | 0.5689758032 |
| 4 | Data analysis, statistics, and probability | 2 | 14 | 0.9872641496 | 1.3448065394 |
| 4 | Data analysis, statistics, and probability | 3 | 7 | 1.0011158749 | -0.5470547074 |
| 4 | Data analysis, statistics, and probability | 4 | 9 | 1.0023083520 | -0.7084196648 |
| 4 | Data analysis, statistics, and probability | 5 | 20 | 1.0051376289 | -0.2654227189 |
| 4 | Data analysis, statistics, and probability | 6 | 13 | 1.0066966690 | -0.2910116976 |
| 4 | Data analysis, statistics, and probability | 7 | 16 | 1.0075519846 | -0.8098925643 |
| 4 | Data analysis, statistics, and probability | 8 | 8 | 1.0015432515 | -0.2858119498 |
| 4 | Data analysis, statistics, and probability | 9 | 4 | 0.9914669506 | 1.9976615877 |
| 4 | Data analysis, statistics, and probability | 10 | 11 | 0.9927629315 | 1.3120652802 |
| 4 | Data analysis, statistics, and probability | 11 | 19 | 0.9914263197 | 2.0772716751 |
| 4 | Data analysis, statistics, and probability | 12 | 1 | 1.0015941620 | -0.3290049431 |
| 4 | Data analysis, statistics, and probability | 13 | 18 | 1.0086936092 | -1.6673754764 |
| 4 | Data analysis, statistics, and probability | 14 | 10 | 0.9953874098 | -0.3824577630 |
| 4 | Data analysis, statistics, and probability | 15 | 6 | 1.0075934129 | -1.5276879211 |
| 4 | Data analysis, statistics, and probability | 16 | 12 | 0.9968048846 | 0.4865068604 |
| 4 | Data analysis, statistics, and probability | 17 | 15 | 1.0015510405 | -0.9257691956 |
| 4 | Data analysis, statistics, and probability | 18 | 3 | 1.0109242976 | -1.7041115207 |
| 4 | Data analysis, statistics, and probability | 19 | 5 | 0.9916350420 | 1.7248860452 |
| 4 | Data analysis, statistics, and probability | 20 | 17 | 0.9985379135 | -0.1145937550 |
| 4 | Algebra | 1 | 2 | 1.0056444139 | -0.8528352940 |
| 4 | Algebra | 2 | 14 | 1.0186964297 | -3.0103563689 |
| 4 | Algebra | 3 | 7 | 0.9974211456 | 0.1778466468 |
| 4 | Algebra | 4 | 9 | 0.9992679782 | 0.4544368094 |
| 4 | Algebra | 5 | 20 | 1.0002118367 | -0.1497232879 |
| 4 | Algebra | 6 | 13 | 0.9992316488 | 0.0920504594 |
| 4 | Algebra | 7 | 16 | 0.9994604704 | 0.4678746731 |
| 4 | Algebra | 8 | 8 | 0.9980284449 | 0.5739791948 |
| 4 | Algebra | 9 | 4 | 1.0022076744 | -0.3323600549 |
| 4 | Algebra | 10 | 11 | 1.0091776075 | -1.4851123668 |
| 4 | Algebra | 11 | 19 | 1.0057767055 | -0.5737575799 |
| 4 | Algebra | 12 | 1 | 1.0021470394 | -0.3138612842 |
| 4 | Algebra | 13 | 18 | 0.9948748561 | 0.7151347545 |
| 4 | Algebra | 14 | 10 | 1.0027560625 | -0.7583923945 |
| 4 | Algebra | 15 | 6 | 0.9848800097 | 2.3240132128 |
| 4 | Algebra | 16 | 12 | 0.9967252817 | 0.1022970481 |
| 4 | Algebra | 17 | 15 | 1.0032045112 | -0.5258219029 |
| 4 | Algebra | 18 | 3 | 0.9910749527 | 1.2983689435 |
| 4 | Algebra | 19 | 5 | 0.9964213906 | 0.6824656619 |
| 4 | Algebra | 20 | 17 | 0.9934226335 | 1.0163689928 |
| 5 | Number properties and operations | 1 | 19 | 0.9958216732 | -0.1752500607 |
| 5 | Number properties and operations | 2 | 10 | 0.9981812810 | -0.6839273715 |
| 5 | Number properties and operations | 3 | 13 | 0.9993733869 | 0.1588583767 |
| 5 | Number properties and operations | 4 | 8 | 0.9999953645 | -0.5244283882 |
| 5 | Number properties and operations | 5 | 17 | 1.0108543758 | -2.0965104770 |
| 5 | Number properties and operations | 6 | 12 | 0.9848679476 | 1.8243924905 |
| 5 | Number properties and operations | 7 | 1 | 1.0096144460 | -1.3151198229 |
| 5 | Number properties and operations | 8 | 11 | 0.9883523229 | 1.5339484914 |
| 5 | Number properties and operations | 9 | 5 | 0.9927959117 | 1.8611413072 |
| 5 | Number properties and operations | 10 | 6 | 1.0043958835 | -0.4799628557 |
| 5 | Number properties and operations | 11 | 18 | 1.0031572489 | -1.4444164224 |
| 5 | Number properties and operations | 12 | 9 | 0.9793609694 | 3.1399350458 |
| 5 | Number properties and operations | 13 | 15 | 1.0296865324 | -4.2235138865 |
| 5 | Number properties and operations | 14 | 2 | 0.9836169728 | 3.0901719543 |
| 5 | Number properties and operations | 15 | 3 | 1.0070112891 | -0.5538487571 |
| 5 | Number properties and operations | 16 | 7 | 1.0003153358 | 0.7962754104 |
| 5 | Number properties and operations | 17 | 14 | 0.9914653925 | 1.6307927635 |
| 5 | Number properties and operations | 18 | 20 | 1.0088764147 | -1.6859641116 |
| 5 | Number properties and operations | 19 | 16 | 1.0039342858 | 0.1259325149 |
| 5 | Number properties and operations | 20 | 4 | 1.0091334518 | -1.1180541756 |
| 5 | Measurement and geometry | 1 | 19 | 0.9920888608 | 1.3200231107 |
| 5 | Measurement and geometry | 2 | 10 | 1.0104290214 | -1.4232231014 |
| 5 | Measurement and geometry | 3 | 13 | 1.0056359950 | -1.0445050905 |
| 5 | Measurement and geometry | 4 | 8 | 0.9948600613 | 0.6594477652 |
| 5 | Measurement and geometry | 5 | 17 | 0.9947932325 | 0.3487023144 |
| 5 | Measurement and geometry | 6 | 12 | 0.9995364063 | 0.3662979784 |
| 5 | Measurement and geometry | 7 | 1 | 0.9929975808 | 1.3155011179 |
| 5 | Measurement and geometry | 8 | 11 | 1.0019132756 | -0.2349458320 |
| 5 | Measurement and geometry | 9 | 5 | 0.9793976033 | 3.5768052802 |
| 5 | Measurement and geometry | 10 | 6 | 1.0082948626 | -1.3088710311 |
| 5 | Measurement and geometry | 11 | 18 | 0.9991769468 | -0.3231262368 |
| 5 | Measurement and geometry | 12 | 9 | 1.0010733959 | 0.0708166612 |
| 5 | Measurement and geometry | 13 | 15 | 0.9965472442 | 0.5767924337 |
| 5 | Measurement and geometry | 14 | 2 | 1.0121253696 | -1.8282855337 |
| 5 | Measurement and geometry | 15 | 3 | 1.0084063236 | -0.9661673540 |
| 5 | Measurement and geometry | 16 | 7 | 0.9901726365 | 1.2767487842 |
| 5 | Measurement and geometry | 17 | 14 | 1.0020641525 | -0.6468229518 |
| 5 | Measurement and geometry | 18 | 20 | 0.9953407769 | 0.6541469563 |
| 5 | Measurement and geometry | 19 | 16 | 1.0019977017 | -0.3717149550 |
| 5 | Measurement and geometry | 20 | 4 | 1.0138560312 | -2.1301046030 |
| 5 | Data analysis, statistics, and probability | 1 | 19 | 0.9944762405 | 1.6612604119 |
| 5 | Data analysis, statistics, and probability | 2 | 10 | 0.9954602324 | 0.0603683378 |
| 5 | Data analysis, statistics, and probability | 3 | 13 | 0.9991469605 | 0.4937556966 |
| 5 | Data analysis, statistics, and probability | 4 | 8 | 1.0066785771 | -1.1464237325 |
| 5 | Data analysis, statistics, and probability | 5 | 17 | 0.9980635942 | 0.3016966597 |
| 5 | Data analysis, statistics, and probability | 6 | 12 | 1.0094164247 | -1.4982216201 |
| 5 | Data analysis, statistics, and probability | 7 | 1 | 0.9972308770 | 0.7589012805 |
| 5 | Data analysis, statistics, and probability | 8 | 11 | 0.9908573155 | 1.2932080120 |
| 5 | Data analysis, statistics, and probability | 9 | 5 | 0.9879581682 | 2.2247497580 |
| 5 | Data analysis, statistics, and probability | 10 | 6 | 1.0105490265 | -1.4378342825 |
| 5 | Data analysis, statistics, and probability | 11 | 18 | 0.9904293561 | 1.3660318733 |
| 5 | Data analysis, statistics, and probability | 12 | 9 | 1.0052815258 | -1.0857055721 |
| 5 | Data analysis, statistics, and probability | 13 | 15 | 1.0073892574 | -1.2876796446 |
| 5 | Data analysis, statistics, and probability | 14 | 2 | 1.0032292038 | -0.6552917134 |
| 5 | Data analysis, statistics, and probability | 15 | 3 | 1.0023111902 | -0.7371253027 |
| 5 | Data analysis, statistics, and probability | 16 | 7 | 0.9960781158 | 0.6499128577 |
| 5 | Data analysis, statistics, and probability | 17 | 14 | 0.9935922939 | -0.1242961596 |
| 5 | Data analysis, statistics, and probability | 18 | 20 | 1.0087211680 | -0.8419765842 |
| 5 | Data analysis, statistics, and probability | 19 | 16 | 1.0038682751 | -0.4974127863 |
| 5 | Data analysis, statistics, and probability | 20 | 4 | 0.9995627063 | 0.4557889666 |
| 5 | Algebra | 1 | 19 | 1.0078527533 | -1.0655823862 |
| 5 | Algebra | 2 | 10 | 1.0075165920 | -1.6598239002 |
| 5 | Algebra | 3 | 13 | 0.9979023917 | 0.4964592729 |
| 5 | Algebra | 4 | 8 | 0.9910014337 | 1.5939249689 |
| 5 | Algebra | 5 | 17 | 0.9894839830 | 1.5900490575 |
| 5 | Algebra | 6 | 12 | 1.0022559057 | -0.8136977261 |
| 5 | Algebra | 7 | 1 | 0.9959728930 | 0.8159480214 |
| 5 | Algebra | 8 | 11 | 1.0087835176 | -1.4025734998 |
| 5 | Algebra | 9 | 5 | 1.0032974204 | -0.4871215824 |
| 5 | Algebra | 10 | 6 | 1.0004064599 | 0.0136729676 |
| 5 | Algebra | 11 | 18 | 0.9960800275 | 0.7057879505 |
| 5 | Algebra | 12 | 9 | 1.0006055387 | 0.3220224499 |
| 5 | Algebra | 13 | 15 | 0.9970538305 | 0.5280686242 |
| 5 | Algebra | 14 | 2 | 1.0055725355 | -1.1279119686 |
| 5 | Algebra | 15 | 3 | 0.9929366187 | 0.8876786686 |
| 5 | Algebra | 16 | 7 | 0.9932384853 | 0.6864232561 |
| 5 | Algebra | 17 | 14 | 1.0168771651 | -2.3855282617 |
| 5 | Algebra | 18 | 20 | 0.9931188463 | 1.1498195490 |
| 5 | Algebra | 19 | 16 | 1.0032601694 | -0.2246208479 |
| 5 | Algebra | 20 | 4 | 0.9974066049 | 0.2829005274 |
| NOTE: DBA = Digitally based assessment. PBA = Paper-based assessment. Since 2005, the measurement and geometry scales are combined at grade 12. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment. | |||||
Last updated 09 January 2024 (ML)