Some Median Problems

<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-some-median-problems" target="_blank">Some Median Problems Exercise</a></p><p>The <strong><span style="color:#8e44ad;">Median</span></strong> is a measure of central tendency that gives you the &quot;middle&quot; number in a set of data. The way you calculate the median depends on whether there is an odd number of items in a dataset or an even number of items.</p> <p><strong><span style="color:#27ae60;">Odd Number of Items in the Dataset</span></strong></p> <p style="margin-left: 40px;"><strong><u>Example</u></strong>: What is the median of the seven numbers below?</p> <p>$$7, 12, 10, 3, 1, 17, 19$$</p> <center><svg height="245.19375610351562" style=" width:661.6000366210938px; height:245.19375610351562px; 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=" M89,72 L526.2,71.6" stroke-dasharray="" style="stroke: rgb(218, 218, 218); stroke-width: 1; fill: none; fill-opacity: 1; stroke-opacity: 1;"></path></g><g class="arrow-line"><path 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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(1,0,0,1,170.80001831054688,60.279987792968754)"><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 -3Z" 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(1,0,0,1,210.80001831054688,59.279987792968754)"><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 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103 842 15 750 15C653 15 612 116 612 360C612 571 649 654 744 654Z" 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(1,0,0,1,346.8000183105469,59.279987792968754)"><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(1,0,0,1,402.8000183105469,59.279987792968754)"><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 -3ZM908 603L546 -1L656 -1L996 659L996 689L543 689L543 477L573 477L580 533C588 595 595 603 641 603Z" 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(1,0,0,1,456.8000183105469,59.279987792968754)"><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 -3ZM595 -20C706 16 754 39 808 85C905 168 956 283 956 417C956 586 875 689 743 689C615 689 519 589 519 455C519 340 594 256 698 256C732 256 771 267 789 282L859 340C851 172 742 49 561 5L561 -3ZM739 656C784 656 817 637 839 597C857 565 869 516 869 471C869 379 816 317 739 317C659 317 605 388 605 492C605 593 657 656 739 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><text style="white-space:pre;stroke:none;fill:rgb(208,2,27);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(208, 2, 27);" x="135.80001831054688" y="6.399993896484375">Step 1</text></g><g><text style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);" x="174.83126831054688" y="6.399993896484375">: </text></g><g><text style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:italic;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);" x="182.33749389648438" y="6.399993896484375">Put the numbers in order from low to high.</text></g></g></g><g><g><g><g transform="matrix(1,0,0,1,169.80001831054688,142.2800030517578)"><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 -3Z" 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(1,0,0,1,209.80001831054688,141.27998779296874)"><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 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584 57C619 8 675 -20 737 -20C888 -20 964 110 964 366C964 585 899 689 762 689ZM744 654C841 654 880 556 880 316C880 103 842 15 750 15C653 15 612 116 612 360C612 571 649 654 744 654Z" fill="rgb(84,157,0)" fill-opacity="1" stroke="rgb(84,157,0)" stroke-opacity="1" stroke-width="24" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,345.8000183105469,141.27998779296874)"><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(1,0,0,1,401.8000183105469,141.27998779296874)"><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 -3ZM908 603L546 -1L656 -1L996 659L996 689L543 689L543 477L573 477L580 533C588 595 595 603 641 603Z" 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(1,0,0,1,455.8000183105469,141.27998779296874)"><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 -3ZM595 -20C706 16 754 39 808 85C905 168 956 283 956 417C956 586 875 689 743 689C615 689 519 589 519 455C519 340 594 256 698 256C732 256 771 267 789 282L859 340C851 172 742 49 561 5L561 -3ZM739 656C784 656 817 637 839 597C857 565 869 516 869 471C869 379 816 317 739 317C659 317 605 388 605 492C605 593 657 656 739 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><text style="white-space:pre;stroke:none;fill:rgb(208,2,27);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(208, 2, 27);" x="134.80001831054688" y="88.39999389648438">Step 2</text></g><g><text style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);" x="173.83126831054688" y="88.39999389648438">: </text></g><g><text style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:italic;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);" x="181.33749389648438" y="88.39999389648438">Identify the middle number.</text></g></g></g><g><g><g><g transform="matrix(1,0,0,1,170.80001831054688,228.2800030517578)"><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 -3Z" 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(1,0,0,1,210.80001831054688,227.2800030517578)"><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 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27L96 -3C250 0 250 0 261 0C292 0 402 -3 418 -3ZM762 689C607 689 528 566 528 324C528 207 549 106 584 57C619 8 675 -20 737 -20C888 -20 964 110 964 366C964 585 899 689 762 689ZM744 654C841 654 880 556 880 316C880 103 842 15 750 15C653 15 612 116 612 360C612 571 649 654 744 654Z" fill="rgb(84,157,0)" fill-opacity="1" stroke="rgb(84,157,0)" stroke-opacity="1" stroke-width="24" transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,337.8000183105469,227.2800030517578)"><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(1,0,0,1,393.8000183105469,227.2800030517578)"><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 -3ZM908 603L546 -1L656 -1L996 659L996 689L543 689L543 477L573 477L580 533C588 595 595 603 641 603Z" 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(1,0,0,1,447.8000183105469,227.2800030517578)"><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 -3ZM595 -20C706 16 754 39 808 85C905 168 956 283 956 417C956 586 875 689 743 689C615 689 519 589 519 455C519 340 594 256 698 256C732 256 771 267 789 282L859 340C851 172 742 49 561 5L561 -3ZM739 656C784 656 817 637 839 597C857 565 869 516 869 471C869 379 816 317 739 317C659 317 605 388 605 492C605 593 657 656 739 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><text style="white-space:pre;stroke:none;fill:rgb(208,2,27);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(208, 2, 27);" x="135.80001831054688" y="174.40000915527344">Step 3</text></g><g><text style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);" x="174.83126831054688" y="174.40000915527344">: </text></g><g><text style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:italic;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);" x="182.33749389648438" y="174.40000915527344">Confirm that there is an equal number of items to the left and right.</text></g></g></g><g><g><g><g transform="matrix(1,0,0,1,181.80001831054688,215.30000915527344)"><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 -3Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.0119,0,0,-0.0119,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,223.80001831054688,215.30000915527344)"><path d="M16 23L16 -3C203 -3 203 0 239 0C275 0 275 -3 468 -3L468 82C353 77 307 81 122 77L304 270C401 373 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transform="matrix(1,0,0,1,472.8000183105469,215.30000915527344)"><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(0.0119,0,0,-0.0119,0,0)"></path></g></g></g></g></svg> </svg></center> <p><strong><span style="color:#27ae60;">Even Number of Items in the Dataset</span></strong></p> <p style="margin-left: 40px;"><strong><u>Example</u></strong>: What is the median of the eight numbers below?</p> <p>$$22, 6, 4, 9, 3, 14, 7, 2$$</p> <center><svg xmlns="http://www.w3.org/2000/svg" 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transform="matrix(0.024480000000000002,0,0,-0.024480000000000002,0,0)" 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" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" fill="rgb(0,0,0)" fill-opacity="1"></path></g></g></g></g><g><g><g><text x="135.80001831054688" y="6.400001525878906" style="white-space:pre;stroke:none;fill:rgb(208,2,27);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(208, 2, 27);">Step 1</text></g><g><text x="174.83126831054688" y="6.400001525878906" style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);">: </text></g><g><text x="182.33749389648438" y="6.400001525878906" style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:italic;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);">Put the numbers in order from low to high.</text></g></g></g><g><g><g><text x="134.80001831054688" y="88.4000015258789" style="white-space:pre;stroke:none;fill:rgb(208,2,27);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(208, 2, 27);">Step 2</text></g><g><text x="173.83126831054688" y="88.4000015258789" style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);">: </text></g><g><text x="181.33749389648438" y="88.4000015258789" style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:italic;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);">Identify the two middle numbers.</text></g></g></g><g><g><g><text x="135.80001831054688" y="174.40001678466797" style="white-space:pre;stroke:none;fill:rgb(208,2,27);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(208, 2, 27);">Step 3</text></g><g><text x="174.83126831054688" y="174.40001678466797" style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);">: </text></g><g><text x="182.33749389648438" y="174.40001678466797" style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:italic;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);">Take the average of the two middle numbers</text></g><g><text x="448.2499694824219" y="174.40001678466797" style="white-space:pre;stroke:none;fill:rgb(0,0,0);fill-opacity:1;font-size:13.5px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(0, 0, 0);">.</text></g></g></g><g><g><g><g transform="matrix(1,0,0,1,448.8000183105469,56.28000305175782)"><path 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