TERVER-TIPOVIK (Лабораторные работы)

дана выборка: 1 25.0116 2 31.7334 3 35.4043 4 34.3555 5 25.2027 6 22.3273 7 37.8330 8 21.8399 9 27.2789 10 30.9961 11 23.4020 12 34.4700 13 23.7855 14 41.0779 15 36.2127 16 27.3728 17 33.2222 18 31.1565 19 18.8504 20 37.4952 21 27.2809 22 20.8257 23 35.7432 24 38.5199 25 32.2146 26 31.1096 27 19.5037 28 27.0880 29 31.0639 30 28.7735 31 24.6165 32 25.9498 33 30.3365 34 30.0126 35 37.5655 36 27.5948 37 36.9789 38 19.8456 39 14.9425 40 30.8636 41 35.2842 42 29.0324 43 35.2588 44 26.0342 45 25.8741 46 25.2639 47 26.0790 48 37.6509 49 27.6451 50 20.8639 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 30.0282 32.1528 20.8070 15.4646 30.9450 18.6890 40.2197 19.6328 22.6142 31.7907 22.7250 24.3814 33.2676 18.7776 27.0521 31.1923 27.7708 33.1025 24.4781 22.3673 26.4943 33.7437 17.5874 20.5744 18.4079 20.4797 37.7541 34.1853 22.7121 15.7688 24.5166 20.5894 30.2975 21.6740 14.3501 33.6397 11.6947 22.9365 33.5608 21.5403 37.3817 18.8768 26.7393 33.9625 42.4149 33.8363 38.0983 37.7112 21.2961 Упорядочим ее по возрастанию, т.е.

представим ее в вариационный ряд: 1 11.6947 2 14.3501 3 14.9425 4 15.4646 5 15.7688 6 17.5874 7 18.4079 8 18.6890 9 18.7776 10 18.8504 11 18.8768 12 19.5037 13 19.6328 14 19.8456 15 20.4797 16 20.5744 17 20.5894 18 20.8070 19 20.8257 20 20.8639 21 21.2961 22 21.5403 23 21.6740 24 21.8399 25 22.3273 26 22.3673 27 22.6142 28 22.7121 29 22.7250 30 22.9365 31 23.4020 32 23.7855 33 24.3814 34 24.4781 35 24.5166 36 24.6165 37 25.0116 38 25.2027 39 25.2639 40 25.8741 41 25.9498 42 26.0342 43 26.0790 44 26.4943 45 26.7393 46 27.0521 47 27.0880 48 27.2789 49 27.2809 50 27.3728 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 27.5948 27.6451 27.7708 28.7735 29.0324 30.0126 30.0282 30.2975 30.3365 30.8636 30.9450 30.9961 31.0639 31.1096 31.1565 31.1923 31.7334 31.7907 32.1528 32.2146 33.1025 33.2222 33.2676 33.5608 33.6397 33.7437 33.8363 33.9625 34.1853 34.3555 34.4700 35.2588 35.2842 35.4043 35.7432 36.2127 36.9789 37.3817 37.4952 37.5655 37.6509 37.7112 37.7541 37.8330 38.0983 38.5199 40.2197 41.0779 42.4149 Обработка результатов: 1.

Рассчитаем границы доверительного интервала для Мх и Dх по известным формулам: 99 1 M X= ∑ x =27 . 87 99 i=1 i D x=M x2 −M 2x =824 .6677−776 . 7369=47 . 9308 σ X =√ D x=6. 9232 99 ∑ ( x i− M x )3⋅p i i=1 As= 99 [∑ i=1 ( x i −M x )2⋅pi ] 3 2 = −16 . 8994 47 . 9326 3 2 =−0. 0509 99 ∑ ( xi −M x ) 4⋅p i i =1 Ex= 99 [∑ i=1 2 ( x i−M x )2⋅p i ] −3= 4943.

4911 −3=−0 . 8484 47 . 93262 посчитаем доверительные интервалы для доверительной вероятности 90%: n=99 Ön= Ö99»9.9499 n=98 b=0.9Þa/2=0.05 t=1,984 6.9232 6.9232 27.87−1.984⋅ ≤M X≤27.87+1.9854 9.9499 9.9499 2 χ 1 =122 .1077 2 χ 2 =76 . 1638 26 . 4900≤M X≤29 .

2515 98⋅47 . 9308 98⋅47. 9308 ≤D X≤ 122. 1077 76 . 1638 38 . 4678≤D X ≤61 . 6726 посчитаем доверительные интервалы для доверительной вероятности 95%: n=99 Ön= Ö99»9.9499 n=98 b=0.95Þa/2=0.025 6 . 9232 6 . 9232 27 . 87−2. 3⋅ ≤M X ≤27 . 87+2 . 3⋅ 9 . 9499 9 . 9499 t=2,3 26 . 2696≤M X ≤29 . 4704 χ 21 =127 . 2821 98⋅47 .

9308 98⋅47. 9308 ≤D X ≤ 127 . 2821 72 . 5009 2 χ 2 =72 .5009 36 . 9100≤D X ≤64 . 7884 Построение Гистограммы: посчитаем количество интервалов k на гистограмме: k =1+3 .2⋅lg( N )=1+3 .2⋅lg(99 )=7. 38→7 разобьем вариационный ряд на 7 интервалов, вычислим длину каждого интервала: (42.4149-11,6947)/7=4,3886 № интервал 11,6947-16,0833 16,0833-20,4719 20,4719-24,8605 24,8605-29,2491 29,2491-33,6377 33,6377-38,0263 38,0263-42,4149 1 2 3 4 5 6 7 - длина интервала частота 5 9 22 19 19 20 5 относительная частота 0.71 1.29 3.14 2.71 2.71 2.86 0.71 472.8507 478.5325 484.2143 489.8961 495.5779 501.2597 506.9415 22 20 18 отн.частота 16 14 12 10 8 6 4 2 0 472.8507 478.5325 484.2143 489.8961 495.5779 знчение величины 501.2597 506.9415 отн.ча 10 8 6 4 2 0 472.8507 478.5325 484.2143 489.8961 495.5779 знчение величины 501.2597 506.9415 Вывод: С увеличением доверительной вероятности доверительные интервалы мат.ожидания и дисперсии увеличиваются, что ведет к снижению точности их оценки, увеличение объема выборки же напротив ведет к уменьшению доверительнх интервалов, т.

е. увеличению точности оценки. x x*x 11.6947 14.3501 14.9425 15.4646 15.7688 17.5874 18.4079 18.6890 18.7776 18.8504 18.8768 19.5037 19.6328 19.8456 20.4797 20.5744 20.5894 20.8070 20.8257 20.8639 21.2961 21.5403 21.6740 21.8399 22.3273 22.3673 22.6142 22.7121 22.7250 22.9365 23.4020 23.7855 24.3814 24.4781 24.5166 24.6165 25.0116 25.2027 25.2639 25.8741 25.9498 26.0342 26.0790 26.4943 26.7393 27.0521 27.0880 27.2789 27.2809 27.3728 27.5948 x*x*x 136.7660 205.9254 223.2783 239.1539 248.6551 309.3166 338.8508 349.2787 352.5983 355.3376 356.3336 380.3943 385.4468 393.8478 419.4181 423.3059 423.9234 432.9312 433.7098 435.3023 453.5239 463.9845 469.7623 476.9812 498.5083 500.2961 511.4020 515.8395 516.4256 526.0830 547.6536 565.7500 594.4527 599.1774 601.0637 605.9721 625.5801 635.1761 638.2646 669.4691 673.3921 677.7796 680.1142 701.9479 714.9902 731.8161 733.7597 744.1384 744.2475 749.2702 761.4730 x*x*x*x 1599.4374 2955.0497 3336.3361 3698.4187 3920.9918 5440.0755 6237.5313 6527.6700 6620.9491 6698.2555 6726.4377 7419.0966 7567.4006 7816.1467 8589.5571 8709.2656 8728.3283 9008.0005 9032.3098 9082.1041 9658.2898 9994.3658 10181.6276 10417.2224 11130.3449 11190.2732 11564.9481 11715.7980 11735.7723 12066.5035 12816.1896 13456.6469 14493.5882 14666.7238 14736.0377 14916.9115 15646.7601 16008.1524 16125.0541 17321.9092 17474.3908 17645.4489 17736.6993 18597.6191 19118.3365 19797.1627 19876.0839 20299.2766 20303.7418 20509.6228 21012.6948 18704.9410 42405.2580 49853.2020 57194.5655 61829.3356 95676.7830 114819.8527 121995.6249 124325.5342 126264.7959 126973.6190 144699.8339 148569.2633 155116.1206 175911.5527 179187.9149 179711.0426 187429.4664 188104.1737 189488.1126 205683.9054 215281.6386 220676.5960 227511.0957 248510.5504 250296.1970 261532.0482 266090.3757 266695.4262 276763.3568 299924.4700 320073.0741 353373.9721 359013.5322 361277.5421 367202.1523 391350.5048 403448.6619 407381.7548 448188.8100 453456.9473 459385.1450 462555.3808 492730.8999 511210.9353 535554.8253 538403.3619 553741.9363 553904.3484 561405.8024 579841.1100 68455.115149238 33411.022295875 27928.900719578 23683.100753826 21444.163740319 11179.08623629 8015.7506688404 7104.8323341188 6834.5190372845 6618.245701797 6541.0996207664 4899.2209084769 4603.7488830522 4146.1334783146 2982.9136095089 2832.9333825591 2809.7066082069 2488.5643477164 2462.3138157121 2409.3356828918 1867.5998580436 1605.1796170365 1473.7932863702 1322.1744040202 943.7899774264 916.83913095123 763.03531506994 707.75147821218 700.69755586987 592.39195031023 398.51079509388 278.31835838994 148.11144196826 132.3596484621 126.45170670862 112.04332422895 66.753242843781 50.613504377788 46.125677557512 15.868174918633 13.594292771433 11.357189572904 10.288474635592 3.5814107443572 1.6343305819586 0.4474372926559 0.3738997770091 0.1220531072866 0.1204095051024 0.0610958260884 0.0057331019987 -4232.085 -2471.254 -2160.431 -1909.101 -1772.074 -1087.188 -847.1458 -773.8653 -751.6765 -733.7653 -727.341 -585.5922 -558.8995 -516.6929 -403.6273 -388.3088 -385.9186 -352.3398 -349.5486 -343.8927 -284.0945 -253.5962 -237.8633 -219.2636 -170.2772 -166.6172 -145.1806 -137.2178 -136.1909 -120.0762 -89.19286 -68.14067 -42.45623 -39.02265 -37.70887 -34.43812 -23.35362 -18.97579 -17.69934 -7.950515 -7.079743 -6.186616 -5.744646 -2.603398 -1.445456 -0.547078 -0.478152 -0.206496 -0.204407 -0.122888 -0.020835 261.6393 182.7868 167.1194 153.8931 146.4383 105.7312 89.53072 84.29017 82.67115 81.3526 80.87706 69.99443 67.85093 64.39048 54.61606 53.22531 53.00667 49.88551 49.62171 49.08498 43.21574 40.06469 38.39002 36.36172 30.72116 30.27935 27.62309 26.6036 26.47069 24.3391 19.96274 16.68288 12.1701 11.50477 11.24507 10.58505 8.170266 7.114317 6.791589 3.983488 3.687044 3.370043 3.207565 1.892462 1.278409 0.668908 0.611473 0.349361 0.347001 0.247176 0.075717 27.6451 27.7708 28.7735 29.0324 30.0126 30.0282 30.2975 30.3365 30.8636 30.9450 30.9961 31.0639 31.1096 31.1565 31.1923 31.7334 31.7907 32.1528 32.2146 33.1025 33.2222 33.2676 33.5608 33.6397 33.7437 33.8363 33.9625 34.1853 34.3555 34.4700 35.2588 35.2842 35.4043 35.7432 36.2127 36.9789 37.3817 37.4952 37.5655 764.2516 771.2173 827.9143 842.8802 900.7562 901.6928 917.9385 920.3032 952.5618 957.5930 960.7582 964.9659 967.8072 970.7275 972.9596 1007.0087 1010.6486 1033.8025 1037.7805 1095.7755 1103.7146 1106.7332 1126.3273 1131.6294 1138.6373 1144.8952 1153.4514 1168.6347 1180.3004 1188.1809 1243.1830 1244.9748 1253.4645 1277.5763 1311.3596 1367.4390 1397.3915 1405.8900 1411.1668 21127.8106 21417.3223 23821.9922 24470.8366 27034.0343 27076.2116 27811.2419 27918.7790 29399.4865 29632.7162 29779.7577 29975.6037 30108.0952 30244.4711 30348.8471 31955.8091 32129.2267 33239.6466 33431.6822 36272.9087 36667.8263 36818.3577 37800.4451 38067.6741 38421.8351 38739.0174 39174.0934 39950.1290 40549.8097 40956.5956 43833.1400 43927.9388 44378.0317 45664.6669 47487.8733 50566.3917 52236.8696 52714.1276 53011.1861 37.6509 1417.5903 53373.5495 2009562.1759 9152.1054562523 935.7089 95.66664 37.7112 37.7541 1422.1346 1425.3721 53630.4025 2022466.8360 9379.894150057 953.1219 96.84985 53813.6395 2031685.5288 9544.5224418615 965.6409 97.69607 37.8330 1431.3359 54151.7307 2048722.4271 9852.9472394577 988.9506 99.26201 38.0983 1451.4805 55298.9381 2106795.5342 10945.089571117 1070.076 104.6188 38.5199 40.2197 41.0779 42.4149 27.8700 Mx 1483.7827 57155.1611 1617.6243 65060.3628 1687.3939 69314.5966 1799.0237 76305.4121 824.6677 25638.3216 M2 M3 As -16.89843937164 Ex 4943.4911061 584080.4378 594776.1742 685442.0919 710447.1154 811361.6575 813049.8970 842611.1013 846958.0393 907373.9923 916984.4015 923056.3481 931159.1558 936650.7999 942311.8642 946650.3429 1014066.4727 1021410.6058 1068747.7079 1076988.2690 1200723.9601 1218185.8583 1224858.3976 1268613.1792 1280585.1354 1296494.8775 1310785.0137 1330450.1466 1365707.1464 1393108.9876 1411773.8511 1545503.9154 1549962.1770 1571173.1487 1632201.3205 1719664.1088 1869889.5424 1952702.9900 1976526.7569 1991391.7099 2201611.0890 2616708.2727 2847298.0671 3236486.4243 829762.5495 M4 209.99683016 0.0025568669641 9.671204263E-05 0.6664610530812 1.8258736062237 21.076117404705 21.696654346998 34.726425750998 37.012399792113 80.31447736703 89.412603527173 95.505729835917 104.06455663078 110.14959225581 116.66796744794 121.83506126054 222.78873931904 236.30274814444 336.45290840018 356.29695909778 749.63124393524 820.61570826419 848.81528510224 1048.8253081701 1108.2115218587 1190.3004674789 1267.1550513432 1377.8164572413 1590.6873785769 1769.2227393948 1897.5107714731 2980.5968932057 3021.7933539655 3222.3973249691 3842.4857638853 4844.3246216997 6884.4603276198 8185.373099983 8583.1140493159 8836.6292530011 12864.336508862 23261.096231367 30432.619765674 44755.541840769 4943.4911060997 Dx 47.932575252895 -0.011371 -0.000975 0.737617 1.570735 9.836553 10.05297 14.30524 15.00584 26.82844 29.07696 30.55076 32.58195 34.00065 35.4988 36.67155 57.66601 60.27005 78.55851 82.00854 143.2636 153.3221 157.257 184.3009 192.0733 202.6481 212.3843 226.1484 251.8771 272.7953 287.5002 403.3921 407.5666 427.6951 488.0442 580.664 755.7922 860.5555 891.7306 911.4125 1207.927 1883.53 2304.117 3077.054 -16.89844 CKO 6.923336 0.050565 0.009834 0.816371 1.351249 4.590873 4.657967 5.892913 6.083782 8.961834 9.455824 9.772703 10.2012 10.49522 10.80129 11.03789 14.92611 15.37214 18.34265 18.87583 27.37939 28.64639 29.13443 32.38557 33.28981 34.50073 35.59712 37.11895 39.88342 42.06213 43.56043 54.59484 54.97084 56.76616 61.98779 69.60118 82.97265 90.47305 92.6451 94.00335 113.4211 152.5159 174.4495 211.5551 47.93258 2297.532 -0.051708192223 19.6188233 392.5526821 7978.950256559 164243.40608 0.92478536029 2.151653 -0.050921 5 1 5 5 4 #DIV/0! 16.36 #DIV/0! #DIV/0! #DIV/0! 72.50094 -0.848347 дана выборка: 1 25.0116 2 31.7334 3 35.4043 4 34.3555 5 25.2027 6 22.3273 7 37.8330 8 21.8399 9 27.2789 10 30.9961 11 23.4020 12 34.4700 13 23.7855 14 41.0779 15 36.2127 16 27.3728 17 33.2222 18 31.1565 19 18.8504 20 37.4952 21 27.2809 22 20.8257 23 35.7432 24 38.5199 25 32.2146 26 31.1096 27 19.5037 28 27.0880 29 31.0639 30 28.7735 31 24.6165 32 25.9498 33 30.3365 34 30.0126 35 37.5655 36 27.5948 37 36.9789 38 19.8456 39 14.9425 40 30.8636 41 35.2842 42 29.0324 43 35.2588 44 26.0342 45 25.8741 46 25.2639 47 26.0790 48 37.6509 49 27.6451 50 20.8639 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 30.0282 32.1528 20.8070 15.4646 30.9450 18.6890 40.2197 19.6328 22.6142 31.7907 22.7250 24.3814 33.2676 18.7776 27.0521 31.1923 27.7708 33.1025 24.4781 22.3673 26.4943 33.7437 17.5874 20.5744 18.4079 20.4797 37.7541 34.1853 22.7121 15.7688 24.5166 20.5894 30.2975 21.6740 14.3501 33.6397 11.6947 22.9365 33.5608 21.5403 37.3817 18.8768 26.7393 33.9625 42.4149 33.8363 38.0983 37.7112 21.2961 Упорядочим ее по возрастанию, т.е.