8.6. Ejercicios#
Criterio de Chauvenet
1. Usted ha medido un campo magnético (los datos se presentan abajo) obteniendo un total de 500 datos. Obtiene dos arreglos de datos: datosX corresponden al valor en el tiempo en que fue medido el campo, en \(s\), y datosY corresponden al valor de campo magnético en \(\mu T\). (a) Realice una gráfica de los datos y reporte el valor esperado de campo magnético con su incertidumbre. Habrá notado que algunos datos no parecen corresponder a fluctuaciones normales, siendo más parecido a una chispa causada por algún mal funcionamiento del instrumento, o interferencia externa, (b) utilice el criterio de Chauvenet para determinar si puede eliminar dichos datos. Reporte cuales datos eliminó finalmente, y cuál fue el valor del criterio para hacerlo. (c) Realice una nueva gráfica y vuelva a reportar el valor de campo magnético con su incertidumbre.
Show code cell content
import numpy as np
datosX = np.array([0.005632, 0.015652, 0.035891, 0.036246, 0.045104, 0.054451,
0.064454, 0.074963, 0.084597, 0.095501, 0.104404, 0.114554,
0.124418, 0.135022, 0.144454, 0.154527, 0.164786, 0.174868,
0.184558, 0.196365, 0.204394, 0.214911, 0.224368, 0.234538,
0.245652, 0.255369, 0.26522 , 0.276284, 0.285722, 0.294926,
0.304535, 0.316268, 0.324458, 0.334575, 0.345461, 0.354586,
0.364969, 0.375192, 0.385756, 0.394671, 0.406614, 0.41483 ,
0.425103, 0.435301, 0.444832, 0.455498, 0.46484 , 0.479933,
0.485527, 0.496199, 0.506205, 0.515769, 0.524858, 0.534731,
0.544378, 0.554524, 0.564389, 0.574442, 0.584392, 0.594822,
0.604489, 0.614533, 0.624572, 0.634537, 0.644528, 0.654865,
0.664927, 0.67485 , 0.68438 , 0.694864, 0.704534, 0.714609,
0.725384, 0.735302, 0.7457 , 0.755802, 0.765069, 0.775764,
0.784162, 0.794728, 0.804533, 0.814785, 0.824475, 0.834713,
0.844449, 0.85484 , 0.864496, 0.878299, 0.884432, 0.894826,
0.90455 , 0.914747, 0.924468, 0.9347 , 0.944783, 0.954598,
0.968475, 0.975558, 0.985713, 0.995606, 1.00501 , 1.014474,
1.024528, 1.034717, 1.044628, 1.054607, 1.064563, 1.074807,
1.084301, 1.094655, 1.104363, 1.114559, 1.124358, 1.134689,
1.144609, 1.154527, 1.164488, 1.174884, 1.184257, 1.194733,
1.205787, 1.215262, 1.225508, 1.235693, 1.24501 , 1.254969,
1.264704, 1.275071, 1.284217, 1.294842, 1.304706, 1.314657,
1.32433 , 1.334807, 1.344501, 1.354581, 1.364354, 1.376446,
1.384306, 1.394715, 1.404832, 1.414753, 1.42449 , 1.434496,
1.44554 , 1.455371, 1.465476, 1.479674, 1.484904, 1.494709,
1.50455 , 1.514672, 1.524495, 1.534892, 1.544674, 1.554963,
1.564467, 1.574637, 1.584469, 1.594849, 1.604663, 1.614667,
1.624665, 1.634604, 1.644701, 1.654716, 1.665506, 1.674911,
1.685537, 1.695639, 1.705691, 1.715349, 1.725122, 1.734671,
1.744485, 1.75461 , 1.76443 , 1.776913, 1.784545, 1.794741,
1.804484, 1.814901, 1.824525, 1.834691, 1.844752, 1.85461 ,
1.864564, 1.878432, 1.884824, 1.895108, 1.904544, 1.914575,
1.925831, 1.935487, 1.945598, 1.955671, 1.96471 , 1.981901,
1.984608, 1.994535, 2.004437, 2.014581, 2.02435 , 2.034673,
2.044479, 2.054654, 2.064555, 2.075911, 2.084485, 2.094906,
2.104811, 2.114738, 2.124595, 2.134696, 2.144785, 2.154705,
2.165472, 2.175533, 2.185524, 2.195571, 2.204843, 2.214581,
2.224535, 2.234665, 2.244504, 2.254956, 2.265295, 2.27676 ,
2.284509, 2.294813, 2.304502, 2.314704, 2.324462, 2.334503,
2.344739, 2.354666, 2.364465, 2.37746 , 2.385168, 2.394494,
2.405276, 2.415754, 2.425447, 2.435399, 2.444989, 2.454673,
2.464428, 2.480167, 2.484517, 2.494775, 2.504731, 2.514651,
2.524521, 2.534841, 2.5445 , 2.554633, 2.564585, 2.575262,
2.584622, 2.594963, 2.604516, 2.6147 , 2.624439, 2.634807,
2.645648, 2.655403, 2.665437, 2.675776, 2.684636, 2.694828,
2.704628, 2.714566, 2.724483, 2.734565, 2.744638, 2.754695,
2.764373, 2.775835, 2.784541, 2.794642, 2.804553, 2.814725,
2.824676, 2.834904, 2.84445 , 2.85526 , 2.865007, 2.875993,
2.885435, 2.895491, 2.905547, 2.915408, 2.924652, 2.934524,
2.944505, 2.954634, 2.964406, 2.978826, 2.984301, 2.99449 ,
3.004388, 3.014668, 3.024563, 3.034734, 3.044812, 3.054528,
3.071041, 3.076353, 3.084309, 3.094803, 3.104493, 3.114777,
3.125294, 3.135442, 3.145583, 3.156226, 3.165198, 3.175991,
3.184373, 3.194673, 3.204517, 3.214594, 3.224507, 3.234736,
3.244442, 3.254568, 3.264487, 3.274602, 3.285381, 3.294602,
3.304442, 3.314721, 3.324475, 3.334588, 3.344524, 3.354636,
3.365476, 3.376694, 3.385258, 3.39531 , 3.404573, 3.414466,
3.424348, 3.434582, 3.444614, 3.455741, 3.465169, 3.474636,
3.486495, 3.494791, 3.504455, 3.514662, 3.524361, 3.534541,
3.544401, 3.554525, 3.564302, 3.575755, 3.584439, 3.59687 ,
3.605399, 3.615274, 3.62541 , 3.635101, 3.644676, 3.654523,
3.664451, 3.680646, 3.688599, 3.694608, 3.704407, 3.714691,
3.724496, 3.734696, 3.744555, 3.75459 , 3.764439, 3.774672,
3.784644, 3.79468 , 3.804456, 3.814746, 3.824524, 3.834675,
3.84551 , 3.85549 , 3.865358, 3.875307, 3.885015, 3.894477,
3.904465, 3.914475, 3.924451, 3.934535, 3.944601, 3.954652,
3.96455 , 3.974547, 3.98938 , 3.994563, 4.004247, 4.014676,
4.024399, 4.034533, 4.044517, 4.054601, 4.064424, 4.075562,
4.088223, 4.095316, 4.105565, 4.115224, 4.125029, 4.13433 ,
4.144495, 4.15459 , 4.16443 , 4.17484 , 4.189476, 4.194679,
4.204327, 4.214733, 4.224452, 4.234772, 4.244553, 4.254495,
4.265065, 4.27468 , 4.286838, 4.294769, 4.304415, 4.314743,
4.32535 , 4.335182, 4.345679, 4.355094, 4.364595, 4.374674,
4.384491, 4.3945 , 4.404329, 4.414573, 4.42458 , 4.434627,
4.444396, 4.454609, 4.464392, 4.475219, 4.485591, 4.494504,
4.504615, 4.51467 , 4.524389, 4.534451, 4.544565, 4.555724,
4.565794, 4.57542 , 4.588861, 4.595175, 4.604581, 4.614393,
4.624322, 4.63456 , 4.644443, 4.654617, 4.664405, 4.674694,
4.688516, 4.696608, 4.704303, 4.714639, 4.72447 , 4.734474,
4.744461, 4.754593, 4.7644 , 4.78166 , 4.787234, 4.795475,
4.805476, 4.815341, 4.825423, 4.835309, 4.844677, 4.854456,
4.864561, 4.874714, 4.885619, 4.894485, 4.904516, 4.914717,
4.924417, 4.934634, 4.944593, 4.954882, 4.964431, 4.974556,
4.984965, 4.994847])
datosY = np.array([30.57, 30.42, 30.62, 30.51, 30.56, 30.31, 30.25, 30.4 , 30.25,
30.25, 30.17, 30.39, 30.26, 30.4 , 30.54, 30.26, 30.57, 30.51,
30.5 , 30.21, 30.29, 30.39, 30.49, 30.7 , 30.51, 30.55, 30.59,
30.81, 30.6 , 30.46, 30.32, 30.41, 30.44, 30.48, 30.62, 30.57,
30.79, 30.8 , 30.69, 30.64, 30.87, 30.87, 30.73, 30.67, 30.62,
30.61, 30.87, 30.83, 30.54, 30.6 , 30.37, 30.31, 30.26, 30.19,
30.1 , 30.04, 29.99, 29.81, 29.83, 30.05, 30.1 , 30.12, 29.88,
30. , 30. , 30.25, 30.35, 30.16, 30.01, 30.17, 30.2 , 30.24,
30.42, 30.28, 30.12, 30.33, 30.42, 30.34, 30.42, 30.31, 30.22,
30.32, 30.47, 30.43, 30.53, 30.49, 30.42, 30.39, 30.15, 29.95,
29.98, 29.82, 29.9 , 29.91, 30.02, 30.13, 30.31, 30.51, 30.45,
30.54, 30.45, 30.46, 30.34, 30.23, 30.12, 29.93, 29.82, 29.74,
29.74, 29.87, 29.97, 30.12, 30.15, 30.12, 30.34, 30.41, 30.54,
30.38, 30.31, 30.26, 30.44, 30.75, 30.75, 30.72, 30.58, 30.6 ,
30.74, 30.62, 30.73, 30.45, 30.34, 30.49, 30.37, 30.2 , 30.11,
30.34, 30.06, 30.35, 30.34, 30.16, 30.15, 30.26, 30.49, 30.29,
30.44, 30.23, 30.12, 30.12, 30.3 , 30.24, 30.04, 30.1 , 29.88,
29.85, 30. , 30.15, 30.1 , 30.06, 30.15, 30.09, 30.37, 30.37,
30.32, 30.25, 30.14, 30.47, 30.24, 30.31, 30.3 , 30.4 , 30.48,
30.4 , 30.5 , 30.23, 30.35, 30.4 , 30.48, 30.5 , 30.44, 30.69,
30.64, 30.93, 30.95, 31.05, 30.88, 30.78, 30.66, 30.58, 30.74,
30.5 , 30.47, 30.25, 30.42, 30.6 , 30.79, 30.93, 30.89, 30.97,
31.04, 31.07, 30.91, 31.01, 30.93, 30.87, 30.65, 30.65, 30.6 ,
30.78, 30.63, 30.28, 30.3 , 30.06, 30.12, 30.09, 30.06, 30.05,
30.1 , 30.27, 30.49, 30.58, 30.63, 30.65, 30.84, 30.51, 30.68,
30.68, 30.35, 30.12, 30.16, 30.23, 30.03, 30.47, 30.32, 29.97,
30.15, 30.35, 30.21, 29.97, 30.03, 29.94, 29.93, 30.26, 30.21,
30.3 , 30.31, 30.41, 30.35, 30.3 , 30.27, 29.99, 29.82, 29.89,
29.8 , 29.89, 29.99, 29.78, 29.81, 29.89, 29.88, 29.86, 30.09,
30.05, 30.18, 30.37, 30.19, 30.14, 30.33, 30.32, 30.19, 30.16,
29.86, 29.89, 30.27, 30.6 , 30.44, 30.38, 30.47, 30.74, 30.97,
30.77, 30.73, 30.59, 30.75, 30.67, 30.57, 30.23, 30.22, 30.25,
30.22, 30.09, 30.05, 30.11, 30.22, 30.38, 30.12, 30.32, 30.34,
30.51, 30.4 , 30.51, 30.44, 30.42, 30.52, 30.26, 30.22, 30.23,
30.18, 30.31, 30.26, 30.39, 30.3 , 30.4 , 30.21, 30.26, 30.61,
30.55, 30.65, 30.83, 31. , 31.19, 31.46, 31.38, 31.24, 31.07,
31.02, 30.82, 30.97, 30.93, 31. , 31.2 , 31.24, 31.39, 32.23,
32.94, 31.84, 31.16, 31.03, 30.88, 30.98, 31.13, 31.06, 31.07,
31.02, 31.04, 30.93, 30.87, 30.58, 30.4 , 30.59, 30.48, 30.32,
30.31, 30.37, 30.21, 30.17, 30.06, 29.79, 29.94, 29.98, 30.18,
30.08, 30.18, 30.23, 30.32, 30.3 , 30.3 , 30.3 , 30.28, 30.29,
30.47, 30.51, 30.55, 30.67, 30.71, 30.91, 30.59, 30.64, 30.52,
30.55, 30.54, 30.51, 30.27, 30.02, 30.2 , 30.27, 30.23, 30.16,
29.93, 29.9 , 30.04, 30.09, 30.31, 30.04, 30.06, 29.99, 30.04,
30. , 29.93, 29.96, 29.81, 29.87, 29.83, 30.03, 29.99, 30.01,
30.17, 30.27, 30.14, 30.35, 30.46, 30.34, 30.45, 30.48, 30.4 ,
30.37, 30.58, 30.59, 30.56, 30.45, 30.54, 30.28, 30.27, 30.5 ,
30.34, 30.31, 30.53, 30.82, 30.62, 30.87, 30.87, 30.56, 30.72,
30.7 , 30.45, 30.26, 30.29, 30.25, 30.31, 30.16, 29.94, 29.92,
29.76, 29.64, 29.78, 29.87, 29.89, 30.05, 30.16, 30.34, 30.53,
30.83, 30.8 , 30.59, 30.62, 30.67, 30.58, 30.45, 30.48, 30.56,
30.53, 30.71, 30.61, 30.61, 30.44, 30.46, 30.53, 30.28, 30.22,
30.09, 30.14, 30.03, 30.39, 30.33, 30.13, 30.09, 30.05, 30.25,
30.35, 30.45, 30.19, 30.35, 30.41, 30.59, 30.82, 30.68, 30.59,
30.46, 30.36, 30.15, 30.33, 30.39, 30.2 , 30.33, 30.14, 30.47,
30.64, 30.78, 30.49, 30.41, 30.53])
Combinación de resultados
2 La constante de Hubble (\(H_o\)) indica la razón a la que se está expandiendo el universo. Una medición de dicha constante a partir de las anisotropías de la radiación de fondo de microondas obtuvo el valor \(H_{o(Planck)} = (67.4 \pm 0.6)\,\text{km s}^{-1}\,\text{Mpc}^{-1}\). Por otro lado, una medición a partir del efecto de lente de los cuasares obtuvo \(H_{o(HOliCOW)} = (73.3 \pm 1.7)\,\text{km s}^{-1}\,\text{Mpc}^{-1}\). (a) Verifique si las cantidades coinciden, y en caso de que coincidan combine los resultados y repórtelo. (b) Una reciente medición a partir de las estrellas gigantes rojas obtuvo el valor de \(H_{o(CCHP)} = (69.8 \pm 1.9)\,\text{km s}^{-1}\,\text{Mpc}^{-1}\), compare esta medición con la del «Planck», y si no discrepan realice la combinación de resultados y repórtelo.