On étudie la fréquence d’un événement grâce au graphique ci-dessous représentant \( 100 \) échantillons.
{"graphInit": {"range": [[-3, 101], [0.20400000000000001, 0.316]], "scale": [6.0, 4017.857142857143], "axisOpacity": 0.5, "axisArrows": "->", "gridOpacity": 0.15, "gridStep": [100, 0.005], "tickStep": [1, 1], "labelStep": [1, 10], "xLabel": "N\u00b0 d'\u00e9chantillon", "yLabel": "Fr\u00e9quences"}, "label": [[[0.20000000000000018, 0.2], "0\\mbox{,}2", "left", {"font-size": 13}], [[0.20000000000000018, 0.21000000000000002], "0\\mbox{,}21", "left", {"font-size": 13}]], "path": [[[[0, 0.26], [100, 0.26]]], [[[1, 0.294468], [1, 0.29693200000000003]], {"stroke": "red"}], [[[0.29999999999999993, 0.2957], [1.7000000000000002, 0.2957]], {"stroke": "red"}], [[[2, 0.293068], [2, 0.295532]], {"stroke": "red"}], [[[1.2999999999999998, 0.2943], [2.7, 0.2943]], {"stroke": "red"}], [[[3, 0.25096799999999997], [3, 0.253432]], {"stroke": "red"}], [[[2.3, 0.2522], [3.7, 0.2522]], {"stroke": "red"}], [[[4, 0.254568], [4, 0.25703200000000004]], {"stroke": "red"}], [[[3.3, 0.2558], [4.7, 0.2558]], {"stroke": "red"}], [[[5, 0.23896799999999999], [5, 0.241432]], {"stroke": "red"}], [[[4.3, 0.2402], [5.7, 0.2402]], {"stroke": "red"}], [[[6, 0.253668], [6, 0.256132]], {"stroke": "red"}], [[[5.3, 0.2549], [6.7, 0.2549]], {"stroke": "red"}], [[[7, 0.296468], [7, 0.29893200000000003]], {"stroke": "red"}], [[[6.3, 0.2977], [7.7, 0.2977]], {"stroke": "red"}], [[[8, 0.254168], [8, 0.256632]], {"stroke": "red"}], [[[7.3, 0.2554], [8.7, 0.2554]], {"stroke": "red"}], [[[9, 0.231268], [9, 0.23373200000000002]], {"stroke": "red"}], [[[8.3, 0.2325], [9.7, 0.2325]], {"stroke": "red"}], [[[10, 0.24426799999999999], [10, 0.246732]], {"stroke": "red"}], [[[9.3, 0.2455], [10.7, 0.2455]], {"stroke": "red"}], [[[11, 0.262168], [11, 0.26463200000000003]], {"stroke": "red"}], [[[10.3, 0.2634], [11.7, 0.2634]], {"stroke": "red"}], [[[12, 0.22186799999999998], [12, 0.224332]], {"stroke": "red"}], [[[11.3, 0.2231], [12.7, 0.2231]], {"stroke": "red"}], [[[13, 0.254368], [13, 0.256832]], {"stroke": "red"}], [[[12.3, 0.2556], [13.7, 0.2556]], {"stroke": "red"}], [[[14, 0.25446799999999997], [14, 0.256932]], {"stroke": "red"}], [[[13.3, 0.2557], [14.7, 0.2557]], {"stroke": "red"}], [[[15, 0.287868], [15, 0.29033200000000003]], {"stroke": "red"}], [[[14.3, 0.2891], [15.7, 0.2891]], {"stroke": "red"}], [[[16, 0.29336799999999996], [16, 0.295832]], {"stroke": "red"}], [[[15.3, 0.2946], [16.7, 0.2946]], {"stroke": "red"}], [[[17, 0.24076799999999998], [17, 0.243232]], {"stroke": "red"}], [[[16.3, 0.242], [17.7, 0.242]], {"stroke": "red"}], [[[18, 0.23096799999999998], [18, 0.233432]], {"stroke": "red"}], [[[17.3, 0.2322], [18.7, 0.2322]], {"stroke": "red"}], [[[19, 0.24226799999999998], [19, 0.244732]], {"stroke": "red"}], [[[18.3, 0.2435], [19.7, 0.2435]], {"stroke": "red"}], [[[20, 0.227768], [20, 0.23023200000000002]], {"stroke": "red"}], [[[19.3, 0.229], [20.7, 0.229]], {"stroke": "red"}], [[[21, 0.257168], [21, 0.25963200000000003]], {"stroke": "red"}], [[[20.3, 0.2584], [21.7, 0.2584]], {"stroke": "red"}], [[[22, 0.290568], [22, 0.293032]], {"stroke": "red"}], [[[21.3, 0.2918], [22.7, 0.2918]], {"stroke": "red"}], [[[23, 0.277568], [23, 0.280032]], {"stroke": "red"}], [[[22.3, 0.2788], [23.7, 0.2788]], {"stroke": "red"}], [[[24, 0.224768], [24, 0.22723200000000002]], {"stroke": "red"}], [[[23.3, 0.226], [24.7, 0.226]], {"stroke": "red"}], [[[25, 0.27016799999999996], [25, 0.272632]], {"stroke": "red"}], [[[24.3, 0.2714], [25.7, 0.2714]], {"stroke": "red"}], [[[26, 0.266768], [26, 0.269232]], {"stroke": "red"}], [[[25.3, 0.268], [26.7, 0.268]], {"stroke": "red"}], [[[27, 0.257268], [27, 0.259732]], {"stroke": "red"}], [[[26.3, 0.2585], [27.7, 0.2585]], {"stroke": "red"}], [[[28, 0.284168], [28, 0.286632]], {"stroke": "red"}], [[[27.3, 0.2854], [28.7, 0.2854]], {"stroke": "red"}], [[[29, 0.274768], [29, 0.27723200000000003]], {"stroke": "red"}], [[[28.3, 0.276], [29.7, 0.276]], {"stroke": "red"}], [[[30, 0.21376799999999999], [30, 0.216232]], {"stroke": "red"}], [[[29.3, 0.215], [30.7, 0.215]], {"stroke": "red"}], [[[31, 0.235668], [31, 0.238132]], {"stroke": "red"}], [[[30.3, 0.2369], [31.7, 0.2369]], {"stroke": "red"}], [[[32, 0.270068], [32, 0.272532]], {"stroke": "red"}], [[[31.3, 0.2713], [32.7, 0.2713]], {"stroke": "red"}], [[[33, 0.244868], [33, 0.24733200000000002]], {"stroke": "red"}], [[[32.3, 0.2461], [33.7, 0.2461]], {"stroke": "red"}], [[[34, 0.27066799999999996], [34, 0.273132]], {"stroke": "red"}], [[[33.3, 0.2719], [34.7, 0.2719]], {"stroke": "red"}], [[[35, 0.261368], [35, 0.263832]], {"stroke": "red"}], [[[34.3, 0.2626], [35.7, 0.2626]], {"stroke": "red"}], [[[36, 0.241468], [36, 0.243932]], {"stroke": "red"}], [[[35.3, 0.2427], [36.7, 0.2427]], {"stroke": "red"}], [[[37, 0.29026799999999997], [37, 0.292732]], {"stroke": "red"}], [[[36.3, 0.2915], [37.7, 0.2915]], {"stroke": "red"}], [[[38, 0.254368], [38, 0.256832]], {"stroke": "red"}], [[[37.3, 0.2556], [38.7, 0.2556]], {"stroke": "red"}], [[[39, 0.272768], [39, 0.27523200000000003]], {"stroke": "red"}], [[[38.3, 0.274], [39.7, 0.274]], {"stroke": "red"}], [[[40, 0.22996799999999998], [40, 0.232432]], {"stroke": "red"}], [[[39.3, 0.2312], [40.7, 0.2312]], {"stroke": "red"}], [[[41, 0.271468], [41, 0.273932]], {"stroke": "red"}], [[[40.3, 0.2727], [41.7, 0.2727]], {"stroke": "red"}], [[[42, 0.264968], [42, 0.267432]], {"stroke": "red"}], [[[41.3, 0.2662], [42.7, 0.2662]], {"stroke": "red"}], [[[43, 0.257668], [43, 0.26013200000000003]], {"stroke": "red"}], [[[42.3, 0.2589], [43.7, 0.2589]], {"stroke": "red"}], [[[44, 0.250068], [44, 0.25253200000000003]], {"stroke": "red"}], [[[43.3, 0.2513], [44.7, 0.2513]], {"stroke": "red"}], [[[45, 0.259468], [45, 0.261932]], {"stroke": "red"}], [[[44.3, 0.2607], [45.7, 0.2607]], {"stroke": "red"}], [[[46, 0.237368], [46, 0.23983200000000002]], {"stroke": "red"}], [[[45.3, 0.2386], [46.7, 0.2386]], {"stroke": "red"}], [[[47, 0.26506799999999997], [47, 0.267532]], {"stroke": "red"}], [[[46.3, 0.2663], [47.7, 0.2663]], {"stroke": "red"}], [[[48, 0.23876799999999998], [48, 0.241232]], {"stroke": "red"}], [[[47.3, 0.24], [48.7, 0.24]], {"stroke": "red"}], [[[49, 0.27016799999999996], [49, 0.272632]], {"stroke": "red"}], [[[48.3, 0.2714], [49.7, 0.2714]], {"stroke": "red"}], [[[50, 0.268968], [50, 0.271432]], {"stroke": "red"}], [[[49.3, 0.2702], [50.7, 0.2702]], {"stroke": "red"}], [[[51, 0.253568], [51, 0.25603200000000004]], {"stroke": "red"}], [[[50.3, 0.2548], [51.7, 0.2548]], {"stroke": "red"}], [[[52, 0.247168], [52, 0.24963200000000002]], {"stroke": "red"}], [[[51.3, 0.2484], [52.7, 0.2484]], {"stroke": "red"}], [[[53, 0.23476799999999998], [53, 0.237232]], {"stroke": "red"}], [[[52.3, 0.236], [53.7, 0.236]], {"stroke": "red"}], [[[54, 0.275968], [54, 0.278432]], {"stroke": "red"}], [[[53.3, 0.2772], [54.7, 0.2772]], {"stroke": "red"}], [[[55, 0.257768], [55, 0.260232]], {"stroke": "red"}], [[[54.3, 0.259], [55.7, 0.259]], {"stroke": "red"}], [[[56, 0.24106799999999998], [56, 0.243532]], {"stroke": "red"}], [[[55.3, 0.2423], [56.7, 0.2423]], {"stroke": "red"}], [[[57, 0.251868], [57, 0.254332]], {"stroke": "red"}], [[[56.3, 0.2531], [57.7, 0.2531]], {"stroke": "red"}], [[[58, 0.254068], [58, 0.25653200000000004]], {"stroke": "red"}], [[[57.3, 0.2553], [58.7, 0.2553]], {"stroke": "red"}], [[[59, 0.24406799999999998], [59, 0.246532]], {"stroke": "red"}], [[[58.3, 0.2453], [59.7, 0.2453]], {"stroke": "red"}], [[[60, 0.27666799999999997], [60, 0.279132]], {"stroke": "red"}], [[[59.3, 0.2779], [60.7, 0.2779]], {"stroke": "red"}], [[[61, 0.303768], [61, 0.306232]], {"stroke": "red"}], [[[60.3, 0.305], [61.7, 0.305]], {"stroke": "red"}], [[[62, 0.21376799999999999], [62, 0.216232]], {"stroke": "red"}], [[[61.3, 0.215], [62.7, 0.215]], {"stroke": "red"}], [[[63, 0.22436799999999998], [63, 0.226832]], {"stroke": "red"}], [[[62.3, 0.2256], [63.7, 0.2256]], {"stroke": "red"}], [[[64, 0.278468], [64, 0.280932]], {"stroke": "red"}], [[[63.3, 0.2797], [64.7, 0.2797]], {"stroke": "red"}], [[[65, 0.28826799999999997], [65, 0.290732]], {"stroke": "red"}], [[[64.3, 0.2895], [65.7, 0.2895]], {"stroke": "red"}], [[[66, 0.24786799999999998], [66, 0.250332]], {"stroke": "red"}], [[[65.3, 0.2491], [66.7, 0.2491]], {"stroke": "red"}], [[[67, 0.236068], [67, 0.23853200000000002]], {"stroke": "red"}], [[[66.3, 0.2373], [67.7, 0.2373]], {"stroke": "red"}], [[[68, 0.275268], [68, 0.27773200000000003]], {"stroke": "red"}], [[[67.3, 0.2765], [68.7, 0.2765]], {"stroke": "red"}], [[[69, 0.24506799999999998], [69, 0.247532]], {"stroke": "red"}], [[[68.3, 0.2463], [69.7, 0.2463]], {"stroke": "red"}], [[[70, 0.302968], [70, 0.30543200000000004]], {"stroke": "red"}], [[[69.3, 0.3042], [70.7, 0.3042]], {"stroke": "red"}], [[[71, 0.280368], [71, 0.28283200000000003]], {"stroke": "red"}], [[[70.3, 0.2816], [71.7, 0.2816]], {"stroke": "red"}], [[[72, 0.22846799999999998], [72, 0.230932]], {"stroke": "red"}], [[[71.3, 0.2297], [72.7, 0.2297]], {"stroke": "red"}], [[[73, 0.286468], [73, 0.288932]], {"stroke": "red"}], [[[72.3, 0.2877], [73.7, 0.2877]], {"stroke": "red"}], [[[74, 0.284868], [74, 0.28733200000000003]], {"stroke": "red"}], [[[73.3, 0.2861], [74.7, 0.2861]], {"stroke": "red"}], [[[75, 0.25906799999999996], [75, 0.261532]], {"stroke": "red"}], [[[74.3, 0.2603], [75.7, 0.2603]], {"stroke": "red"}], [[[76, 0.263968], [76, 0.266432]], {"stroke": "red"}], [[[75.3, 0.2652], [76.7, 0.2652]], {"stroke": "red"}], [[[77, 0.255968], [77, 0.258432]], {"stroke": "red"}], [[[76.3, 0.2572], [77.7, 0.2572]], {"stroke": "red"}], [[[78, 0.257268], [78, 0.259732]], {"stroke": "red"}], [[[77.3, 0.2585], [78.7, 0.2585]], {"stroke": "red"}], [[[79, 0.242968], [79, 0.245432]], {"stroke": "red"}], [[[78.3, 0.2442], [79.7, 0.2442]], {"stroke": "red"}], [[[80, 0.247668], [80, 0.250132]], {"stroke": "red"}], [[[79.3, 0.2489], [80.7, 0.2489]], {"stroke": "red"}], [[[81, 0.24606799999999998], [81, 0.248532]], {"stroke": "red"}], [[[80.3, 0.2473], [81.7, 0.2473]], {"stroke": "red"}], [[[82, 0.229268], [82, 0.23173200000000002]], {"stroke": "red"}], [[[81.3, 0.2305], [82.7, 0.2305]], {"stroke": "red"}], [[[83, 0.24686799999999998], [83, 0.249332]], {"stroke": "red"}], [[[82.3, 0.2481], [83.7, 0.2481]], {"stroke": "red"}], [[[84, 0.295768], [84, 0.298232]], {"stroke": "red"}], [[[83.3, 0.297], [84.7, 0.297]], {"stroke": "red"}], [[[85, 0.21376799999999999], [85, 0.216232]], {"stroke": "red"}], [[[84.3, 0.215], [85.7, 0.215]], {"stroke": "red"}], [[[86, 0.272868], [86, 0.275332]], {"stroke": "red"}], [[[85.3, 0.2741], [86.7, 0.2741]], {"stroke": "red"}], [[[87, 0.248268], [87, 0.250732]], {"stroke": "red"}], [[[86.3, 0.2495], [87.7, 0.2495]], {"stroke": "red"}], [[[88, 0.285368], [88, 0.28783200000000003]], {"stroke": "red"}], [[[87.3, 0.2866], [88.7, 0.2866]], {"stroke": "red"}], [[[89, 0.25706799999999996], [89, 0.259532]], {"stroke": "red"}], [[[88.3, 0.2583], [89.7, 0.2583]], {"stroke": "red"}], [[[90, 0.281668], [90, 0.284132]], {"stroke": "red"}], [[[89.3, 0.2829], [90.7, 0.2829]], {"stroke": "red"}], [[[91, 0.288568], [91, 0.291032]], {"stroke": "red"}], [[[90.3, 0.2898], [91.7, 0.2898]], {"stroke": "red"}], [[[92, 0.264268], [92, 0.266732]], {"stroke": "red"}], [[[91.3, 0.2655], [92.7, 0.2655]], {"stroke": "red"}], [[[93, 0.287868], [93, 0.29033200000000003]], {"stroke": "red"}], [[[92.3, 0.2891], [93.7, 0.2891]], {"stroke": "red"}], [[[94, 0.25856799999999996], [94, 0.261032]], {"stroke": "red"}], [[[93.3, 0.2598], [94.7, 0.2598]], {"stroke": "red"}], [[[95, 0.278468], [95, 0.280932]], {"stroke": "red"}], [[[94.3, 0.2797], [95.7, 0.2797]], {"stroke": "red"}], [[[96, 0.21376799999999999], [96, 0.216232]], {"stroke": "red"}], [[[95.3, 0.215], [96.7, 0.215]], {"stroke": "red"}], [[[97, 0.244868], [97, 0.24733200000000002]], {"stroke": "red"}], [[[96.3, 0.2461], [97.7, 0.2461]], {"stroke": "red"}], [[[98, 0.272068], [98, 0.274532]], {"stroke": "red"}], [[[97.3, 0.2733], [98.7, 0.2733]], {"stroke": "red"}], [[[99, 0.233868], [99, 0.23633200000000001]], {"stroke": "red"}], [[[98.3, 0.2351], [99.7, 0.2351]], {"stroke": "red"}], [[[100, 0.24206799999999998], [100, 0.244532]], {"stroke": "red"}], [[[99.3, 0.2433], [100.7, 0.2433]], {"stroke": "red"}]]}
Déduire de ce graphique une valeur approchée de la taille \( N \) des échantillons puis choisir
la valeur exacte la plus proche parmis les choix suivant.