积极 AI Logo 积极 AI

极端值对一元统计的影响

极端值对一元统计的影响
几何画板及绘图内容加载中，请稍等……
2016-09-08 08:47
函数概率统计几何作图
①本范例演示极端值对一元统计数据（如标准差）的影响；②涉及核心数学概念：标准差、统计、函数图像、菱形、三角形、相似三角形、超几何分布；③作图要点：使用 GeoGebra 命令 Point（点）、Sequence（数列）、Append（追加）、BoxPlot（箱线图）、Segment（线段）、Polygon（多边形）等构建图形；④适合高中及以上数学学习者，用于理解数据分布与统计指标变化的关系。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Sequence(RandomNormal[0, 1], k, 1, N) → list1
  3. Append({(-1.1104960221269111, 0.08574072492174134), (-1.8190365233188575, 0.3508333515047224), (-0.20007037183328683, 0.27120198937705575), (0.796789486291938, -0.06128570256733745), (-1.7871325027493998, -0.47208708813269296), (-0.30438280954545494, 0.20143882730279106), (-1.5349371476227247, -0.33602737632801327), (2.4104611407616883, 0.002525301372311217), (0.7009937402612261, -0.33382952947805855), (-0.38144191430055935, 0.2100260980316001), (0.7456328591588697, -0.29333533871561634), (0.5866276880997935, 0.416472959615641), (1.7383390004760935, -0.4867554413923473), (0.30730393629983116, -0.057961671859986685), (-0.2688653424527746, 0.1057705761191402), (0.8099180946577149, 0.2509472317943202), (0.18523441394410475, -0.42966913885376634), (0.8180176305957311, 0.03324596353693854), (-0.7387416676314755, 0.36784948459777045), (1.392352819939226, -0.017646559896873693), (2.0175307521184993, -0.34467383564177534), (2.0509510078622952, -0.2666084852201749), (-0.2112142330571661, 0.23558237689007244), (-1.0908831492388904, -0.48188907484080545), (0.9740307933621483, 0.045335000862474106), (1.2583974948167107, -0.16070007184562984), (-0.5274764282424854, -0.4583871450486521), (-0.9544643337986605, -0.1291173189803848), (0.35782089272876605, -0.047022471309817515), (-0.9851464741726335, 0.34948533556161276), (-1.074875394403061, 0.12470498877654823), (0.16503216308460433, 0.43906716446755145), (-0.17808624803942025, -0.3939701598450719), (0.4384062200805528, 0.4222856782084602), (1.7768218078279832, -0.29725089865470455), (1.8162428097076782, 0.10058356680931402), (-1.3146547127957815, 0.44992821326984866), (1.3992177742958714, 0.4695565836136919), (0.7813407531939855, -0.15285301808956075), (-1.39704243625944, -0.4230181747510471), (-0.5520806698932105, 0.24266824098315598), (-0.5306609827476495, 0.46795520861452267), (-1.3792983737808282, 0.45310792669996747), (0.49313522016916184, -0.2250914198735856), (-0.9969680934541406, 0.06163023916444843), (1.3078802914851013, -0.18015392391371587), (-1.8309413617288444, 0.3503864435832549), (-0.5435885054600312, 0.0619603625364048), (-1.721822009766407, 0.4918623379995758), (-0.14303170648077607, 0.345859461598112), (1.2175834773270946, -0.05100679396401364), (0.9061554846561231, -0.31604489314469986), (1.1973125547541719, -0.48464793086934466), (-0.09824669639452485, 0.24113399263874902), (-1.5799267393348289, 0.06441044313202438), (-0.42699771406664994, -0.21934640693179097), (-1.122615508628326, -0.12918178172255823), (0.23186142098674276, 0.0772745009230914), (0.7985078985952866, 0.3168428070041739), (0.0735994188028798, -0.2930384069514387), (0.924992843260281, -0.09644614746580193), (0.6056670149770925, 0.18205654454442666), (-0.0641587645694172, -0.2509645963089828), (0.3933728271010155, -0.3833554731519919), (0.8960536794488793, 0.17485177798820883), (-1.063954594429376, -0.0210913371652659), (0.16707381784701628, -0.4428102766620369), (-0.12576762758814258, -0.4844147682143508), (-1.1621177370004039, 0.3505439701534332), (0.018574468312284213, 0.11820386265438221), (1.4981704683866632, 0.07950910351562146), (0.05732495965465117, 0.24161671744960078), (-0.9346312060916316, 0.1381857932811852), (-0.2966375358944505, 0.482391182906756), (1.5782038105752791, 0.4369047074928074)}, A) → data
  4. BoxPlot(1.5, 0.5, x(data), true) → a
  5. Segment((MeanX[data], 1), (MeanX[data], 2)) → f
  6. Polygon((MeanX[data], 1), (MeanX[data] - SDX[data], 1.5), (MeanX[data], 2), (MeanX[data] + SDX[data], 1.5)) → poly1, g, h, i, j

AI 绘图提示语参考

画一个展示极端值对一变量统计指标影响的图表。首先绘制一条水平线代表均值，再在线上画出代表标准差的两个垂直线段。接着，在均值线上方绘制一个菱形，其顶点分别位于均值加减标准差的位置。最后，添加一个包含随机正态分布数据的箱线图，以展示数据分布情况。
以上提示语为根据原始绘图命令整理而来，仅供参考。