Weighted Mean Problems

<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-weighted-mean-problems" target="_blank">Weighted Mean Problems Exercise</a></p><p><strong><span style="color:#8e44ad;">The Weighted Mean</span></strong>&nbsp;is like an average, but it gives more importance to some numbers than others based on their &quot;weight.&quot; Instead of treating every number equally, it considers that some numbers might count more because they&rsquo;re more significant or happen more often (from ChatGTP, pretty good explanation).</p> <p><strong><span style="color:#e74c3c;">Example</span></strong></p> <p>Look at the frequency table below and the two different ways to calculate the mean.</p> <center><svg height="199.9875030517578" style=" width:661.6000366210938px; height:199.9875030517578px; 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="composite-shape"><path class="real" d=" M58,8.6 L213.2,8.6 L213.2,181.6 L58,181.6 Z" style="stroke-width: 1; stroke: rgb(0, 0, 0); fill: none; fill-opacity: 1;"></path></g><g class="arrow-line"><path class="connection real" d=" M58.2,36.6 L213.2,36.6" stroke-dasharray="" style="stroke: rgb(0, 0, 0); stroke-width: 1; fill: none; fill-opacity: 1;"></path></g><g class="arrow-line"><path class="connection real" d=" M131.2,181.6 L130.2,8.6" stroke-dasharray="" style="stroke: rgb(0, 0, 0); stroke-width: 1; fill: none; fill-opacity: 1;"></path></g><g class="arrow-line"><path class="connection real" d=" M58.2,155.6 L213.2,155.6" 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="198.3874969482422" style="width:660px;height:198.3874969482422px;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(1,0,0,1,67.80001831054688,27.699993896484376)"><path d="M24 388L31 368L63 389C100 412 103 414 110 414C121 414 128 404 128 389C128 338 87 145 46 2L53 -9C78 -2 101 4 123 8C142 134 163 199 209 268C263 352 338 414 383 414C394 414 400 405 400 390C400 372 397 351 389 319L337 107C328 70 324 47 324 31C324 6 335 -9 354 -9C380 -9 416 12 514 85L504 103L478 86C449 67 427 56 417 56C410 56 404 65 404 76C404 81 405 92 406 96L472 372C479 401 483 429 483 446C483 469 472 482 452 482C410 482 341 444 282 389C244 354 216 320 164 247L202 408C206 426 208 438 208 449C208 470 200 482 185 482C164 482 125 460 52 408ZM1047 473L1040 482L972 465L962 414C947 336 922 268 891 221C832 130 754 59 714 59C706 59 701 68 701 85C701 99 703 112 708 137L765 408C768 424 770 438 770 451C770 470 761 482 747 482C727 482 689 461 615 408L587 388L594 368L626 389C654 407 665 412 674 412C683 412 691 403 691 392C691 388 690 378 689 374L626 77C624 68 622 44 622 30C622 7 637 -11 657 -11C720 -11 841 101 925 239L888 97C881 73 877 46 877 31C877 6 888 -9 907 -9C933 -9 969 12 1067 85L1057 103L1031 86C1007 70 981 59 970 59C962 59 957 66 957 76C957 112 1032 416 1047 473ZM1840 103L1814 86C1785 67 1763 56 1753 56C1746 56 1740 65 1740 76C1740 86 1742 95 1747 116L1822 413C1826 430 1829 446 1829 454C1829 471 1819 482 1803 482C1774 482 1736 464 1675 421C1612 376 1577 341 1528 272L1558 409C1562 429 1565 444 1565 451C1565 470 1555 482 1539 482C1509 482 1463 460 1408 418C1364 384 1344 363 1279 275L1312 408C1316 424 1318 439 1318 451C1318 470 1309 482 1295 482C1274 482 1236 461 1162 408L1134 388L1141 368C1178 391 1213 414 1220 414C1231 414 1238 404 1238 389C1238 338 1197 145 1156 2L1159 -9L1227 6L1249 108C1273 219 1300 278 1355 338C1397 384 1442 414 1470 414C1477 414 1481 406 1481 393C1481 358 1459 244 1418 69L1402 2L1407 -9L1476 6L1497 113C1513 194 1547 269 1591 318C1646 379 1696 414 1728 414C1736 414 1741 405 1741 389C1741 365 1738 351 1716 264C1676 105 1660 84 1660 31C1660 6 1671 -9 1690 -9C1716 -9 1752 12 1850 85ZM2122 722L2110 733C2058 707 2022 698 1950 691L1946 670L1994 670C2018 670 2028 663 2028 646C2028 639 2027 628 2026 622L1925 71C1924 68 1924 64 1924 61C1924 22 1972 -11 2027 -11C2064 -11 2115 8 2158 39C2254 107 2320 244 2320 376C2320 414 2311 453 2299 468C2292 477 2279 482 2264 482C2240 482 2210 474 2182 460C2131 433 2098 403 2036 324ZM2209 424C2235 424 2248 401 2248 352C2248 288 2227 202 2197 137C2164 68 2124 36 2070 36C2024 36 1999 59 1999 101C1999 135 2014 276 2095 361C2128 395 2180 424 2209 424ZM2677 111L2653 94C2600 56 2552 36 2516 36C2469 36 2440 73 2440 133C2440 158 2443 185 2448 214C2465 218 2574 248 2599 259C2684 296 2723 342 2723 404C2723 451 2689 482 2639 482C2571 496 2461 423 2424 349C2394 299 2364 180 2364 113C2364 35 2408 -11 2480 -11C2537 -11 2593 17 2685 92ZM2462 274C2479 343 2499 386 2528 412C2546 428 2577 440 2601 440C2630 440 2649 420 2649 388C2649 344 2614 297 2562 272C2534 258 2498 247 2453 237ZM3105 365C3108 403 3113 435 3121 476C3110 481 3106 482 3101 482C3070 482 3039 458 3003 407C2964 351 2925 291 2909 256L2941 408C2945 425 2947 438 2947 450C2947 470 2939 482 2924 482C2903 482 2865 461 2791 408L2763 388L2770 368L2802 389C2830 407 2841 412 2850 412C2860 412 2867 403 2867 390C2867 332 2824 126 2784 -2L2794 -9C2809 -4 2825 -1 2848 4L2861 6L2887 126C2905 209 2928 262 2972 319C3006 363 3033 384 3055 384C3070 384 3080 379 3091 365Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" 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(1,0,0,1,137.80001831054688,27.699993896484376)"><path d="M345 437L329 437L350 549C366 635 394 673 440 673C470 673 497 658 512 634L522 638C527 654 537 685 545 705L550 720C534 727 503 733 480 733C469 733 453 730 445 726C421 715 339 654 316 630C294 608 282 578 271 521L256 442C215 422 195 414 170 405L165 383L246 383L237 327C207 132 170 -54 148 -123C130 -182 100 -213 64 -213C41 -213 30 -206 12 -184L-2 -188C-6 -211 -20 -259 -25 -268C-16 -273 -1 -276 10 -276C51 -276 105 -245 144 -198C215 -114 235 -18 319 383L423 383C427 402 434 425 440 439L436 446C407 439 408 437 345 437ZM918 365C921 403 926 435 934 476C923 481 919 482 914 482C883 482 852 458 816 407C777 351 738 291 722 256L754 408C758 425 760 438 760 450C760 470 752 482 737 482C716 482 678 461 604 408L576 388L583 368L615 389C643 407 654 412 663 412C673 412 680 403 680 390C680 332 637 126 597 -2L607 -9C622 -4 638 -1 661 4L674 6L700 126C718 209 741 262 785 319C819 363 846 384 868 384C883 384 893 379 904 365ZM1266 111L1242 94C1189 56 1141 36 1105 36C1058 36 1029 73 1029 133C1029 158 1032 185 1037 214C1054 218 1163 248 1188 259C1273 296 1312 342 1312 404C1312 451 1278 482 1228 482C1160 496 1050 423 1013 349C983 299 953 180 953 113C953 35 997 -11 1069 -11C1126 -11 1182 17 1274 92ZM1051 274C1068 343 1088 386 1117 412C1135 428 1166 440 1190 440C1219 440 1238 420 1238 388C1238 344 1203 297 1151 272C1123 258 1087 247 1042 237ZM1711 458C1668 475 1639 482 1610 482C1535 482 1447 394 1429 374C1389 327 1350 181 1350 78C1350 19 1362 -11 1386 -11C1408 -11 1427 -3 1459 19C1506 51 1585 121 1634 209L1558 -205C1553 -229 1543 -249 1531 -262L1540 -276C1571 -268 1602 -262 1626 -259C1630 -205 1636 -150 1645 -100L1731 356C1742 417 1748 443 1758 474L1744 480ZM1444 59C1430 59 1422 80 1422 113C1422 209 1465 359 1507 409C1519 424 1548 433 1580 433C1608 433 1629 427 1677 406L1656 311C1627 174 1486 59 1444 59ZM2280 473L2273 482L2205 465L2195 414C2180 336 2155 268 2124 221C2065 130 1987 59 1947 59C1939 59 1934 68 1934 85C1934 99 1936 112 1941 137L1998 408C2001 424 2003 438 2003 451C2003 470 1994 482 1980 482C1960 482 1922 461 1848 408L1820 388L1827 368L1859 389C1887 407 1898 412 1907 412C1916 412 1924 403 1924 392C1924 388 1923 378 1922 374L1859 77C1857 68 1855 44 1855 30C1855 7 1870 -11 1890 -11C1953 -11 2074 101 2158 239L2121 97C2114 73 2110 46 2110 31C2110 6 2121 -9 2140 -9C2166 -9 2202 12 2300 85L2290 103L2264 86C2240 70 2214 59 2203 59C2195 59 2190 66 2190 76C2190 112 2265 416 2280 473ZM2671 111L2647 94C2594 56 2546 36 2510 36C2463 36 2434 73 2434 133C2434 158 2437 185 2442 214C2459 218 2568 248 2593 259C2678 296 2717 342 2717 404C2717 451 2683 482 2633 482C2565 496 2455 423 2418 349C2388 299 2358 180 2358 113C2358 35 2402 -11 2474 -11C2531 -11 2587 17 2679 92ZM2456 274C2473 343 2493 386 2522 412C2540 428 2571 440 2595 440C2624 440 2643 420 2643 388C2643 344 2608 297 2556 272C2528 258 2492 247 2447 237ZM2755 388L2762 368L2794 389C2831 412 2834 414 2841 414C2852 414 2859 404 2859 389C2859 338 2818 145 2777 2L2784 -9C2809 -2 2832 4 2854 8C2873 134 2894 199 2940 268C2994 352 3069 414 3114 414C3125 414 3131 405 3131 390C3131 372 3128 351 3120 319L3068 107C3059 70 3055 47 3055 31C3055 6 3066 -9 3085 -9C3111 -9 3147 12 3245 85L3235 103L3209 86C3180 67 3158 56 3148 56C3141 56 3135 65 3135 76C3135 81 3136 92 3137 96L3203 372C3210 401 3214 429 3214 446C3214 469 3203 482 3183 482C3141 482 3072 444 3013 389C2975 354 2947 320 2895 247L2933 408C2937 426 2939 438 2939 449C2939 470 2931 482 2916 482C2895 482 2856 460 2783 408ZM3628 330L3651 330C3659 395 3666 432 3675 458C3651 473 3616 482 3579 482C3534 483 3461 463 3404 400C3350 352 3311 241 3311 136C3311 40 3353 -11 3433 -11C3487 -11 3535 9 3590 54L3640 95L3632 115L3617 105C3545 57 3507 40 3472 40C3416 40 3387 80 3387 159C3387 267 3422 371 3471 409C3492 425 3516 433 3547 433C3592 433 3628 414 3628 390ZM3685 -180C3684 -187 3684 -193 3684 -198C3684 -241 3721 -276 3766 -276C3872 -276 3982 -152 4041 33L4182 473L4171 482C4142 471 4119 465 4097 463L4062 331C4050 284 4015 211 3982 162C3947 111 3898 67 3876 67C3864 67 3855 90 3856 115L3872 322C3874 353 3876 391 3876 419C3876 464 3869 482 3852 482C3839 482 3825 475 3777 442L3695 386L3706 368L3756 398C3761 401 3772 410 3781 410C3795 410 3803 391 3803 358C3803 357 3803 351 3802 343L3785 100L3784 60C3784 18 3802 -11 3827 -11C3864 -11 3948 74 4023 187L3974 16C3923 -161 3873 -234 3803 -234C3768 -234 3741 -207 3741 -172C3741 -167 3742 -159 3743 -150L3733 -146Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" 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(1,0,0,1,87.80001831054688,65.39999389648438)"><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(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,164.80001831054688,65.39999389648438)"><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(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,87.80001831054688,101.40000915527344)"><path d="M409 603L47 -1L157 -1L497 659L497 689L44 689L44 477L74 477L81 533C89 595 96 603 142 603Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,164.80001831054688,101.40000915527344)"><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(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,83.80001831054688,137.40000915527344)"><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 -3ZM917 -3L917 27L865 30C810 33 800 44 800 96L800 700L559 598L566 548L716 614L716 96C716 44 705 33 651 30L595 27L595 -3C749 0 749 0 760 0C791 0 901 -3 917 -3Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,164.80001831054688,137.40000915527344)"><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(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,164.80001831054688,174.40000915527344)"><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(0.017,0,0,-0.017,0,0)"></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:15px;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="277.8000183105469" y="21.79998779296875">We could do this...</text></g></g></g><g><g><g><g><g><g><g transform="matrix(1,0,0,1,316.4999694824219,66.79998779296875)"><path d="M146 266C146 526 243 632 301 700L282 726C225 675 60 542 60 266C60 159 85 58 133 -32C168 -99 200 -138 282 -215L301 -194C255 -137 146 -15 146 266Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,322.1499938964844,66.39999389648438)"><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(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,334.0375061035156,66.39999389648438)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,348.7937316894531,66.39999389648438)"><path d="M409 603L47 -1L157 -1L497 659L497 689L44 689L44 477L74 477L81 533C89 595 96 603 142 603Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,360.6812438964844,66.39999389648438)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,375.4374694824219,66.39999389648438)"><path d="M409 603L47 -1L157 -1L497 659L497 689L44 689L44 477L74 477L81 533C89 595 96 603 142 603Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,387.3249816894531,66.39999389648438)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,402.0812683105469,66.39999389648438)"><path d="M409 603L47 -1L157 -1L497 659L497 689L44 689L44 477L74 477L81 533C89 595 96 603 142 603Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,413.9687194824219,66.39999389648438)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,428.7250061035156,66.39999389648438)"><path d="M409 603L47 -1L157 -1L497 659L497 689L44 689L44 477L74 477L81 533C89 595 96 603 142 603Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,440.6125183105469,66.39999389648438)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,455.3687438964844,66.39999389648438)"><path d="M409 603L47 -1L157 -1L497 659L497 689L44 689L44 477L74 477L81 533C89 595 96 603 142 603Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,467.2562561035156,66.39999389648438)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,482.0124816894531,66.39999389648438)"><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 -3ZM917 -3L917 27L865 30C810 33 800 44 800 96L800 700L559 598L566 548L716 614L716 96C716 44 705 33 651 30L595 27L595 -3C749 0 749 0 760 0C791 0 901 -3 917 -3Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,502.3812561035156,66.39999389648438)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,517.1374816894531,66.39999389648438)"><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 -3ZM917 -3L917 27L865 30C810 33 800 44 800 96L800 700L559 598L566 548L716 614L716 96C716 44 705 33 651 30L595 27L595 -3C749 0 749 0 760 0C791 0 901 -3 917 -3Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,537.5062561035156,66.39999389648438)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,552.2624816894531,66.39999389648438)"><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 -3ZM917 -3L917 27L865 30C810 33 800 44 800 96L800 700L559 598L566 548L716 614L716 96C716 44 705 33 651 30L595 27L595 -3C749 0 749 0 760 0C791 0 901 -3 917 -3Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,569.2312316894531,66.79998779296875)"><path d="M51 726L32 700C87 636 187 526 187 266C187 -10 83 -131 32 -194L51 -215C104 -165 273 -23 273 265C273 542 108 675 51 726Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,441.4437561035156,92.19999694824219)"><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(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><line style="fill:none;stroke-width:0.8px;stroke:rgb(0, 0, 0);" x1="316.4999694824219" x2="574.8812255859375" y1="74.74999696016312" y2="74.74999696016312"></line></g></g></g><g><g><g><text style="white-space:pre;stroke:none;fill:rgb(112,200,0);fill-opacity:1;font-size:15px;font-family:Arial, Helvetica, sans-serif;font-weight:400;font-style:normal;dominant-baseline:text-before-edge;text-decoration:none solid rgb(112, 200, 0);" x="277.8000183105469" y="109.80000305175781">Or this...</text></g></g></g><g><g><g><g><g><g><g transform="matrix(1,0,0,1,373.4999694824219,150.40000915527344)"><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(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,381.9875183105469,150.8000030517578)"><path d="M146 266C146 526 243 632 301 700L282 726C225 675 60 542 60 266C60 159 85 58 133 -32C168 -99 200 -138 282 -215L301 -194C255 -137 146 -15 146 266Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,387.6374816894531,150.40000915527344)"><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(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,396.1249694824219,150.8000030517578)"><path d="M51 726L32 700C87 636 187 526 187 266C187 -10 83 -131 32 -194L51 -215C104 -165 273 -23 273 265C273 542 108 675 51 726Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,401.7749938964844,150.40000915527344)"><path d="" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,409.4125061035156,150.40000915527344)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,424.1687316894531,150.40000915527344)"><path d="M658 603L296 -1L406 -1L746 659L746 689L293 689L293 477L323 477L330 533C338 595 345 603 391 603Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,436.8874816894531,150.8000030517578)"><path d="M146 266C146 526 243 632 301 700L282 726C225 675 60 542 60 266C60 159 85 58 133 -32C168 -99 200 -138 282 -215L301 -194C255 -137 146 -15 146 266Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,442.5375061035156,150.40000915527344)"><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(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,451.0249938964844,150.8000030517578)"><path d="M51 726L32 700C87 636 187 526 187 266C187 -10 83 -131 32 -194L51 -215C104 -165 273 -23 273 265C273 542 108 675 51 726Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,456.6750183105469,150.40000915527344)"><path d="" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,464.3124694824219,150.40000915527344)"><path d="M604 241L604 300L364 300L364 538L305 538L305 300L65 300L65 241L305 241L305 0L364 0L364 241Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,479.0687561035156,150.40000915527344)"><path d="M667 -3L667 27L615 30C560 33 550 44 550 96L550 700L309 598L316 548L466 614L466 96C466 44 455 33 401 30L345 27L345 -3C499 0 499 0 510 0C541 0 651 -3 667 -3ZM1166 -3L1166 27L1114 30C1059 33 1049 44 1049 96L1049 700L808 598L815 548L965 614L965 96C965 44 954 33 900 30L844 27L844 -3C998 0 998 0 1009 0C1040 0 1150 -3 1166 -3Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,500.2687683105469,150.8000030517578)"><path d="M146 266C146 526 243 632 301 700L282 726C225 675 60 542 60 266C60 159 85 58 133 -32C168 -99 200 -138 282 -215L301 -194C255 -137 146 -15 146 266Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,505.9187316894531,150.40000915527344)"><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(0.017,0,0,-0.017,0,0)"></path></g></g><g><g transform="matrix(1,0,0,1,514.4062194824219,150.8000030517578)"><path d="M51 726L32 700C87 636 187 526 187 266C187 -10 83 -131 32 -194L51 -215C104 -165 273 -23 273 265C273 542 108 675 51 726Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,442.5312194824219,176.1999969482422)"><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(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><line style="fill:none;stroke-width:0.8px;stroke:rgb(0, 0, 0);" x1="373.4999694824219" x2="520.0562286376953" y1="158.74999696016312" y2="158.74999696016312"></line></g></g></g></svg> </svg></center> <p>In the first method, we gave equal weight to every element in the dataset, but that meant having to write out all nine numbers. In the much more efficient method, we gave the most weight to the $7$ (because it appears five times), then the $11$ (because it appears three times), and last the $3$, appearing only once. This is what we mean by &quot;weighted mean.&quot;</p> <p><strong><span style="color:#e74c3c;">Another Common Example</span></strong></p> <p>The grade for a class is calculated as follows: all homework assignments account for $15\%$ of the final grade, the class project accounts for $25\%$, the midterm accounts for $20\%$, and the final exam accounts for $40\%$. If John&#39;s homework assignments averaged $80\%$, he received a $75$ out of $100$ on his class project, a $45$ out of $50$ on his midterm, and a $88$ out of $100$ on his final exam, what was his final grade?</p> <p>This is a perfect weighted mean problem. Notice how the final exam has the most weight and homework the least. To solve, we need to make sure all of his individual grades are in the decimal format:</p> <ul> <li>Homework Assignments: $80\% = 0.8$</li> <li>Class Project: $75$ out of $100 = 0.75$</li> <li>Midterm: $45$ out of $50 = 0.90$</li> <li>Final Exam: $88$ out of $100 = 0.88$</li> </ul> <p>Now we solve with the following math calculation, factoring in the &quot;weight&quot; of each assignment type:</p> <p>$$(0.8)(15\%) + (0.75)(25\%) + (0.9)(20\%) + (0.88)(40\%)$$</p> <p>$$= 12 + 18.75 + 18 + 35.2$$</p> <p><span style="color:#27ae60;">$$=83.95\% = final \ grade$$</span></p>