Create a graph based on the statistics. Players' match activity according to different age groups depending on playing position.*Independent of positionVariablesTotal distance (m)MSR (m)HSR (m)VHSR (m)Sprint (m)No. of HSRNo. of VHSRNo. of sprintsMaximal speed(km-h¹)VariablesTotal distance (m)MSR (m)HSR (m)VHSR (m)Sprint (m)No. of HSRNo. of VHSRNo. of sprintsMaximal speed(km-h1¹)VariablesTotal distance (m)MSR (m)HSR (m)VHSR (m)Sprint (m)No. of HSRNo. of VHSRNo. of sprintsMaximal speed(km-h-¹)<20 y10,211 ± 784+1,988 495259 ± 77541194281 145+24 + 739 1216 + 731.01.9<20 y10,336 ± 6712,099 368315 + 101675 +216350 + 16525743 1218731.7 1.8<20 y########20-24.9 y10,381 990+2,141 ± 555+282102568 238285 + 161125+ 8411516830.8 1.920-24.9 y10,315 +6742,057 339317 +88688 + 207370 14828 +7481320 + 7§31.61.520-24.9 y10,281 ± 1,4872,110 + 607345 + 115756 ± 257+410 + 175+30 + 1052 ± 1622 +8+31.42.325-29.9 y10,164 9142,054 + 581266 112524 24225715424938 1614830.5 1.9External defenders25-29.9 y10,268 ± 6532,107 396317 + 104669223352 +14728 +7471419 ± 731.2 1.5External midfielders25-29.9 y10.398 1,4132,214 ± 635345 1348704+ 268359 + 16530 + 1150 ± 1819 ± 831.12.2*MSR = medium-speed running; HSR = high-speed running; VHSR = very high-speed running.+Significantly different (p <0.01) from 25 to 29.9 years, 30-34.9 years, and ≥35 years.+Significantly different (p < 0.05) from all other age groups.§Significantly different (p < 0.01) from 30-34.9 years and ≥35 years.Significantly different (p < 0.01) from <20 years, 20-24.9 years, and 25-29.9 years.Significantly different (p <0.01) from <20 years, 30-34.9 years, and ≥35 years.#There are no observations in this age group.30-34.9 y10,156 ± 1,0912,059 ± 601254 ± 97+491 + 204+236 13323836 1314+630.2 1.830-34.9 y10,049 + 714+1,986 417283 ± 81579170296 12025+741 +1116 +530.8 0.930-34.9 y10,420 + 9142,213 468310 + 105654 +24134416628 ± 846 + 1518 + 731.2 1.8235 y10,142 +9721,987 ± 549227 + 88+418 181190 112+19 + 7+30 1210+ 6+29.6 1.8>35 y9,757555+1,813 401259 106513 + 220||253 ± 13222 +8+36 ± 14+13 + 6+30.21.0≥35 y10,266 + 4952,103 ± 22128298577 + 130295 + 11526 ± 643 + 817 +531.6 1.5<20 y10,086 ± 796+2,064 + 390+265 +66+548 + 168+250 + 103+23 ± 6381115630.90.9<20 y10,577 +685+2,169 518239 ± 77430 + 158191 ± 10821 + 732 1111 +529.8 1.9<20 y9,6137151,570 428261 83570 152308 +9925+7431118 + 531.71.4§20-24.9 y9,823 ± 695+1,813 ± 408+213 ± 66+409 131+196 ± 94+19 ± 5+30 + 911 +5+30.6 1.620-24.9 y11,0357642,557 ± 551266 92463 + 176196 + 10723 +735 + 1211 +529.9 ± 1.7†20-24.9 y10,092 + 7381,941 456327 + 96707 + 218380 + 151§30 + 851 ± 14921 ± 7§31.61.58Central defenders25-29.9 y9,473 + 6271,655 349194 + 69372 135178 + 8817 +628 +910+530.4 1.7Central midfielders25-29.9 y10,819 + 1,325+2,460 655262 ± 105453 199191 ± 11623 ± 834 1411629.3 ± 1.9Forwards25-29.9 y10.2318642.068 4663269546982274372 + 16329 ± 850 ± 15920 + 831.61.5§30-34.9 y9,4316251,588 34817466333 133+158 + 8716 + 525 ± 99 +430.11.730-34.9 y11,063 + 7152,675 529266 +97448183181 ± 10823 ± 8331210 + 529.11.630-34.9 y9,843 1,0331,895 530288 + 83581 + 15629210926 ± 742 ± 1017 +630.8 ± 1.5>35 y9,343 6461,605 ± 347184 ± 66338 1261537916 +525 +99 +429.4 1.4>35 y11,014 +6882,500 439232 +97390 + 200+158 11619 ± 8+29 13+9±628.7 ± 1.8≥35 y10,032 + 4981.693 +370+242 ± 67417 + 112+228 ± 83+21 +534 +7+13+ 4+30.6±1.4

There are several types of graphs that we can draw based on the given dataset but given the time…

Players' match activity according to different age groups depending on playing position.* Independent of position Variables Total distance (m) MSR (m) HSR (m) VHSR (m) Sprint (m) No. of HSR No. of VHSR No. of sprints Maximal speed (km-h¹) Variables Total distance (m) MSR (m) HSR (m) VHSR (m) Sprint (m) No. of HSR No. of VHSR No. of sprints Maximal speed (km-h¹) Variables <20 y 10,211 + 784+ 1,988 495 25977 541 194 281 ± 145+ 24 ± 7 39 12 16+7 31.0 1.9 <20 y 10,336 671 2,099 368 315 101 675 ± 216 350 165 25+ 7 4312 187 31.7 1.8 <20 y 20-24.9 y 10,381 9901 2,141 555+ 282 102 568 238 285 1611 258 4115 168 30.8 1.9 20-24.9 y 10,315 674 2,057 339 317 +88 688207 370 148 287 4813 207§ 31.6 1.5 20-24.9 y 25-29.9 y 10,164 ± 914 2,054 581 266 112 524 242 257 + 154 249 38 16 148 30.5 1.9 External defenders 25-29.9 y 10,268 653 2,107 396 317 104 669 ± 223 352 147 287 47 14 197 31.2 ± 1.5 External midfielders 25-29.9 y 30-34.9 y 10,156 1,091 2,059 601 254 ± 97+ 491 204 236± 133 23±8 36 13 146 30.2 1.8 30-34.9 y 10,049714 1,986 417 28381 579 170 296 120 25 ± 7 4111 16 +5 30.8 0.9 30-34.9 y 235 y 10,142 972 1,987 549 227 88 418 181 190 112 19 + 7+ 30 12 10+ 6+ 29.6 1.8 235 y 9,757 ± 555+ 1,813 401 259 ± 106+ 513 220 253132 22+8+ 36 14 13 6 30.2 1.0 235 y <20 y 10,086 796† 2,064 390t 265 66 548 168 250 103 23 ± 6+ 38 ± 11 15+ 6+ 30.9 ± 0.9 <20 y 10,577 685+ 2,169 518 239 ± 77 158 108 430 191 217 32 11 11+5 29.8 1.9t <20 y 20-24.9 y 9,823 6951 1,813 4081 213 +66+ 4091311 196 ± 94 19 ± 5t 309 11:5 30.61.61 20-24.9 y 11,035 764 2,557 551 266 92 463 + 176 196 107 23 ± 7 3512 115 29.9 1.71 20-24.9 y Central defenders 25-29.9 y 9,473 627 1,655 349 194±69 372 135 17888 176 289 105 30.4 1.7 Central midfielders 25-29.9 y 10,819 ± 1,325+ 2,460 ± 655 262 105 453 199 191 ± 116 23 ± 8 3414 116 29.3 1.9 Forwards 25-29.9 y 30-34.9 y 9,431625 1,588 348 17466 333 133 15887 165 259 9±4 30.11.7 30-34.9 y 11,063715 2,675 529 266 +97 448183 181 108 23 ± 8 33 12 105 29.1 1.6 30-34.9 y 235 y 9,343 646 1,605347 18466 338 126 15379 16 ± 5 25 ± 9 9±4 29.4 1.4 235 y 11,014 688 2,500 439 232 +97 390 ± 200+ 158 116 19 ± 8 29 13 9±6 28.7 1.8 235 y

Players' match activity according to different age groups depending on playing position.* Independent of position Variables Total distance (m) MSR (m) HSR (m) VHSR (m) Sprint (m) No. of HSR No. of VHSR No. of sprints Maximal speed (km-h¹) Variables Total distance (m) MSR (m) HSR (m) VHSR (m) Sprint (m) No. of HSR No. of VHSR No. of sprints Maximal speed (km-h¹) Variables <20 y 10,211 + 784+ 1,988 495 25977 541 194 281 ± 145+ 24 ± 7 39 12 16+7 31.0 1.9 <20 y 10,336 671 2,099 368 315 101 675 ± 216 350 165 25+ 7 4312 187 31.7 1.8 <20 y 20-24.9 y 10,381 9901 2,141 555+ 282 102 568 238 285 1611 258 4115 168 30.8 1.9 20-24.9 y 10,315 674 2,057 339 317 +88 688207 370 148 287 4813 207§ 31.6 1.5 20-24.9 y 25-29.9 y 10,164 ± 914 2,054 581 266 112 524 242 257 + 154 249 38 16 148 30.5 1.9 External defenders 25-29.9 y 10,268 653 2,107 396 317 104 669 ± 223 352 147 287 47 14 197 31.2 ± 1.5 External midfielders 25-29.9 y 30-34.9 y 10,156 1,091 2,059 601 254 ± 97+ 491 204 236± 133 23±8 36 13 146 30.2 1.8 30-34.9 y 10,049714 1,986 417 28381 579 170 296 120 25 ± 7 4111 16 +5 30.8 0.9 30-34.9 y 235 y 10,142 972 1,987 549 227 88 418 181 190 112 19 + 7+ 30 12 10+ 6+ 29.6 1.8 235 y 9,757 ± 555+ 1,813 401 259 ± 106+ 513 220 253132 22+8+ 36 14 13 6 30.2 1.0 235 y <20 y 10,086 796† 2,064 390t 265 66 548 168 250 103 23 ± 6+ 38 ± 11 15+ 6+ 30.9 ± 0.9 <20 y 10,577 685+ 2,169 518 239 ± 77 158 108 430 191 217 32 11 11+5 29.8 1.9t <20 y 20-24.9 y 9,823 6951 1,813 4081 213 +66+ 4091311 196 ± 94 19 ± 5t 309 11:5 30.61.61 20-24.9 y 11,035 764 2,557 551 266 92 463 + 176 196 107 23 ± 7 3512 115 29.9 1.71 20-24.9 y Central defenders 25-29.9 y 9,473 627 1,655 349 194±69 372 135 17888 176 289 105 30.4 1.7 Central midfielders 25-29.9 y 10,819 ± 1,325+ 2,460 ± 655 262 105 453 199 191 ± 116 23 ± 8 3414 116 29.3 1.9 Forwards 25-29.9 y 30-34.9 y 9,431625 1,588 348 17466 333 133 15887 165 259 9±4 30.11.7 30-34.9 y 11,063715 2,675 529 266 +97 448183 181 108 23 ± 8 33 12 105 29.1 1.6 30-34.9 y 235 y 9,343 646 1,605347 18466 338 126 15379 16 ± 5 25 ± 9 9±4 29.4 1.4 235 y 11,014 688 2,500 439 232 +97 390 ± 200+ 158 116 19 ± 8 29 13 9±6 28.7 1.8 235 y

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 62CR

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