Mean and Median's Relationship

<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-mean-and-medians-relationship" target="_blank">Mean and Median&#39;s Relationship Exercise</a></p> <p><strong>NOTE:&nbsp;</strong>It&#39;s possible for the mean to equal the median in cases other than the two mentioned in the video.&nbsp;</p> <p>For example, the set of numbers (0, 4, 5, 7, 9) has a mean and median both equal to 5. But notice that this set is not evenly spaced or symmetrical.</p><p>The <strong><span style="color:#8e44ad;">Relationship beween Mean and Median</span></strong> is fascinating. They can be equal in three cases:</p> <p><strong><span style="color:#27ae60;">1. Sometimes By Pure Accident</span></strong></p> <p style="margin-left: 40px;">Take a look at the dataset below:</p> <p>$$0, 1, 5, 7, 10, 13$$</p> <p style="margin-left: 40px;">If you calculate the mean and median (see previous mountain entries), you&#39;ll notice that they&#39;re both $6$.</p> <p><strong><span style="color:#27ae60;">2. The Dataset is Evenly Spaced</span></strong></p> <p style="margin-left: 40px;">Kindly refer to the dataset below. What do you notice?</p> <p>$$1, 5, 9, 13, 17, 21, 25, 29$$</p> <p style="margin-left: 40px;">Do you see the pattern? The gap between two numbers, the &quot;space,&quot; is equal to $4$ in every case. This results in the mean and median being equal. Really! Test it out. You&#39;ll see they both equal $15$.</p> <p><strong><span style="color:#27ae60;">3. The Dataset is Symmetrical</span></strong></p> <p style="margin-left: 40px;">If you&#39;d be so kind, please refer to the dataset below. What do you notice?</p> <p>$$3, 4, 6, 9, 9, 12, 14, 15$$</p> <p style="margin-left: 40px;">Do you see the pattern? Here&#39;s a hint.</p> <center><svg height="66.98750305175781" style=" width:661.6000366210938px; height:66.98750305175781px; background: #FFF; fill: none; " width="661.6000366210938" x="0" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" y="0"> <svg class="role-diagram-draw-area" xmlns="http://www.w3.org/2000/svg"><g class="shapes-region" style="stroke: black; fill: none;"><g></g></g><g></g><g></g><g></g></svg> <svg height="65.38750457763672" style="width:660px;height:65.38750457763672px;font-family:Asana-Math, Asana;background:#FFF;" width="660" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g><g><g><g transform="matrix(1,0,0,1,184.80001831054688,51.279987792968754)"><path d="M462 224C462 345 355 366 308 374C388 436 418 482 418 541C418 630 344 689 233 689C165 689 120 670 72 622L43 498L74 498L92 554C103 588 166 622 218 622C283 622 336 569 336 506C336 431 277 368 206 368C198 368 187 369 174 370L159 371L147 318L154 312C192 329 211 334 238 334C321 334 369 281 369 190C369 88 308 21 215 21C169 21 128 36 98 64C74 86 61 109 42 163L15 153C36 92 44 56 50 6C103 -12 147 -20 184 -20C307 -20 462 87 462 224Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,224.80001831054688,51.279987792968754)"><path d="M280 181L280 106C280 46 269 32 220 30L158 27L158 -3C291 0 291 0 315 0C339 0 339 0 472 -3L472 27L424 30C375 33 364 46 364 106L364 181C423 181 444 180 472 177L472 248L364 245L365 697L285 667L2 204L2 181ZM280 245L65 245L280 597Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,260.8000183105469,51.279987792968754)"><path d="M131 331C152 512 241 611 421 665L379 689C283 657 242 637 191 593C88 506 32 384 32 247C32 82 112 -20 241 -20C371 -20 468 83 468 219C468 334 399 409 293 409C216 409 184 370 131 331ZM255 349C331 349 382 283 382 184C382 80 331 13 254 13C169 13 123 86 123 220C123 255 127 274 138 291C160 325 207 349 255 349Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,297.8000183105469,51.279987792968754)"><path d="M96 -20C207 16 255 39 309 85C406 168 457 283 457 417C457 586 376 689 244 689C116 689 20 589 20 455C20 340 95 256 199 256C233 256 272 267 290 282L360 340C352 172 243 49 62 5L62 -3ZM240 656C285 656 318 637 340 597C358 565 370 516 370 471C370 379 317 317 240 317C160 317 106 388 106 492C106 593 158 656 240 656Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,335.8000183105469,51.279987792968754)"><path d="M96 -20C207 16 255 39 309 85C406 168 457 283 457 417C457 586 376 689 244 689C116 689 20 589 20 455C20 340 95 256 199 256C233 256 272 267 290 282L360 340C352 172 243 49 62 5L62 -3ZM240 656C285 656 318 637 340 597C358 565 370 516 370 471C370 379 317 317 240 317C160 317 106 388 106 492C106 593 158 656 240 656Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,367.8000183105469,51.279987792968754)"><path d="M418 -3L418 27L366 30C311 33 301 44 301 96L301 700L60 598L67 548L217 614L217 96C217 44 206 33 152 30L96 27L96 -3C250 0 250 0 261 0C292 0 402 -3 418 -3ZM515 23L515 -3C702 -3 702 0 738 0C774 0 774 -3 967 -3L967 82C852 77 806 81 621 77L803 270C900 373 930 428 930 503C930 618 852 689 725 689C653 689 604 669 555 619L538 483L567 483L580 529C596 587 632 612 699 612C785 612 840 558 840 473C840 398 798 324 685 204Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,412.8000183105469,51.279987792968754)"><path d="M418 -3L418 27L366 30C311 33 301 44 301 96L301 700L60 598L67 548L217 614L217 96C217 44 206 33 152 30L96 27L96 -3C250 0 250 0 261 0C292 0 402 -3 418 -3ZM779 181L779 106C779 46 768 32 719 30L657 27L657 -3C790 0 790 0 814 0C838 0 838 0 971 -3L971 27L923 30C874 33 863 46 863 106L863 181C922 181 943 180 971 177L971 248L863 245L864 697L784 667L501 204L501 181ZM779 245L564 245L779 597Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,455.8000183105469,51.279987792968754)"><path d="M418 -3L418 27L366 30C311 33 301 44 301 96L301 700L60 598L67 548L217 614L217 96C217 44 206 33 152 30L96 27L96 -3C250 0 250 0 261 0C292 0 402 -3 418 -3ZM958 253C958 366 877 446 763 446C715 446 679 443 626 396L626 605L931 604L931 689L574 690L574 322L594 316C641 363 668 377 717 377C813 377 873 309 873 201C873 90 809 25 700 25C646 25 596 43 582 69L536 151L512 137C535 80 547 48 561 4C589 -11 629 -20 672 -20C800 -20 958 89 958 253Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,293.8000183105469,26.887493896484376)"><path d="M555 243L555 299L51 299L51 243Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,303.0624694824219,26.887493896484376)"><path d="M263 689C108 689 29 566 29 324C29 207 50 106 85 57C120 8 176 -20 238 -20C389 -20 465 110 465 366C465 585 400 689 263 689ZM245 654C342 654 381 556 381 316C381 103 343 15 251 15C154 15 113 116 113 360C113 571 150 654 245 654Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,330.8000183105469,26.699993896484376)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,341.0249938964844,26.699993896484376)"><path d="M263 689C108 689 29 566 29 324C29 207 50 106 85 57C120 8 176 -20 238 -20C389 -20 465 110 465 366C465 585 400 689 263 689ZM245 654C342 654 381 556 381 316C381 103 343 15 251 15C154 15 113 116 113 360C113 571 150 654 245 654Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,257.8000183105469,26.699993896484376)"><path d="M555 243L555 299L51 299L51 243Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,267.0624694824219,26.699993896484376)"><path d="M462 224C462 345 355 366 308 374C388 436 418 482 418 541C418 630 344 689 233 689C165 689 120 670 72 622L43 498L74 498L92 554C103 588 166 622 218 622C283 622 336 569 336 506C336 431 277 368 206 368C198 368 187 369 174 370L159 371L147 318L154 312C192 329 211 334 238 334C321 334 369 281 369 190C369 88 308 21 215 21C169 21 128 36 98 64C74 86 61 109 42 163L15 153C36 92 44 56 50 6C103 -12 147 -20 184 -20C307 -20 462 87 462 224Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,220.80001831054688,26.699993896484376)"><path d="M555 243L555 299L51 299L51 243Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,230.06246948242188,26.699993896484376)"><path d="M459 253C459 366 378 446 264 446C216 446 180 443 127 396L127 605L432 604L432 689L75 690L75 322L95 316C142 363 169 377 218 377C314 377 374 309 374 201C374 90 310 25 201 25C147 25 97 43 83 69L37 151L13 137C36 80 48 48 62 4C90 -11 130 -20 173 -20C301 -20 459 89 459 253Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,179.80001831054688,26.699993896484376)"><path d="M555 243L555 299L51 299L51 243Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,189.06246948242188,26.699993896484376)"><path d="M131 331C152 512 241 611 421 665L379 689C283 657 242 637 191 593C88 506 32 384 32 247C32 82 112 -20 241 -20C371 -20 468 83 468 219C468 334 399 409 293 409C216 409 184 370 131 331ZM255 349C331 349 382 283 382 184C382 80 331 13 254 13C169 13 123 86 123 220C123 255 127 274 138 291C160 325 207 349 255 349Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,371.8000183105469,25.699993896484376)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,382.0249938964844,25.699993896484376)"><path d="M462 224C462 345 355 366 308 374C388 436 418 482 418 541C418 630 344 689 233 689C165 689 120 670 72 622L43 498L74 498L92 554C103 588 166 622 218 622C283 622 336 569 336 506C336 431 277 368 206 368C198 368 187 369 174 370L159 371L147 318L154 312C192 329 211 334 238 334C321 334 369 281 369 190C369 88 308 21 215 21C169 21 128 36 98 64C74 86 61 109 42 163L15 153C36 92 44 56 50 6C103 -12 147 -20 184 -20C307 -20 462 87 462 224Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,417.8000183105469,25.699993896484376)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,428.0249938964844,25.699993896484376)"><path d="M459 253C459 366 378 446 264 446C216 446 180 443 127 396L127 605L432 604L432 689L75 690L75 322L95 316C142 363 169 377 218 377C314 377 374 309 374 201C374 90 310 25 201 25C147 25 97 43 83 69L37 151L13 137C36 80 48 48 62 4C90 -11 130 -20 173 -20C301 -20 459 89 459 253Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,458.8000183105469,25.699993896484376)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,469.0249938964844,25.699993896484376)"><path d="M131 331C152 512 241 611 421 665L379 689C283 657 242 637 191 593C88 506 32 384 32 247C32 82 112 -20 241 -20C371 -20 468 83 468 219C468 334 399 409 293 409C216 409 184 370 131 331ZM255 349C331 349 382 283 382 184C382 80 331 13 254 13C169 13 123 86 123 220C123 255 127 274 138 291C160 325 207 349 255 349Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g></svg> </svg></center> <p style="margin-left: 40px;">How about now? Imagine drawing a line right through the center of the data, the median. In this case, that is $9$ (the blue one, not one of the $9$s already in the dataset...remember this is the average of those two).</p> <center><svg height="134.78750610351562" style=" width:661.6000366210938px; height:134.78750610351562px; background: #FFF; fill: none; " width="661.6000366210938" x="0" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" y="0"> <svg class="role-diagram-draw-area" xmlns="http://www.w3.org/2000/svg"><g class="shapes-region" style="stroke: black; fill: none;"><g class="arrow-line"><path class="connection real" d=" M324.2,13.6 L324.2,124.6" stroke-dasharray="" style="stroke: rgb(0, 0, 0); stroke-width: 1; fill: none; fill-opacity: 1;"></path></g><g></g></g><g></g><g></g><g></g></svg> <svg height="133.1875" style="width:660px;height:133.1875px;font-family:Asana-Math, Asana;background:#FFF;" width="660" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g><g><g><g transform="matrix(1,0,0,1,186.80001831054688,87.27998779296875)"><path d="M462 224C462 345 355 366 308 374C388 436 418 482 418 541C418 630 344 689 233 689C165 689 120 670 72 622L43 498L74 498L92 554C103 588 166 622 218 622C283 622 336 569 336 506C336 431 277 368 206 368C198 368 187 369 174 370L159 371L147 318L154 312C192 329 211 334 238 334C321 334 369 281 369 190C369 88 308 21 215 21C169 21 128 36 98 64C74 86 61 109 42 163L15 153C36 92 44 56 50 6C103 -12 147 -20 184 -20C307 -20 462 87 462 224Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,226.80001831054688,87.27998779296875)"><path d="M280 181L280 106C280 46 269 32 220 30L158 27L158 -3C291 0 291 0 315 0C339 0 339 0 472 -3L472 27L424 30C375 33 364 46 364 106L364 181C423 181 444 180 472 177L472 248L364 245L365 697L285 667L2 204L2 181ZM280 245L65 245L280 597Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,262.8000183105469,87.27998779296875)"><path d="M131 331C152 512 241 611 421 665L379 689C283 657 242 637 191 593C88 506 32 384 32 247C32 82 112 -20 241 -20C371 -20 468 83 468 219C468 334 399 409 293 409C216 409 184 370 131 331ZM255 349C331 349 382 283 382 184C382 80 331 13 254 13C169 13 123 86 123 220C123 255 127 274 138 291C160 325 207 349 255 349Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,299.8000183105469,87.27998779296875)"><path d="M96 -20C207 16 255 39 309 85C406 168 457 283 457 417C457 586 376 689 244 689C116 689 20 589 20 455C20 340 95 256 199 256C233 256 272 267 290 282L360 340C352 172 243 49 62 5L62 -3ZM240 656C285 656 318 637 340 597C358 565 370 516 370 471C370 379 317 317 240 317C160 317 106 388 106 492C106 593 158 656 240 656Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,337.8000183105469,87.27998779296875)"><path d="M96 -20C207 16 255 39 309 85C406 168 457 283 457 417C457 586 376 689 244 689C116 689 20 589 20 455C20 340 95 256 199 256C233 256 272 267 290 282L360 340C352 172 243 49 62 5L62 -3ZM240 656C285 656 318 637 340 597C358 565 370 516 370 471C370 379 317 317 240 317C160 317 106 388 106 492C106 593 158 656 240 656Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,369.8000183105469,87.27998779296875)"><path d="M418 -3L418 27L366 30C311 33 301 44 301 96L301 700L60 598L67 548L217 614L217 96C217 44 206 33 152 30L96 27L96 -3C250 0 250 0 261 0C292 0 402 -3 418 -3ZM515 23L515 -3C702 -3 702 0 738 0C774 0 774 -3 967 -3L967 82C852 77 806 81 621 77L803 270C900 373 930 428 930 503C930 618 852 689 725 689C653 689 604 669 555 619L538 483L567 483L580 529C596 587 632 612 699 612C785 612 840 558 840 473C840 398 798 324 685 204Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,414.8000183105469,87.27998779296875)"><path d="M418 -3L418 27L366 30C311 33 301 44 301 96L301 700L60 598L67 548L217 614L217 96C217 44 206 33 152 30L96 27L96 -3C250 0 250 0 261 0C292 0 402 -3 418 -3ZM779 181L779 106C779 46 768 32 719 30L657 27L657 -3C790 0 790 0 814 0C838 0 838 0 971 -3L971 27L923 30C874 33 863 46 863 106L863 181C922 181 943 180 971 177L971 248L863 245L864 697L784 667L501 204L501 181ZM779 245L564 245L779 597Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,457.8000183105469,87.27998779296875)"><path d="M418 -3L418 27L366 30C311 33 301 44 301 96L301 700L60 598L67 548L217 614L217 96C217 44 206 33 152 30L96 27L96 -3C250 0 250 0 261 0C292 0 402 -3 418 -3ZM958 253C958 366 877 446 763 446C715 446 679 443 626 396L626 605L931 604L931 689L574 690L574 322L594 316C641 363 668 377 717 377C813 377 873 309 873 201C873 90 809 25 700 25C646 25 596 43 582 69L536 151L512 137C535 80 547 48 561 4C589 -11 629 -20 672 -20C800 -20 958 89 958 253Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,295.8000183105469,62.88749389648437)"><path d="M555 243L555 299L51 299L51 243Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,305.0624694824219,62.88749389648437)"><path d="M263 689C108 689 29 566 29 324C29 207 50 106 85 57C120 8 176 -20 238 -20C389 -20 465 110 465 366C465 585 400 689 263 689ZM245 654C342 654 381 556 381 316C381 103 343 15 251 15C154 15 113 116 113 360C113 571 150 654 245 654Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,332.8000183105469,62.69999389648437)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,343.0249938964844,62.69999389648437)"><path d="M263 689C108 689 29 566 29 324C29 207 50 106 85 57C120 8 176 -20 238 -20C389 -20 465 110 465 366C465 585 400 689 263 689ZM245 654C342 654 381 556 381 316C381 103 343 15 251 15C154 15 113 116 113 360C113 571 150 654 245 654Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,259.8000183105469,62.69999389648437)"><path d="M555 243L555 299L51 299L51 243Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,269.0624694824219,62.69999389648437)"><path d="M462 224C462 345 355 366 308 374C388 436 418 482 418 541C418 630 344 689 233 689C165 689 120 670 72 622L43 498L74 498L92 554C103 588 166 622 218 622C283 622 336 569 336 506C336 431 277 368 206 368C198 368 187 369 174 370L159 371L147 318L154 312C192 329 211 334 238 334C321 334 369 281 369 190C369 88 308 21 215 21C169 21 128 36 98 64C74 86 61 109 42 163L15 153C36 92 44 56 50 6C103 -12 147 -20 184 -20C307 -20 462 87 462 224Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,222.80001831054688,62.69999389648437)"><path d="M555 243L555 299L51 299L51 243Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,232.06246948242188,62.69999389648437)"><path d="M459 253C459 366 378 446 264 446C216 446 180 443 127 396L127 605L432 604L432 689L75 690L75 322L95 316C142 363 169 377 218 377C314 377 374 309 374 201C374 90 310 25 201 25C147 25 97 43 83 69L37 151L13 137C36 80 48 48 62 4C90 -11 130 -20 173 -20C301 -20 459 89 459 253Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,181.80001831054688,62.69999389648437)"><path d="M555 243L555 299L51 299L51 243Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,191.06246948242188,62.69999389648437)"><path d="M131 331C152 512 241 611 421 665L379 689C283 657 242 637 191 593C88 506 32 384 32 247C32 82 112 -20 241 -20C371 -20 468 83 468 219C468 334 399 409 293 409C216 409 184 370 131 331ZM255 349C331 349 382 283 382 184C382 80 331 13 254 13C169 13 123 86 123 220C123 255 127 274 138 291C160 325 207 349 255 349Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,373.8000183105469,61.69999389648437)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,384.0249938964844,61.69999389648437)"><path d="M462 224C462 345 355 366 308 374C388 436 418 482 418 541C418 630 344 689 233 689C165 689 120 670 72 622L43 498L74 498L92 554C103 588 166 622 218 622C283 622 336 569 336 506C336 431 277 368 206 368C198 368 187 369 174 370L159 371L147 318L154 312C192 329 211 334 238 334C321 334 369 281 369 190C369 88 308 21 215 21C169 21 128 36 98 64C74 86 61 109 42 163L15 153C36 92 44 56 50 6C103 -12 147 -20 184 -20C307 -20 462 87 462 224Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,419.8000183105469,61.69999389648437)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,430.0249938964844,61.69999389648437)"><path d="M459 253C459 366 378 446 264 446C216 446 180 443 127 396L127 605L432 604L432 689L75 690L75 322L95 316C142 363 169 377 218 377C314 377 374 309 374 201C374 90 310 25 201 25C147 25 97 43 83 69L37 151L13 137C36 80 48 48 62 4C90 -11 130 -20 173 -20C301 -20 459 89 459 253Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,460.8000183105469,61.69999389648437)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,471.0249938964844,61.69999389648437)"><path d="M131 331C152 512 241 611 421 665L379 689C283 657 242 637 191 593C88 506 32 384 32 247C32 82 112 -20 241 -20C371 -20 468 83 468 219C468 334 399 409 293 409C216 409 184 370 131 331ZM255 349C331 349 382 283 382 184C382 80 331 13 254 13C169 13 123 86 123 220C123 255 127 274 138 291C160 325 207 349 255 349Z" fill="rgb(108,203,0)" fill-opacity="1" stroke="rgb(108,203,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.015300000000000001,0,0,-0.015300000000000001,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,319.8000183105469,99.20000305175782)"><path d="M96 -20C207 16 255 39 309 85C406 168 457 283 457 417C457 586 376 689 244 689C116 689 20 589 20 455C20 340 95 256 199 256C233 256 272 267 290 282L360 340C352 172 243 49 62 5L62 -3ZM240 656C285 656 318 637 340 597C358 565 370 516 370 471C370 379 317 317 240 317C160 317 106 388 106 492C106 593 158 656 240 656Z" fill="rgb(74,144,226)" fill-opacity="1" stroke="rgb(74,144,226)" stroke-opacity="1" stroke-width="8" transform="matrix(0.020399999999999998,0,0,-0.020399999999999998,0,0)"></path></g></g></g></g></svg> </svg></center> <p style="margin-left: 40px;">Notice that, to the left, the $9$ is zero less, the $6$ is three less, the $4$ is five less, and the $3$ is six less. The &quot;jumps&quot; on the right cancel these out exactly, giving us a symmetrical dataset where the&nbsp;<u><strong>mean is equal to the median</strong></u>.</p>