diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb index 1fee40e3..d8bfbdaa 100644 --- a/工具/寻找阶段末尾空闲题号.ipynb +++ b/工具/寻找阶段末尾空闲题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "text": [ "首个空闲id: 11988 , 直至 020000\n", "首个空闲id: 20227 , 直至 030000\n", - "首个空闲id: 30170 , 直至 999999\n" + "首个空闲id: 30217 , 直至 999999\n" ] } ], @@ -45,7 +45,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -59,12 +59,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/添加关联题目.ipynb b/工具/添加关联题目.ipynb index e44b98f5..f6263811 100644 --- a/工具/添加关联题目.ipynb +++ b/工具/添加关联题目.ipynb @@ -50,7 +50,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -64,12 +64,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index 5e7d91a2..f2c18781 100644 --- a/工具/添加题目到数据库.ipynb +++ b/工具/添加题目到数据库.ipynb @@ -2,20 +2,20 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 30170\n", - "origin = \"高中数学教与学例题与习题\"\n", - "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\临时工作区\\自拟题目2.tex\"\n", + "starting_id = 30217\n", + "origin = \"人教A版2019年必修二教材统计例题与习题\"\n", + "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目1.tex\"\n", "editor = \"20221019\\t王伟叶\"" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -100,7 +100,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -114,12 +114,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb index a4972478..0f4aa244 100644 --- a/工具/识别题库中尚未标注的题目类型.ipynb +++ b/工具/识别题库中尚未标注的题目类型.ipynb @@ -39,7 +39,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -53,12 +53,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/文本处理工具/表格整理.ipynb b/文本处理工具/表格整理.ipynb index 946124a8..c13373f1 100644 --- a/文本处理工具/表格整理.ipynb +++ b/文本处理工具/表格整理.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -68,7 +68,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -82,12 +82,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 92c59f96..8c5e7985 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -293674,5 +293674,1181 @@ "related": [], "remark": "", "space": "12ex" + }, + "030217": { + "id": "030217", + "content": "在以下调查中, 总体、个体各是什么? 哪些适合用全面调查? 哪些适合用抽样调查?\\\\\n(1) 调查一个班级学生每周的体育锻炼时间;\\\\ \n(2) 调查一个地区结核病的发病率;\\\\\n(3) 调查一批炮弹的杀伤半径;\\\\\n(4) 调查一个水库所有鱼中草鱼所占的比例.\\\\\n请你再举一些不宜用全面调查的例子, 并说明理由.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030218": { + "id": "030218", + "content": "由均匀材质制成的一个正$20$面体(每个面都是正三角形), 将$20$个面平分成$10$组, 第$1$组标上$0$, 第$2$组标上$1$, $\\cdots$, 第$10$组标上$9$.\\\\\n(1) 投掷正$20$面体, 若把朝上一面的数字作为投掷结果, 则出现$0, 1, 2, \\cdot , 9$是等可能的吗?\\\\ \n(2) 三个正$20$面体分别涂上红、黄、蓝三种颜色, 分别代表百位、十位、个位, 同时投掷可以产生一个三位数(百位为$0$的也看作三位数), 它是$000$至$999$范围内的随机数吗?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030219": { + "id": "030219", + "content": "实验室的笼子里共有$100$只小白鼠, 现要从中抽取$10$只作试验用. 下列两种情况是否属于简单随机抽样? 请说明理由.\\\\\n(1) 每次不经任何挑选地抓一只, 抓满$10$只为止;\\\\\n(2) 将笼中的$100$只小白鼠按$1$到$100$编号, 任意选出编号范围内的$10$个不重复数字, 把相应编号的小白鼠作为试验用的小白鼠.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030220": { + "id": "030220", + "content": "如果计算器只能生成$[0, 1)$内的随机数, 你有办法把它转化为$[1,100)$范围内的整数随机数吗? 转化为$[1,712)$范围内的整数随机数呢?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030221": { + "id": "030221", + "content": "在抽样调查中, 请你说说通过``随机''选择样本的优、缺点.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030222": { + "id": "030222", + "content": "为了合理调配电力资源, 某市欲了解全市$50000$户居民的日用电量. 若通过简单随机抽样从中抽取了$300$户进行调查, 得到其日用电量的平均数为$5.5\\text{kW}\\cdot \\text{h}$, 则可以推测全市居民用户日用电量的平均数\\bracket{20}.\n\\fourch{一定为$5.5\\text{kW}\\cdot \\text{h}$}{高于$5.5\\text{kW}\\cdot \\text{h}$}{低于$5.5\\text{kW}\\cdot \\text{h}$}{约为$5.5\\text{kW}\\cdot \\text{h}$}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030223": { + "id": "030223", + "content": "在学生身高的调查中, 小明和小华分别独立进行了简单随机抽样调查. 小明调查的样本平均数为$166.4$, 样本量为$100$; 小华调查的样本平均数为$164.7$, 样本量为$200$. 你更愿意把哪个值作为总体平均数的估计? 是不是你选的值一定比另一个更接近总体平均数? 说说你的理由.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030224": { + "id": "030224", + "content": "找一组数据作为总体, 自行设定样本量, 进行多次简单随机抽样. 观察样本量对估计总体平均数的影响, 并试着解释其中的原因.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030225": { + "id": "030225", + "content": "数据$x_1,x_2,\\cdots,x_m$的平均数为$\\overline{x}$, 数据$y_1, y_2, \\cdots,y_m$的平均数为$\\overline{y}$, 证明: $\\dfrac{\\sum_{i=1}^m x_i+\\sum_{i=1}^n y_i}{m+n}=\\dfrac{m}{m+n} \\overline{x}+\\dfrac{n}{m+n} \\overline{y}$.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030226": { + "id": "030226", + "content": "有人说: ``如果抽样方法设计得好, 用样本进行视力调查与对$24300$名学生进行视力普查的结果差不多.而且对于想要掌握学生视力状况的教育部门来说, 节省了人力、物力和财力, 抽样调查更可取.''你认为这种说法有道理吗? 为什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030227": { + "id": "030227", + "content": "高二年级有男生$490$人, 女生$510$人, 张华按男生、女生进行分层, 通过分层随机抽样的方法, 得到男生、女生的平均身高分别为$170.2\\text{cm}$和$160.8\\text{cm}$.\\\\ \n(1) 如果张华在各层中按比例分配样本, 总样本量为$100$, 那么在男生、女生中分别抽取了多少名? 在这种情况下, 请估计高二年级全体学生的平均身高.\\\\\n(2) 如果张华从男生、女生中抽取的样本量分别为$30$和$70$, 那么在这种情况下, 如何估计高二年级全体学生的平均身高更合理?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030228": { + "id": "030228", + "content": "要调查全市普通高中高一年级学生中患色盲的比例, 小明根据性别对总体进行分层, 用分层随机抽样的方法进行调查. 请你查阅有关资料, 说说这样的分层是否合理. 你觉得在选择分层变量时应注意什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030229": { + "id": "030229", + "content": "下列情况中哪些适合用全面调查, 哪些适合用抽样调查? 说明理由.\\\\\n(1) 了解某城市居民的食品消费结构;\\\\ \n(2) 调查一个县各村的粮食播种面积;\\\\\n(3) 了解某地区小学生中患沙眼的人数;\\\\\n(4) 了解一批玉米种子的发芽率;\\\\\n(5) 调查一条河流的水质;\\\\\n(6) 某企业想了解其产品在市场的占有率.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030230": { + "id": "030230", + "content": "某刊物对其读者进行满意度调查, 调查表随刊物送到读者手中, 对寄回的调查表进行分析. 这是不是一项抽样调查? 样本抽取是不是属于简单随机抽样? 为什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030231": { + "id": "030231", + "content": "中央电视台希望在春节联欢晚会播出后一周内获得该节目的收视率. 下面是三名同学为电视台设计的调查方案.\\\\\n同学A: 我把这张《春节联欢晚会收视率调查表》放在互联网上, 只要上网登录该网址的人就可以看到这张表, 他们填表的信息可以很快地反馈到我的电脑中.这样, 我就可以很快统计出收视率了.\\\\\n同学B: 我给我们居民小区的每一个住户发一份是否在除夕晚上看过中央电视台春节联欢晚会的调查表, 只要一两天就可以统计出收视率.\\\\\n同学C: 我在电话号码本上随机地选出一定数量的电话号码, 然后逐个给他们打电话, 问一下他们是否收看了中央电视台春节联欢晚会, 我不出家门就可以统计出中央电视台春节联欢晚会的收视率.\\\\\n请问: 上述三名同学设计的调查方案获得比较准确的收视率的可能性大吗? 为什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030232": { + "id": "030232", + "content": "下列从总体中抽得的样本是否为简单随机样本?\\\\ \n(1) 总体编号为$1\\sim 75$, 在$0\\sim 99$中产生随机整数$r$. 若\n$r=0$或$r>75$, 则舍弃, 重新抽取.\\\\\n(2) 总体编号为$1\\sim 75$, 在$0\\sim 99$中产生随机整数$r$, $r$除以$75$的余数作为抽中的编号. 若余数为$0$, 则抽中$75$.\\\\ \n(3) 总体编号为$6001\\sim 6876$, 在$1\\sim 876$范围内产生一个随机整数$r$, 把$r+6000$作为抽中的编号.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030233": { + "id": "030233", + "content": "一支田径队有男运动员$56$人, 女运动员$42$人, 按性别进行分层, 用分层随机抽样的方法从全体运动员中抽出一个容量为$28$的样本, 如果样本按比例分配, 那么男、女运动员应各抽取多少名?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030234": { + "id": "030234", + "content": "数据$x_1,x_2,\\cdots,x_n$的平均数为$\\overline{x}$, 数据$y_1,y_2,\\cdots,y_n$的平均数为$\\overline{y}$, $a$, $b$为常数. 如果满足$y_1=ax_1+b$, $y_2=ax_2+b$, $\\cdots$, $y_n=ax_n+b$, 证明: $\\overline{y}=a\\overline{x}+b$.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030235": { + "id": "030235", + "content": "已知总体划分为$3$层, 通过分层随机抽样, 得到各层的样本平均数分别为$\\overline{x},\\overline{y},\\overline{z}$.\\\\\n(1) 根据以上信息可以估计总体平均数吗? 如果不能, 还需要什么条件? 写出估计式.\\\\\n(2) 如果样本量是按比例分配, 第$1, 2, 3$层的个体数分别为$L, M, N$, 样本量分别为$l, m, n$, 证明: $\\dfrac{L}{L+M+N}\\overline{x}+\\dfrac{M}{L+M+N}\\overline{y}+\\dfrac{N}{L+M+N}\\overline{z}=\\dfrac{l}{l+m+n}\\overline{x}+\\dfrac{m}{l+m+n}\\overline{y}+\\dfrac{n}{l+m+n}\\overline{z}$.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030236": { + "id": "030236", + "content": "校学生会希望调查学生对本学期学生活动计划的意见. 你自愿担任调查员, 并打算在学校里抽取$10\\%$的同学作为样本.\\\\ \n(1) 怎样安排抽样, 可以提高样本的代表性?\\\\\n(2) 在调查抽样中你可能遇到哪些问题?\\\\\n(3) 这些问题可能会影响什么?\\\\\n(4) 你打算怎样解决这些问题?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030237": { + "id": "030237", + "content": "一般来说, 影响农作物收成的因素有气候、土质、田间管理水平等, 如果你是一个农村调查队成员, 要在麦收季节对你所在地区的小麦进行估产调查, 你将如何设计调查方案?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030238": { + "id": "030238", + "content": "从某小区抽取$100$户居民用户进行月用电量调查, 发现他们的用电量都在$50\\sim 350\\text{kW}\\cdot \\text{h}$之间, 进\n行适当分组后(每组为左闭右开的区间), 画出频率分布直方图如图所示.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.015,yscale = 400]\n\\draw [->] (0,0) -- (450,0) node [below] {月用电量/$\\text{kW}\\cdot\\text{h}$};\n\\draw [->] (0,0) -- (0,0.008) node [left] {频率/组距};\n\\draw (0,0) node [below left] {$O$};\n\\draw (50,0) -- (50,0.0024) -- (100,0.0024) (100,0) -- (100,0.0036) -- (150,0.0036) (150,0) -- (150,0.0060) -- (200,0.0060) -- (200,0) (200,0.0044) -- (250,0.0044) -- (250,0) (250,0.0024) -- (300,0.0024) -- (300,0) (300,0.0012) -- (350,0.0012) -- (350,0);\n\\foreach \\i in {0.0012,0.0024,0.0036,0.0060} {\\draw (0,\\i) node [left] {$\\i$};};\n\\draw (0,0.0044) node [left] {$x$};\n\\foreach \\i in {50,100,...,350} {\\draw (\\i,0) node [below] {$\\i$};};\n\\draw [dashed] (0,0.0012) -- (300,0.0012) (0,0.0024) -- (50,0.0024) (100,0.0024) -- (250,0.0024) (0,0.0036) -- (100,0.0036) (0,0.0044) -- (200,0.0044) (0,0.0060) -- (150,0.0060);\n\\end{tikzpicture}\n\\end{center}\n(1) 直方图中$x$的值为\\blank{50};\\\\\n(2) 在被调查的用户中, 用电量落在区间$[100, 250)$内的户数为\\blank{50}.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030239": { + "id": "030239", + "content": "如图, 胡晓统计了他爸爸9月的手机通话明细清单, 发现他爸爸该月共通话$60$次. 胡晓按每次通话\n时间长短进行分组(每组为左闭右开的区间), 画出了频率分布直方图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.2,yscale = 40]\n\\draw [->] (0,0) -- (40,0) node [below] {通话时间/$\\text{min}$};\n\\draw [->] (0,0) -- (0,0.09) node [left] {频率/组距};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {0.01,0.02,0.03,0.04,0.05,0.06,0.07} {\\draw (0.5,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\foreach \\i in {5,10,...,30} {\\draw (\\i,0) node [below] {$\\i$};};\n\\draw (0,0.06) -- (5,0.06) node [midway,above] {$0.060$} -- (5,0);\n\\draw (5,0.046) -- (10,0.046) node [midway,above] {$0.046$} -- (10,0);\n\\draw (10,0.024) -- (15,0.024) node [midway,above] {$0.024$};\n\\draw (15,0) -- (15,0.03) -- (20,0.03) node [midway,above] {$0.030$} -- (20,0);\n\\draw (20,0.02) -- (30,0.02) node [midway,above] {$0.020$} -- (30,0) (25,0) -- (25,0.02);\n\\end{tikzpicture}\n\\end{center}\n(1) 通话时长在区间$[15, 20)$, $[20, 30)$内的次数分别为多少?\\\\\n(2) 区间$[20, 30)$上的小长方形高度低于$[15, 20)$上的小长方形的高度, 说明什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030240": { + "id": "030240", + "content": "请班上每位同学估计一下自己平均每天的课外学习时间(单位: $\\text{min}$), 然后统计数据, 作出全班同学课外学习时间的频率分布直方图, 能否由这个频率分布直方图估计出你们学校全体学生课外学习时间的分布情况? 可以用它来估计你所在地区(城市、乡镇或村庄)全体学生课外学习时间的分布情况吗? 为什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030241": { + "id": "030241", + "content": "已知某市2015年全年空气质量等级如下表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline\n空气质量等级(空气质量指数(AQI)) & 频数 & 频率 \\\\ \\hline\n优(AQI$\\le 50$) & $83$ & $22.8\\%$ \\\\ \\hline\n良($50<$AQI$\\le 100$) & $121$ & $33.2\\%$ \\\\ \\hline\n轻度污染($100<$AQI$\\le 150$) & $68$ & $18.6\\%$ \\\\ \\hline\n中度污染($150<$AQI$\\le 200$) & $49$ & $13.4\\%$ \\\\ \\hline\n重度污染($200<$AQI$\\le 300$) & $30$ & $8.2\\%$ \\\\ \\hline\n严重污染(AQI$>300$) & $14$ & $3.8\\%$ \\\\ \\hline\n合计 & $365$ & $100\\%$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n5月 & $240$ & $80$ & $56$ & $53$ & $92$ & $126$ & $45$ & $87$ & $56$ & $60$ \\\\ \n& $191$ & $62$ & $55$ & $58$ & $56$ & $53$ & $89$ & $90$ & $125$ & $124$ \\\\ \n& $103$ & $81$ & $89$ & $44$ & $34$ & $53$ & $79$ & $81$ & $62$ & $116$ \\\\ \n& $88$ \n\\end{tabular}\n\\end{center}\n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n6月 & $63$ & $92$ & $110$ & $122$ & $102$ & $116$ & $81$ & $163$ & $158$ & $76$ \\\\\n$$ & $33$ & $102$ & $65$ & $53$ & $38$ & $55$ & $52$ & $76$ & $99$ & $127$ \\\\ \n$$ & $120$ & $80$ & $108$ & $33$ & $35$ & $73$ & $82$ & $90$ & $146$ & $95$\n\\end{tabular}\n\\end{center}\n选择合适的统计图描述数据, 并回答下列问题:\\\\ \n(1) 分析该市2016年6月的空气质量情况.\\\\\n(2) 比较该市2016年5月和6月的空气质量, 哪个月的空气质量较好?\\\\\n(3) 比较该市2016年6月与该市2015年全年的空气质量, 2016年6月的空气质量是否好于去年?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030242": { + "id": "030242", + "content": "某市2016年6月30天的空气质量指数如下:\n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$35$ & $54$ & $80$ & $86$ & $72$ & $85$ & $58$ & $125$ & $111$ & $53$ \\\\ \n$10$ & $66$ & $46$ & $36$ & $18$ & $25$ & $23$ & $40$ & $60$ & $89$ \\\\ \n$88$ & $54$ & $79$ & $14$ & $16$ & $40$ & $59$ & $67$ & $111$ & $62$ \n\\end{tabular}\n\\end{center}\n你觉得这个月的空气质量如何? 请设计适当的频率分布直方图展示这组数据, 并结合空气质量分级标准分析数据.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030243": { + "id": "030243", + "content": "在树人中学的高一年级女生中抽样, 得到27名女生的身高数据按从小到大排序后如下表: \n\\begin{center}\n\\begin{tabular}{ccccccccc}\n$148.0$ & $149.0$ & $154.0$ & $154.0$ & $155.0$ & $155.0$ & $155.5$ & $157.0$ & $157.0$ \\\\ \n$158.0$ & $158.0$ & $159.0$ & $161.0$ & $161.0$ & $162.0$ & $162.5$ & $162.5$ & $163.0$ \\\\ \n$163.0$ & $164.0$ & $164.0$ & $164.0$ & $165.0$ & $170.0$ & $171.0$ & $172.0$ & $172.0$ \n\\end{tabular}\n\\end{center}\n估计树人中学高一年级女生的第$25$, $50$, $75$百分位数.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030244": { + "id": "030244", + "content": "某学校要定制高一年级的校服, 学生根据厂家提供的参考身高选择校服规格. 据统计, 高一年级女生需要不同规格校服的频数如下表所示. \n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n校服规格 & $155$ & $160$ & $165$ & $170$ & $175$ & 合计 \\\\ \\hline\n频数 & $39$ & $64$ & $167$ & $90$ & $26$ & $386$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n如果用一个量来代表该校高一年级女生所需校服的规格, 那么在中位数、平均数和众数中, 哪个量比较合适? 试讨论用下表中的数据估计全国高一年级女生校服规格的合理性.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030245": { + "id": "030245", + "content": "某校举行演讲比赛, $10$位评委对两位选手的评分如下: \n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n甲 & $7.5$ & $7.5$ & $7.8$ & $7.8$ & $8.0$ & $8.0$ & $8.2$ & $8.3$ & $8.4$ & $9.9$ \\\\ \n乙 & $7.5$ & $7.8$ & $7.8$ & $7.8$ & $8.0$ & $8.0$ & $8.3$ & $8.3$ & $8.5$ & $8.5$ \n\\end{tabular}\n\\end{center}\n选手的最终得分为去掉一个最低分和一个最高分之后, 剩下$8$个评分的平均数, 那么, 这两个选手的最后得分是多少? 若直接用$10$位评委评分的平均数作为选手的得分, 两位选手的排名有变化吗? 你认为哪种评分办法更好? 为什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030246": { + "id": "030246", + "content": "不经过计算, 你能给下列各组数的方差排序吗?\\\\ \n\\textcircled{1} $5, 5, 5, 5, 5, 5, 5, 5, 5$;\\\\\n\\textcircled{2} $4, 4, 4, 5, 5, 5, 6, 6, 6$;\\\\\n\\textcircled{3} $3, 3, 4, 4, 5, 6, 6, 7, 7$;\\\\\n\\textcircled{4} $2, 2, 2, 2, 5, 8, 8, 8, 8$.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030247": { + "id": "030247", + "content": "数据$x_1, x_2, \\cdots, x_n$的方差为$s_x^2$, 数据$y_1, y_2, \\cdots,y_n$的方差为$s_y^2$, $a, b$为常数. 证明:\\\\\n(1) 如果$y_1=x_1+b$, $y_2=x_2+b$, $\\cdots$, $y_n=x_n+b$, 那么$s_y^2=s_x^2$;\\\\\n(2) 如果$y_1=ax_1$, $y_2=ax_2$, $\\cdots$, $y_n=ax_n$, 那么$s_y^2=a^2s_x^2$.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030248": { + "id": "030248", + "content": "农场种植的甲、乙两种水稻, 在面积相等的两块稻田中连续$6$年的产量如下:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n品种 & 第$1$年 & 第$2$年 & 第$3$年 & 第$4$年 & 第$5$年 & 第$6$年 \\\\ \\hline\n甲/$\\text{kg}$ & $900$ & $920$ & $900$ & $850$ & $910$ & $920$ \\\\ \\hline\n乙/$\\text{kg}$ & $890$ & $960$ & $950$ & $850$ & $860$ & $890$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n哪种水稻的产量比较稳定?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030249": { + "id": "030249", + "content": "一个小商店从一家有限公司购进$21$袋白糖, 每袋白糖的标准质量是$500\\text{g}$, 为了了解这些白糖的质量情况, 称出各袋白糖的质量(单位: $\\text{g}$)如下:\n\\begin{center}\n\\begin{tabular}{ccccccc}\n$486$ & $495$ & $496$ & $498$ & $499$ & $493$ & $493$ \\\\ \n$498$ & $484$ & $497$ & $504$ & $489$ & $495$ & $503$ \\\\ \n$499$ & $503$ & $509$ & $498$ & $487$ & $500$ & $508$\n\\end{tabular}\n\\end{center}\n(1) $21$袋白糖的平均质量$\\overline{x}$是多少? 标准差$s$是多少?\\\\\n(2) 质量位于$\\overline{x}-s$与$\\overline{x}+s$之间有多少袋白糖? 所占的百分比是多少?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030250": { + "id": "030250", + "content": "某学校有高中学生$500$人, 其中男生$320$人, 女生$180$人, 有人为了获得该校全体高中学生的身高信息, 采用分层抽样的方法抽取样本, 并观测样本的指标值(单位: $\\text{cm}$), 计算得男生样本的均值为$173.5$, 方差为$17$, 女生样本的均值为$163.83$, 方差为$30.03$.\\\\ \n(1) 根据以上信息, 能够计算出总样本的均值和方差吗? 为什么?\\\\ \n(2) 如果已知男、女样本量按比例分配, 你能计算出总样本的均值和方差各为多少吗?\\\\\n(3) 如果已知男、女的样本量都是$25$, 你能计算出总样本的均值和方差各为多少吗? 它们分别作为总体均值和方差的估计合适吗? 为什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030251": { + "id": "030251", + "content": "棉花的纤维长度是棉花质量的重要指标. 在一批棉花中随机抽测了$60$根棉花的纤维长度(单位: $\\text{mm}$), 按从小到大排序结果如下:\n\\begin{center}\n\\begin{tabular}{ccccccccccccccc}\n$25$ & $28$ & $33$ & $50$ & $52$ & $58$ & $59$ & $60$ & $61$ & $62$ & $82$ & $86$ & $113$ & $115$ & $140$ \\\\ \n$143$ & $146$ & $170$ & $175$ & $195$ & $202$ & $206$ & $233$ & $236$ & $238$ & $255$ & $260$ & $263$ & $264$ & $265$ \\\\ \n$293$ & $293$ & $294$ & $296$ & $301$ & $302$ & $303$ & $305$ & $305$ & $306$ & $321$ & $323$ & $325$ & $326$ & $328$ \\\\ \n$340$ & $343$ & $346$ & $348$ & $350$ & $352$ & $355$ & $357$ & $357$ & $358$ & $360$ & $370$ & $380$ & $383$ & $385$ \n\\end{tabular}\n\\end{center}\n(1) 请你选择合适的组距, 作出这个样本的频率分布直方图, 分析这批棉花纤维长度分布的特征;\\\\\n(2) 请你估计这批棉花的第$5$, $95$百分位数.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030252": { + "id": "030252", + "content": "甲、乙两台机床同时生产一种零件, 在$10$天中, 两台机床每天生产的次品数分别为:\n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n甲 & $0$ & $1$ & $0$ & $2$ & $2$ & $0$ & $3$ & $1$ & $2$ & $4$ \\\\\n乙 & $2$ & $3$ & $1$ & $1$ & $0$ & $2$ & $1$ & $1$ & $0$ & $1$ \n\\end{tabular}\n\\end{center}\n分别计算这两组数据的平均数和标准差, 从计算结果看, 哪台机床的性能更好?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030253": { + "id": "030253", + "content": "在去年的足球联赛上, 一队每场比赛平均失球数是$1.5$, 全年比赛失球个数的标准差为$1.1$; 二队每场比赛平均失球数是$2.1$, 全年失球个数的标准差是$0.4$. 你认为下列说法中哪一种是正确的, 为什么?\\\\ \n\\textcircled{1} 平均说来一队比二队防守技术好; \\textcircled{2} 二队比一队技术水平更稳定; \\textcircled{3} 一队有时表现很差, 有时表现又非常好; \\textcircled{4} 二队很少不失球.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030254": { + "id": "030254", + "content": "数据$x_1, x_2,\\cdots , x_n$的方差和标准差分别为$s_x^2$, $s_x$, 数据$y_1, y_2, \\cdots, y_n$的方差和标准差分别为$s_y^2$, $x_y$. 若$y_1=ax_1+b$, $y_2=ax_2+b$, $\\cdots$, $y_n=ax_n+b$成立, $a,b$为常数, 证明: $s_y^2=a^2s_x^2$, $s_y=|a|s_x$.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030255": { + "id": "030255", + "content": "数据$x_1, x_2,\\cdots , x_n$的方差$s^2=0$, 证明: 所有的$x_i \\ (i=1,2,\\cdots,n)$都相同.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030256": { + "id": "030256", + "content": "以往的招生统计数据显示, 某所大学录取的新生高考总分的中位数基本上稳定在$550$分, 你的一位高中校友在今年的高考中得了$520$分, 你是立即劝阻他报考这所大学, 还是先进一步查阅一下这所大学以往招生的其他统计信息? 解释一下你的选择.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030257": { + "id": "030257", + "content": "甲、乙两个班级, 一次数学考试的分数排序如下:\n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n甲班 & $51$ & $54$ & $59$ & $60$ & $64$ & $68$ & $68$ & $68$ & $70$ & $71$ \\\\ \n & $72$ & $72$ & $74$ & $76$ & $77$ & $78$ & $79$ & $79$ & $80$ & $80$ \\\\ \n & $82$ & $85$ & $85$ & $86$ & $86$ & $87$ & $87$ & $87$ & $88$ & $89$ \\\\ \n & $90$ & $90$ & $91$ & $96$ & $97$ & $98$ & $98$ & $98$ & $100$ & $100$ \\\\ \n乙班 & $61$ & $63$ & $63$ & $66$ & $70$ & $71$ & $71$ & $73$ & $75$ & $75$ \\\\ \n & $76$ & $79$ & $79$ & $80$ & $80$ & $80$ & $81$ & $81$ & $82$ & $82$ \\\\ \n & $83$ & $83$ & $83$ & $84$ & $84$ & $84$ & $85$ & $85$ & $85$ & $85$ \\\\ \n & $85$ & $85$ & $86$ & $87$ & $87$ & $88$ & $90$ & $91$ & $94$ & $98$ \n\\end{tabular}\n\\end{center}\n请你就这次考试成绩, 对两个班级的数学学习情况进行评价.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030258": { + "id": "030258", + "content": "有一种鱼的身体吸收汞, 一定量身体中汞的含量超过其体重的$1.00 \\text{ppm}$(即百万分之一)的鱼被人食用后, 就会对人体产生危害. 在$30$条鱼的样本中发现的汞含量(单位: $\\text{ppm}$)如下: \n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$0.07$ & $0.24$ & $0.95$ & $0.98$ & $1.02$ & $0.98$ & $1.37$ & $1.40$ & $0.39$ & $1.02$ \\\\ \n$1.44$ & $1.58$ & $0.54$ & $1.08$ & $0.61$ & $0.72$ & $1.20$ & $1.14$ & $1.62$ & $1.68$ \\\\ \n$1.85$ & $1.20$ & $0.81$ & $0.82$ & $0.84$ & $1.29$ & $1.26$ & $2.10$ & $0.91$ & $1.31$ \n\\end{tabular}\n\\end{center}\n(1) 请用合适的统计图描述上述数据, 并分析这$30$条鱼的汞含量的分布特点;\\\\ \n(2) 求出上述样本数据的平均数和标准差;\\\\\n(3) 从实际情况看, 许多鱼的汞含量超标的原因是这些鱼在出售之前没有被检测过. 你认为每批这种鱼的平均汞含量都比$1.00 \\text{ppm}$大吗?\\\\\n(4) 在上述样本中, 有多少条鱼的汞含量在以平均数为中心、$2$倍标准差的范围内?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030259": { + "id": "030259", + "content": "在一次人才招聘会上, 有一家公司的招聘员告诉你, ``我们公司的收入水平很高''``去年, 在$50$名员工中, 最高年收入达到了$200$万, 员工年收入的平均数是$10$万'', 而你的预期是获得$9$万元年薪.\\\\\n(1) 你是否能够判断年薪为9万元的员工在这家公司算高收入者?\\\\ \n(2) 如果招聘员继续告诉你, ``员工年收入的变化范围是从$3$万到$200$万'', 这个信息是否足以使你作出自己是否受聘的决定? 为什么?\\\\\n(3) 如果招聘员继续给你提供了如下信息, 员工收入的第一四分位数为$4.5$万, 第三四分位数为$9.5$万, 你又该如何使用这条信息来作出是否受聘的决定?\\\\\n(4) 根据(3)中招聘员提供的信息, 你能估计出这家公司员工收入的中位数是多少吗? 为什么平均数比估计出的中位数高很多?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030260": { + "id": "030260", + "content": "有$20$种不同的零食, 每$100\\text{g}$可食部分包含的能量(单位: $\\text{kJ}$)如下:\n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$110$ & $120$ & $123$ & $165$ & $432$ & $190$ & $174$ & $235$ & $428$ & $318$ \\\\ \n$249$ & $280$ & $162$ & $146$ & $210$ & $120$ & $123$ & $120$ & $150$ & $140$ \n\\end{tabular}\n\\end{center}\n(1) 以上述$20$个数据组成总体, 求总体平均数与总体标准差.\\\\\n(2) 设计恰当的随机抽样方法, 从总体中抽取一个容量为$7$的样本, 求样本的平均数与标\n准差.\\\\\n(3) 利用上面的抽样方法, 再抽取容量为$7$的样本, 计算样本的平均数和标准差. 这个样本的平均数和标准差与(2)中的结果一样吗? 为什么?\\\\\n(4) 利用(2)中的随机抽样方法, 分别从总体中抽取一个容量为$10, 13, 16, 19$的样本, 求样本的平均数与标准差. 分析样本容量与样本的平均数和标准差对总体的估计效果之间有什么关系.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030261": { + "id": "030261", + "content": "已知总体划分为$3$层, 通过分层随机抽样, 各层抽取的样本量、样本平均数和样本方差分别为: $l,\\overline{x},s_1^2;m,\\overline{y},s_2^2;n,\\overline{z},s_3^2$. 记总的样本平均数为$\\overline{w}$, 样本方差为$s^2$, 证明:\\\\\n(1) $\\overline{w}=\\dfrac{l}{l+m+n}\\overline{x}+\\dfrac{m}{l+m+n}\\overline{y}+\\dfrac{n}{l+m+n}\\overline{z}$;\\\\\n(2) $s^2=\\dfrac{1}{l+m+n}(l(s_1^2+(\\overline{x}-\\overline{w})^2)+m(s_2^2+(\\overline{y}-\\overline{w})^2)+n(s_3^2+(\\overline{z}-\\overline{w})^2))$.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030262": { + "id": "030262", + "content": "为了了解某地参加计算机水平测试的$5000$名学生的成绩, 从中抽取了$200$名学生进行调查分析, 在这个问题中, 被抽取的$200$名学生是\\bracket{20}.\n\\fourch{总体}{个体}{样本}{样本量}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030263": { + "id": "030263", + "content": "四名同学各掷骰子$5$次, 分别记录每次骰子出现的点数, 根据四名同学的统计结果, 可以判断出一定没有出现点数$6$的是\\bracket{20}.\n\\twoch{平均数为$3$, 中位数为$2$}{中位数为$3$, 众数为$2$}{平均数为$2$, 方差为$2.4$}{中位数为$3$, 方差为$2.8$}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030264": { + "id": "030264", + "content": "如果一组数据的中位数比平均数小很多, 下面哪种叙述一定是错误的? 为什么?\\\\ \\textcircled{1} 数据中可能有异常值; \n\\textcircled{2} 这组数据是近似对称的;\n\\textcircled{3} 数据中可能有极端大的值; \n\\textcircled{4} 数据中众数可能和中位数相同.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030265": { + "id": "030265", + "content": "(1) 在已分组的若干数据中, 每组的频数是指\\blank{50}, 每组的频率是指\\blank{50}.\n(2) 一个公司共有$N$名员工, 下设一些部门, 要采用等比例分层随机抽样的方法从全体员工中抽取样本量为$n$的样本, 如果某部门有$m$名员工, 那么从该部门抽取的员工人数是\\blank{50}.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030266": { + "id": "030266", + "content": "一家著名的全国性连锁服装店进行了一项关于当年秋季服装流行色的民意调查, 调查者通过向顾客发放饮料, 并让顾客通过挑选饮料杯上印着的颜色来对自己喜欢的服装颜色``投票'', 根据这次调查结果, 在某大城市$A$, 服装颜色的众数是红色, 而当年全国服装协会发布的调查结果是咖啡色.\\\\\n(1) 这个结果是否代表$A$城市的人的看法?\\\\\n(2) 你认为这两种调查的差异是由什么引起的?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030267": { + "id": "030267", + "content": "从一本英语书中随机抽取$100$个句子, 数出每个句子中的单词数, 作出这$100$个数据的频率分布表, 由此你可以作出什么估计?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030268": { + "id": "030268", + "content": "在一个文艺比赛中, $12$名专业人士和$12$名观众代表各组成一个评委小组, 给参赛选手打分. 下面是两组评委对同一名选手的打分:\n\\begin{center}\n\\begin{tabular}{ccccccccccccc}\n小组A & $42$ & $45$ & $48$ & $46$ & $52$ & $47$ & $49$ & $55$ & $42$ & $51$ & $47$ & $45$ \\\\ \n小组B & $55$ & $36$ & $70$ & $66$ & $75$ & $49$ & $46$ & $68$ & $42$ & $62$ & $58$ & $47$\n\\end{tabular}\n\\end{center}\n(1) 选择一个可以度量每一组评委打分相似性的量, 并对每组评委的打分计算度量值.\\\\ \n(2) 你能据此判断小组A与小组B中哪一个更像是由专业人士组成的吗?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030269": { + "id": "030269", + "content": "一名学生通过计步仪器, 记录了自己$100$天每天走的步数, 数据如下: \n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$5678$ & $13039$ & $8666$ & $9521$ & $8722$ & $10575$ & $2107$ & $4165$ & $17073$ & $11205$ \\\\ \n$5467$ & $11736$ & $9986$ & $8592$ & $6542$ & $12386$ & $13115$ & $5705$ & $8358$ & $13234$ \\\\ \n$20142$ & $9769$ & $10426$ & $12802$ & $16722$ & $8587$ & $9266$ & $8635$ & $2455$ & $4524$ \\\\ \n$8260$ & $13165$ & $9812$ & $9533$ & $2377$ & $5132$ & $8212$ & $7968$ & $9859$ & $3961$ \\\\ \n$5484$ & $11344$ & $8722$ & $12944$ & $8597$ & $12594$ & $15101$ & $4751$ & $11130$ & $11286$ \\\\ \n$8897$ & $7192$ & $7313$ & $8790$ & $7699$ & $10892$ & $9583$ & $9207$ & $16358$ & $10182$ \\\\ \n$3607$ & $1789$ & $9417$ & $4566$ & $12347$ & $3228$ & $7606$ & $8689$ & $8755$ & $15609$ \\\\ \n$8767$ & $9226$ & $5622$ & $11094$ & $8865$ & $11246$ & $17417$ & $7995$ & $7317$ & $6878$ \\\\ \n$4270$ & $11051$ & $5705$ & $5442$ & $10078$ & $9107$ & $8354$ & $6483$ & $16808$ & $1509$ \\\\ \n$1301$ & $10843$ & $13864$ & $12691$ & $8419$ & $14267$ & $9809$ & $9858$ & $8922$ & $12682$ \n\\end{tabular}\n\\end{center}\n(1) 画出这组数据的频率分布直方图, 并分析数据的分布特点;\\\\\n(2) 计算这组数据的平均数、中位数和标准差, 并根据这些数值描述这名学生的运动情况.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030270": { + "id": "030270", + "content": "一家水果店的店长为了解本店苹果的日销售情况, 记录了过去$30$天苹果的日销售量(单位: $\\text{kg}$), 结果如下: \n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$83$ & $96$ & $107$ & $91$ & $70$ & $75$ & $94$ & $80$ & $80$ & $100$ \\\\ \n$75$ & $99$ & $117$ & $89$ & $74$ & $94$ & $84$ & $85$ & $101$ & $87$ \\\\ \n$93$ & $85$ & $107$ & $99$ & $55$ & $97$ & $86$ & $84$ & $85$ & $104$ \n\\end{tabular}\n\\end{center}\n(1) 请计算该水果店过去$30$天苹果日销售量的中位数、平均数、极差和标准差.\\\\\n(2) 一次进货太多, 水果会变得不新鲜; 进货太少, 又不能满足顾客的需求. 店长希望每天的苹果尽量新鲜, 又能$80\\%$地满足顾客的需求(在$100$天中, 大约有$80$天可以满足顾客的需求). 请问, 每天应该进多少千克苹果?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030271": { + "id": "030271", + "content": "一家保险公司决定对推销员实行目标管理, 即给推销员确定一个具体的销售目标. 确定的销售目标是否合适, 直接影响到公司的经济效益. 如果目标定得过高, 多数推销员完不成任务, 会使推销员失去信心; 如果目标定得太低, 将不利于挖掘推销员的工作潜力.下面一组数据是部分推销员的月销售额(单位: 千元):\n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$19.58$ & $16.11$ & $16.45$ & $20.45$ & $20.24$ & $21.66$ & $22.45$ & $18.22$ & $12.34$ & $19.35$ \\\\ \n$20.55$ & $17.45$ & $18.78$ & $17.96$ & $19.91$ & $18.12$ & $14.65$ & $14.78$ & $16.78$ & $18.78$ \\\\ \n$18.29$ & $18.51$ & $17.86$ & $19.58$ & $19.21$ & $18.55$ & $16.34$ & $15.54$ & $17.55$ & $14.89$ \\\\ \n$18.94$ & $17.43$ & $17.14$ & $18.02$ & $19.98$ & $17.88$ & $17.32$ & $19.35$ & $15.45$ & $19.58$ \\\\ \n$13.45$ & $21.34$ & $14.00$ & $18.42$ & $23.00$ & $17.52$ & $18.51$ & $17.16$ & $24.56$ & $25.14$ \n\\end{tabular}\n\\end{center}\n请根据这组样本数据提出使$65\\%$的职工能够完成销售指标的建议.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030272": { + "id": "030272", + "content": "为了解某市家庭用电量的情况, 该市统计局调查了$200$户居民去年一年的月均用电量(单位: $\\text{kW}\\cdot\\text{h}$), 数据从小到大排序如下:\n\\begin{center}\n\\begin{tabular}{ccccccccccccccc}\n$8$ & $18$ & $22$ & $31$ & $42$ & $48$ & $49$ & $50$ & $51$ & $56$ & $57$ & $57$ & $60$ & $61$ & $61$ \\\\ \n$61$ & $62$ & $62$ & $63$ & $63$ & $65$ & $66$ & $67$ & $69$ & $70$ & $70$ & $71$ & $72$ & $72$ & $74$ \\\\ \n$76$ & $77$ & $77$ & $78$ & $78$ & $80$ & $80$ & $82$ & $82$ & $82$ & $83$ & $84$ & $84$ & $88$ & $88$ \\\\ \n$89$ & $90$ & $91$ & $93$ & $93$ & $94$ & $95$ & $96$ & $96$ & $96$ & $97$ & $98$ & $98$ & $98$ & $99$ \\\\ \n$100$ & $100$ & $100$ & $101$ & $101$ & $101$ & $105$ & $106$ & $106$ & $106$ & $107$ & $107$ & $107$ & $107$ & $108$ \\\\ \n$108$ & $109$ & $109$ & $110$ & $110$ & $110$ & $111$ & $112$ & $113$ & $113$ & $114$ & $115$ & $116$ & $118$ & $120$ \\\\ \n$120$ & $120$ & $121$ & $123$ & $124$ & $127$ & $127$ & $127$ & $130$ & $130$ & $130$ & $131$ & $131$ & $132$ & $132$ \\\\ \n$132$ & $133$ & $133$ & $134$ & $134$ & $134$ & $135$ & $135$ & $135$ & $135$ & $136$ & $137$ & $137$ & $138$ & $139$ \\\\ \n$139$ & $140$ & $141$ & $142$ & $144$ & $146$ & $146$ & $147$ & $148$ & $149$ & $151$ & $152$ & $154$ & $156$ & $159$ \\\\ \n$160$ & $162$ & $163$ & $163$ & $164$ & $165$ & $167$ & $169$ & $170$ & $170$ & $172$ & $174$ & $174$ & $177$ & $178$ \\\\ \n$178$ & $180$ & $182$ & $182$ & $187$ & $189$ & $191$ & $191$ & $192$ & $194$ & $194$ & $200$ & $201$ & $201$ & $202$ \\\\ \n$203$ & $203$ & $206$ & $208$ & $212$ & $213$ & $214$ & $216$ & $223$ & $224$ & $237$ & $247$ & $250$ & $250$ & $251$ \\\\ \n$253$ & $254$ & $258$ & $260$ & $265$ & $274$ & $274$ & $283$ & $288$ & $289$ & $304$ & $319$ & $320$ & $324$ & $339$ \\\\\n$462$ & $498$ & $530$ & $542$ & $626$\n\\end{tabular}\n\\end{center}\n为了既满足居民的基本用电需求, 又提高能源的利用效率, 市政府计划采用阶梯电价, 使$75\\%$的居民缴费在第一档, $20\\%$的居民缴费在第二档, 其余$5\\%$的居民缴费在第三档. 请确定各档的范围.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版2019年必修二教材统计例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" } } \ No newline at end of file