histograms corbett maths

394 2999 2999 450 3000 3000 394 3001 3001 709 /Subtype /Image This tool will create a histogram representing the frequency distribution of your data. 815 815 394 816 816 514 817 817 812 818 500 1812 1812 666 1813 1813 556 1814 1814 666 136 136 537 137 137 610 138 139 736 141 2091 382 2092 2096 542 2097 2097 382 2098 2102 Histograms. 1205 1205 556 1206 1206 666 1207 1207 556 1208 0000053581 00000 n 1524 932 1525 1525 394 1526 1526 514 1527 1527 /ImageB endobj 638 906 906 588 907 908 244 909 909 207 Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 981 982 581 983 983 267 984 984 262 985 Calculate an estimate of the number of cars that were travelling between 42 and 49 mph. 806 750 807 807 562 808 808 525 809 810 777 1822 1822 556 1823 1823 777 1824 1824 556 Just enter your scores into the textbox below, either one value per line or as a comma delimited list, and then hit the "Generate" button. 0000069088 00000 n and 5-a-day. /Fit ] endobj 556 2437 2437 666 2438 2438 556 2439 2439 722 412 752 752 207 753 760 0 761 771 525 562 1395 1395 525 1396 1397 529 1398 1398 562 2057 382 2058 2062 542 2063 2063 382 2064 2068 3149 3149 932 3150 3150 394 3151 3151 514 3152 /Font << 3032 83 3033 3033 0 3034 3034 736 3035 3035 747 0 748 749 318 750 750 356 751 751 3096 3097 244 3098 3099 713 3100 3101 244 3102 1611 0 1612 1612 1123 1613 1613 1084 1614 1619 570 2641 2646 556 2647 2648 826 2649 2650 1021 Q /MediaBox [ 0 0 612 792 ] /BaseFont /Helvetica (a) Draw a histogram to represent the data. 1862 552 1863 1863 556 1864 1864 790 1865 1865 /Length 93 1734 583 1735 1735 277 1736 1736 1333 1737 1737 0000060883 00000 n 0000032486 00000 n This video shows how to find frequencies from a drawn histogram. 333 2523 2523 722 2524 2524 333 2525 2525 722 739 593 593 666 594 594 916 595 595 937 Histograms provide a visual interpretation of numerical data by indicating the number of data points that lie within a range of values. 409 500 410 410 722 411 411 500 412 412 1048 1769 1769 777 1770 1770 556 1771 1771 1034 2526 2526 333 2527 2527 666 2528 2528 500 2529 (Total for question 2 is 4 marks) Speed (mph) Frequency 40 < s 55 6 55 < s 60 10 60 < s 65 46 65 < s 75 48 75 < s 90 6 (a) On the grid, draw a histogram for the information in the table. 0000003026 00000 n 1390 562 1391 1391 525 1392 1393 529 1394 1394 Corbett Maths offers outstanding, original /Filter /FlateDecode 2569 610 2570 2570 500 2571 2571 610 2572 2572 /Length 3136 74 0 obj /OpenAction [ 72 0 R 3368 3368 610 3369 3370 500 3371 3371 577 3372 In other words, a histogram provides a visual interpretation of numerical data by showing the number of data points that fall within a specified range of values (called “bins”). 556 1282 1282 722 1283 1283 556 1284 1284 722 0000069885 00000 n 2579 556 2580 2580 222 2581 2588 578 2589 2590 2975 439 2976 2976 343 2977 2977 740 2978 2978 ET 2342 2342 556 2343 2343 666 2344 2344 556 2346 542 2069 2069 382 2070 2074 542 2075 2075 382 556 645 645 437 646 646 500 647 647 552 2260 695 2261 2261 828 2262 2262 685 2263 2263 (a) Use the information in the histogram to complete the frequency table below. 610 1802 1802 277 1803 1803 544 1804 1804 436 2936 2936 622 2937 2938 372 2939 2939 376 2940 docx, 172 KB. /Text Wolfram Science. 3142 394 3143 3143 514 3144 3144 812 3145 3145 /Fabc9 76 0 R /Length 227 endobj %%EOF 69 40 Age (x) in years Frequency 1600 < x 10 10 < x 25 25 < x 30 30 < x 40 100 40 < x 70 120 (2) (b) Complete the histogram. 532 532 546 533 533 575 534 534 500 535 2433 666 2434 2434 556 2435 2435 666 2436 2436 �n�D*��g����_��[email protected]����� And best of all they /Iabc91 101 0 R 1321 244 1322 1322 267 1323 1323 262 1324 1324 If you are in step 2: Describe, you can click on the header of a column with numbers, to display a histogram, the min, max, median, mean, and the number of potential invalid values.Here's a quick explanation of what all of these mean. /Iabc63 95 0 R >> 426 426 722 427 427 556 428 434 277 435 1348 1351 432 1352 1352 638 1353 1353 588 1354 ����c��;zw��Y]e�ٺ�4�͘�ۙߙ/]x�{�uC�EWKfi������迻�6�ܱ�)�ˈz��A�n�l[E5׺�y`�}�K���y��*��n]��>��?��}�v�>F���]t�dDt^��{�����WD[M��^���'��=�/rj4��E.�l�o����u���.�Z2�Z�EWKfY����\��z#�;���s\�[av;�[�=s��ͺ��61���qi��;����'⢻�n1EWZw���G�J����D��������'��Rۼ��RӰJ�݊�{:����U�@wUaݏ:�m��R�e����G7�n}X�ӭ6�EYA�!����U�P�]^��^�[w_]]]���ca>���*���غd~�U-�n��-5 ���t�ՒAׂ.�Z2�Z��b�[�B����RӰJʠkA]-t-被%���غd~�U-�n��-5 ���t�ՒAׂ.�Z2�ZЍ�K��F���\ h�x��*s(�n�����Fӭ���`�y? << /Subtype /Type1 /FontBBox [ -664 -324 2000 1005 ] 638 1595 1595 588 1596 1597 244 1598 1598 638 1238 777 1239 1239 556 1240 1240 777 1241 1241 Graphs: histograms (draw) Video 157 Graphs: histograms (find frequency) Video 158 Graphs: histograms harder Video 159 Maths Genie keyboard_arrow_up 364 3337 3337 666 3338 3338 500 3339 3339 666 1856 1856 571 1857 1859 833 1860 1861 556 1862 722 1792 1792 333 1793 1793 722 1794 1794 333 2322 2322 666 2323 2323 861 2324 2324 666 2325 /Type /Font /BaseFont /Helvetica-Oblique 902 432 903 903 207 904 904 229 905 905 Read more. 695 549 696 696 509 697 697 694 698 698 Videos, worksheets, 5-a-day and much more endobj 2994 337 2995 2996 488 2997 2997 450 2998 2998 1561 562 1562 1562 525 1563 1564 529 1565 1565 648 648 488 649 649 411 651 651 1072 652 Draw a histogram … 3199 3200 222 3201 3201 556 3202 3202 546 3203 What I just plotted here, this is a histogram. trailer 3215 386 3216 3218 500 3219 3222 556 3223 3224 2280 851 2281 2281 0 2282 2282 1337 2283 2283 Calculate an estimate of the number of athletes between 70 and 95kg. I did this as a total coverage of histograms - hope it's of some use. Links to the Best Maths Websites in the World, AQA Level 2 Certificate in Further Mathematics, Graphs: xref 617 306 306 395 307 307 648 308 308 552 1341 229 1342 1342 207 1343 1343 229 1344 1344 /W [ 1 1 0 2 4 277 5 5 354 6 600 1019 1019 543 1020 1020 600 1021 1022 750 /Fabc13 79 0 R 638 638 500 639 639 222 640 640 277 641 731 731 574 732 732 566 733 733 546 734 /Iabc103 104 0 R 627 627 822 628 628 625 629 629 718 630 1478 1478 262 1479 1480 788 1481 1481 267 1482 2546 2546 556 2547 2547 722 2548 2548 556 2549 724 589 725 725 286 726 726 509 727 727 endobj << endobj 2228 674 2229 2229 556 2230 2230 673 2231 2231 1707 1707 556 1708 1709 666 1710 1710 500 1711 81 0 obj 244 1382 1382 562 1383 1383 525 1384 1385 529 1228 277 1229 1229 222 1230 1230 277 1231 1231 2929 429 2930 2930 511 2931 2931 382 2932 2932 2809 2809 894 2810 2810 796 2811 2811 747 2812 0000067379 00000 n 2008 2016 542 2017 2017 382 2018 2022 542 2023 endobj 2363 2363 777 2364 2364 556 2365 2365 718 2366 443 443 722 444 444 556 445 445 723 446 388 531 389 389 656 390 390 593 391 391 721 721 602 722 722 286 723 723 411 724 2872 889 2873 2873 531 2874 2874 500 2875 2876 /Filter /FlateDecode A video explaining how to interpret histograms. come with answers. 453 453 666 454 454 500 455 455 610 456 712 3208 3208 500 3209 3209 222 3210 3210 833 926 926 525 927 928 529 929 929 562 930 0000075782 00000 n 556 1242 1242 777 1243 1243 556 1244 1244 777 458 1839 1839 631 1840 1840 507 1841 1841 277 0000067723 00000 n 382 3252 3252 381 3253 3253 377 3254 3254 375 772 772 318 773 773 525 774 775 750 776 /Length 5708 0 3153 337 3154 3155 394 3156 3157 337 3158 3159 2624 1015 2625 2632 222 2633 2634 375 2635 2640 /Iabc42 90 0 R 1399 1399 525 1400 1401 529 1402 1402 562 1403 556 1748 1748 0 1749 1749 666 1750 1750 556 2904 2904 500 2905 2905 458 2906 2906 427 2907 /BitsPerComponent 8 /ColorSpace /DeviceRGB They are like bar charts, but show the frequency density instead of the frequency. >> 2110 2113 542 2114 2204 0 2205 2207 333 2208 581 1325 1330 244 1331 1331 269 1332 1333 0 2236 2236 736 2237 2237 553 2238 2238 463 2239 << 2076 2084 542 2085 2085 382 2086 2090 542 2091 Tolerance €small square of their scale A1 ft (b)€€€€ €or €× 100 or 8. 1890 500 1891 1891 541 1892 1893 544 1894 1897 1511 1511 812 1512 1512 932 1513 1513 394 1514 704 704 815 705 705 246 706 707 509 708 1923 1925 239 1926 1926 364 1927 1927 480 1928 578 529 529 445 530 530 556 531 531 222 2499 722 2500 2500 556 2501 2501 722 2502 2502 635 2370 2370 500 2371 2371 635 2372 2372 500 3290 578 3291 3298 222 3299 3306 546 3307 3310 258 258 666 259 259 556 260 260 666 261 752 2350 2350 556 2351 2351 923 2352 2352 668 1375 713 1376 1377 244 1378 1379 713 1380 1381 556 2447 2447 722 2448 2448 556 2449 2449 722 666 100 100 722 101 101 666 102 102 722 2918 449 2919 2920 410 2921 2921 496 2922 2922 556 2503 2503 722 2504 2504 556 2505 2505 722 /DescendantFonts [ 78 0 R ] GCSE Revision Cards. /Type /Page 2982 2982 238 2983 2983 543 2984 2992 0 2993 worksheet, complete with answers. 556 2457 2457 666 2458 2458 556 2459 2459 666 1208 666 1209 1209 556 1210 1210 666 1211 1211 500 3026 3026 333 3027 3027 250 3028 3028 166 915 282 916 916 375 917 918 713 919 920 << 352 689 689 574 690 690 529 691 691 566 /Height 486 952 530 953 954 1098 955 956 846 957 958 20 25 30 35 55 60 65 Speed, miles per hour 14 cars were travelling over 50 mph. 741 741 460 742 742 546 743 743 575 744 2484 500 2485 2485 556 2486 2486 222 2487 2487 >> 45 athletes weigh under 60kg. 226 666 227 227 500 228 228 610 229 229 /Iabc26 86 0 R 1721 610 1722 1722 500 1723 1724 610 1725 1726 /Registry () 690 2319 2319 666 2320 2320 520 2321 2321 861 /Type /Font /Flags 32 2247 2247 666 2248 2248 718 2249 2249 556 2250 1235 1235 556 1236 1236 777 1237 1237 556 1238 Ronnie, the manager of the snooker club, says that the average age of the members of the snooker club is under 32. 2605 2608 927 2609 2616 556 2617 2618 819 2619 stream 568 635 569 569 718 570 570 666 571 571 709 462 710 710 535 711 714 694 715 717 3211 3212 556 3213 3213 333 3214 3214 500 3215 1464 1464 525 1465 1465 394 1466 1468 788 1469 They can be used to determine information about the distribution of data. 1311 500 1312 1312 666 1313 1313 520 1314 1314 1514 514 1515 1515 812 1516 1516 932 1517 1517 3203 568 3204 3205 556 3206 3206 277 3207 3207 682 682 509 683 683 460 684 684 462 685 1808 604 1809 1809 565 1810 1810 610 1811 1811 Higher and Foundation Revision for Edexcel, AQA or OCR - Duration: 2:06:55. ]x���KM�*)��]t�dеx^ƍ���ލݻ��a��Aׂ.�Z2�Z�EWK]���C�x�Z��ؽ[jVIt-被%��]t�dе�[�̏���ލݻ��a��Aׂ.�Z2�Z�EWK]���C�x�Z�]�ޭ�Hv�yr������s�]t�ܔ��Ue��F,vVW�CU�ߪ�^x������t�ս�*�w��6b�����*�+�|��¼ϼ��*���غd~�U-�n��-5 ���t�ՒAׂ.�Z2�Z��b�[�B����RӰJʠkA]-t-被%���غd~�U-�n��-5 ���t�ՒAׂ.�Z2�Z��b�[�B� 542 2103 2103 382 2104 2108 542 2109 2109 382 /Type /FontDescriptor endstream 1589 588 1590 1591 244 1592 1593 432 1594 1594 docx, 170 KB. 3246 157 3247 3247 274 3248 3249 571 3250 3251 0000068563 00000 n /Root 70 0 R /FontDescriptor 77 0 R 435 222 436 436 500 437 437 222 438 438 0 Tr 750 786 786 0 787 794 750 795 795 638 /BitsPerComponent 8 /Subtype /Type1 endobj 318 2947 2947 376 2948 2948 157 2949 2949 338 2346 889 2347 2347 666 2348 2348 556 2349 2349 /Type /Catalog /Iabc71 97 0 R 1265 1265 669 1266 1266 854 1267 1267 669 1268 2965 377 2966 2966 439 2967 2967 343 2968 2968 0000041722 00000 n 2332 2332 722 2333 2333 552 2334 2334 722 2335 3083 713 3084 3085 244 3086 3087 713 3088 3089 500 541 541 576 542 542 500 543 543 447 157 2969 2969 239 2970 2970 382 2971 2971 321 630 520 631 631 510 632 632 750 633 633 /Type /Font 3327 3327 722 3328 3328 333 3329 3329 666 3330 557 864 558 558 541 559 559 718 560 560 /Type /Font 2335 552 2336 2336 666 2337 2337 520 2338 2338 stream /BaseFont /NQOAKR+ArialMT 562 3107 3107 525 3108 3109 529 3110 3113 337 creating online and paper-based assessments and homeworks. 333 497 497 667 498 498 784 499 499 837 796 798 750 799 800 713 801 802 244 803 71 0 obj 3166 3167 244 3168 3169 525 3170 3171 244 3172 556 1212 1212 666 1213 1213 556 1214 1214 666 942 2743 2749 578 2750 2754 666 2755 2759 333 0 Ts Histograms Answers. 43 722 44 44 277 45 45 500 46 46 1298 1298 923 1299 1299 668 1300 1300 582 1301 1846 616 1847 1849 556 1850 1851 222 1852 1852 556 1192 1192 666 1193 1193 556 1194 1194 666 (2) (Total 4 marks) The histogram shows the speeds in miles per hour of 82 cars on a road. 1782 1782 556 1783 1786 277 1787 1787 777 1788 0000070166 00000 n q 5-a-day Workbooks. 3014 3014 333 3015 3015 354 3016 3019 207 3020 666 1315 1315 556 1316 1316 752 1317 1317 556 This website and its content is subject to our Terms and Conditions. 1031 750 1032 1033 0 1034 1036 750 1037 1042 3005 609 3006 3006 745 3007 3007 655 3008 3008 1446 1447 530 1448 1449 821 1450 1451 530 1452 155 548 156 156 273 157 157 370 158 158 999 1000 244 1001 1001 282 1002 1002 375 1003 1453 1098 1454 1455 846 1456 1457 1098 1458 1459 0000001978 00000 n 458 3225 3225 650 3226 3226 222 3227 3227 500 642 699 701 493 702 702 235 703 703 416 la < aa © Corbettmaths 2015 aa (4) 16. 1798 556 1799 1799 666 1800 1800 500 1801 1801 Drawing Histograms Practice Questions Practice Questions; Post navigation. rM. 2312 2312 520 2313 2313 722 2314 2314 500 2315 /Iabc18 84 0 R /Encoding /WinAnsiEncoding 2681 2682 578 2683 2684 445 2685 2686 556 2687 500 3324 3324 222 3325 3325 737 3326 3326 556 833 583 583 722 584 584 777 585 585 718 2450 2450 556 2451 2451 666 2452 2452 556 2453 655 1252 1252 857 1253 1253 655 1254 1254 857 268 269 556 270 270 222 271 271 556 272 279 279 777 280 280 556 281 281 722 282 Contents. 1222 1738 1738 1048 1739 1739 1062 1740 1740 833 500 1683 1683 722 1684 1684 809 1685 1685 656 It is the area of the bar that tells us the frequency in a histogram, not its height. /Iabc87 100 0 R 543 1637 1637 450 1638 1638 525 1639 1639 394 986 601 987 988 394 989 990 506 991 992 << 2940 599 2941 2942 377 2943 2944 371 2945 2946 0000063095 00000 n 535 440 536 537 556 538 538 222 539 540 /StemV 80 460 728 728 462 729 729 601 730 730 352 72 0 obj 3173 506 3174 3175 207 3176 3179 488 3180 3181 /Width 478 /Parent 68 0 R The whole of GCSE 9-1 Maths in only 2 hours!! April 4, 2018 August 12, 2019 corbettmaths. Search for: 575 575 666 576 576 923 577 577 604 578 556 2513 2513 777 2514 2514 556 2515 2515 666 3333 500 3334 3334 222 3335 3335 541 3336 3336 1765 222 1766 1766 1333 1767 1767 1222 1768 1768 2481 2481 666 2482 2482 500 2483 2483 666 2484 0 1620 1620 193 1621 1621 370 1622 1623 0 These videos are made by Corbett Maths. 2270 556 2271 2271 803 2272 2272 630 2273 2273 /Ascent 728 1805 1805 722 1806 1806 556 1807 1807 706 1808 2796 862 2797 2797 886 2798 2798 764 2799 2801 >> 3372 425 3373 3373 648 3374 3379 0 3380 3380 Whether you want a homework, some cover work, or a lovely bit of A histogram is a plot that lets you discover, and show, the underlying frequency distribution (shape) of a set of continuous data. 463 463 722 464 464 556 465 465 943 466 1755 777 1756 1756 556 1757 1757 666 1758 1758 Primary Study Cards. 722 1305 1305 552 1306 1306 556 1307 1307 500 2760 2764 556 2765 2766 813 2767 2768 868 2769 620 458 621 621 500 622 622 822 623 623 541 2911 2911 520 2912 2912 712 2913 2913 583 /T 201310 61 61 610 62 64 277 65 65 469 66 ���A��y�y�9�]U]��C�x�Z��ؽ[jVIt-被%��]t�dе�[�̏���ލݻ��a��Aׂ.�Z2�Z�EWK]���C�x�Z��ؽ[jVIt-被%��]t�dе�[��ύx��fyzW�ws�tn����sH��#;��̡����kv���a�M�>,t��:^� 2688 222 2689 2690 556 2691 2692 546 2693 2694 1643 244 1644 1644 320 1645 1649 244 1650 1650 942 3355 3355 489 3356 3356 500 3357 3357 556 >> 3114 3115 488 3116 3117 821 3118 3119 530 3120 525 935 936 529 937 940 337 941 944 488 1624 1624 600 1625 1627 0 1628 1629 821 1630 >> 487 556 488 488 600 489 492 833 493 496 /Fabc8 9 Tf 2267 2267 796 2268 2268 688 2269 2269 777 2270 1334 1335 333 1336 1339 0 1340 1340 207 1341 Videos, worksheets, 5-a-day and much more 510 392 392 500 393 393 750 394 394 734 arrow_back Back to Histograms Histograms: Worksheets with Answers. 456 277 457 457 722 458 458 556 459 459 500 1272 1272 666 1273 1273 500 1274 1274 666 histograms (find frequency), Graphs: 932 3146 3146 394 3147 3147 514 3148 3148 812 /S 292 1842 1843 556 1844 1844 558 1845 1845 500 1846 776 282 777 777 750 778 780 525 781 785 1775 666 1776 1776 556 1777 1777 666 1778 1778 554 554 546 555 555 780 556 556 667 557 556 1292 1295 0 1296 1296 541 1297 1297 364 /ABCpdf 7023 355 1853 1853 327 1854 1854 303 1855 1855 222 endobj 500 1898 1898 777 1899 1899 531 1900 1900 507 /Subtype /Type0 2315 610 2316 2316 458 2317 2317 925 2318 2318 394 3124 3124 543 3125 3125 450 3126 3126 525 And best of all they all (well, most!) 500 71 72 556 73 73 277 74 75 556 79 0 obj 1795 1795 722 1796 1796 556 1797 1797 722 1798 267 1474 1474 262 1475 1476 788 1477 1477 267 /Type /XObject 183 548 184 184 494 185 185 500 186 186 3239 3239 383 3240 3243 157 3244 3244 270 3245 277 207 209 777 210 212 722 213 213 277 1538 207 1539 1540 506 1541 1542 207 1543 1544 1 0 0 1 548.961 17.3 Tm 2302 2302 458 2303 2303 582 2304 2304 437 2305 733 2901 2901 596 2902 2902 500 2903 2903 722 1268 854 1269 1269 669 1270 1270 666 1271 1271 394 1518 1518 514 1519 1519 812 1520 1520 932 556 1779 1779 666 1780 1780 556 1781 1781 666 These ranges of values are called classes or bins. 694 738 738 642 739 739 246 740 740 541 /Subtype /CIDFontType2 startxref 2386 909 2387 2387 1034 2388 2388 878 2389 2389 /Iabc107 105 0 R >> 222 2477 2478 277 2479 2479 666 2480 2480 500 313 500 315 315 500 317 318 500 319 319 394 977 978 788 979 979 267 980 980 262 The Corbettmaths video tutorial on median and quartiles from frequency tables and Histograms - linear interpolation 2215 2215 601 2216 2216 777 2217 2217 556 2218 3102 562 3103 3103 525 3104 3105 529 3106 3106 76 77 222 78 78 500 79 79 222 80 2897 458 2898 2898 546 2899 2899 596 2900 2900 3404 3404 840 3405 3405 277 3406 3406 437 3407 272 291 273 273 556 274 274 333 275 275 /FontFile2 107 0 R 3020 792 3021 3021 1221 3022 3022 500 3024 3024 The incomplete table and histogram give some information about the ages of the people who live in a village. 500 3048 3048 580 3049 3053 0 3054 3054 568 609 458 610 611 558 612 612 437 613 613 /FontName /NQOAKR+ArialMT endobj 1053 2264 2264 867 2265 2265 604 2266 2266 458 0000071231 00000 n 2790 2791 568 2792 2793 546 2794 2795 666 2796 428 2923 2923 166 2924 2924 314 2925 2925 424 1815 1815 556 1816 1816 777 1817 1817 556 1818 84 0 obj 685 598 686 686 601 687 687 246 688 688 262 3066 3066 289 3067 3073 0 3074 3075 713 50 50 777 51 51 666 52 52 777 53 488 1440 1441 821 1442 1443 530 1444 1445 821 2239 409 2240 2240 601 2241 2241 572 2242 2242 1386 1386 562 1387 1387 525 1388 1389 529 1390 777 2254 2254 612 2255 2255 949 2256 2256 713 846 1460 1461 581 1462 1462 543 1463 1463 450 3076 3077 244 3078 3079 713 3080 3081 244 3082 500 2573 2573 610 2574 2574 500 2575 2575 556 1586 1586 638 1587 1587 588 1588 1588 638 1589 3039 3040 886 3041 3041 666 3042 3042 722 3043 666 561 562 277 563 563 500 564 564 1057 543 1661 1661 600 1662 1662 543 1663 1663 600 0000038397 00000 n /Iabc79 98 0 R /Height 486 3273 372 3274 3274 371 3275 3275 377 3276 3276 373 3235 3235 318 3236 3237 229 3238 3238 376 78 0 obj 556 131 131 399 132 134 556 135 135 350 474 474 777 475 475 610 476 476 277 477 382 2959 2959 407 2960 2960 572 2961 2961 321 466 722 467 467 666 468 468 500 469 469 1700 890 1701 1701 722 1702 1702 556 1703 1703 2825 594 2826 2829 0 2830 2831 222 2832 2832

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