From f5462da4de7e14445a2c727e06e106bf37ff1b39 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 6 Jul 2023 16:04:14 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A5=E7=A9=BA=E4=B8=AD=E8=AF=BE?= =?UTF-8?q?=E5=A0=82=E7=BB=9F=E8=AE=A1=E4=BE=8B=E9=A2=98=E4=B8=8E=E4=B9=A0?= =?UTF-8?q?=E9=A2=98=E5=B9=B6=E5=AF=B9=E5=BA=94=E5=8D=95=E5=85=83?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/批量收录题目.py | 2 +- 题库0.3/Problems.json | 1034 ++++++++++++++++++++++++++++++++++++++++ 2 files changed, 1035 insertions(+), 1 deletion(-) diff --git a/工具v2/批量收录题目.py b/工具v2/批量收录题目.py index e60b115c..b77e2acb 100644 --- a/工具v2/批量收录题目.py +++ b/工具v2/批量收录题目.py @@ -1,5 +1,5 @@ #修改起始id,出处,文件名 -starting_id = 18725 #起始id设置, 来自"寻找空闲题号"功能 +starting_id = 18784 #起始id设置, 来自"寻找空闲题号"功能 raworigin = "" #题目来源的前缀(中缀在.tex文件中) filename = r"C:\Users\wangweiye\Documents\wwy sync\临时工作区\空中课堂必修第二册例题与习题.tex" #题目的来源.tex文件 editor = "王伟叶" #编辑者姓名 diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 991a286a..c3bdfe41 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -482925,6 +482925,1040 @@ "space": "4em", "unrelated": [] }, + "018784": { + "id": "018784", + "content": "为客观了解上海市民家庭存书量, 上海市统计局社情民意调查中心通过$12340$电话调查系统开展专项调查, 成功访问了$2007$位上海市民. 在这项调查中, 总体和样本分别是什么? 样本量是多少?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018785": { + "id": "018785", + "content": "为了调查$2020$年中央电视台春节联欢晩会在某地播出的收视率, 节目组设置了《春节联欢晩会收视率调查表》, 并向社会广泛征求调查意见. 某校有两名同学为电视台设计了调查方案:\n同学$\\mathrm{A}$: 我把《春节联欢晩会收视率调查表》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$\\mathrm{B}$: 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晩会, 我不出家门就可以统计出中央电视台春节联欢晩会的收视率了.\n请问上述两名同学设计的调查方案能够获得比较准确的收视率吗? 为什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018786": { + "id": "018786", + "content": "人们常认为$16^{\\circ} \\mathrm{C}$是宜人的年平均温度, 单纯根据平均气温的报告来选择野营地点是否恰当? 为什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018787": { + "id": "018787", + "content": "下面的数据是观测数据还是实验数据?\\\\\n(1) 2010 年第六次全国人口普查登记的全国 1339724852 人(未包括中国香港、澳门特别行政区和台湾省的人口数据) 的年龄;\\\\\n(2) 在体育课上, 教师抽查了$10$名学生, 测量他们的$100$米跑用时, 得到$10$个数据;\\\\\n(3) 为了检验某疫苗的有效性, 在实验中, 工作人员为$20$万名儿童注射了无效的生理盐水, 而另外$20$万名儿童被注射了该疫苗. 结果注射了该疫苗的儿童中只有$33$人患了小儿麻痹症, 而注射了生理盐水的儿童中有$115$人患了小儿麻痹症.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018788": { + "id": "018788", + "content": "统计年鉴是一个国家或地区统计局编印的资料性年刊, 收录全国或者某个地区上一年经济、社会等各方面的统计数据, 以及重要历史年份的主要统计数据, 是全面反映经济和社会发展情况的资料性年刊. 试从《2018上海统计年鉴》中找出上海市普通高等学校$2017$年的招生人数、在校学生人数以及毕业生人数.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018789": { + "id": "018789", + "content": "请从国家统计局网站上查找我国水资源及其使用情况的一些数据, 根据数据谈谈当前保护水资源的重要性.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018790": { + "id": "018790", + "content": "为了缓解城市的交通拥堵情况, 某市准备出台限制私家车的政策, 为此要进行民意调查. 某个调查小组调查了一些拥有私家车的市民, 你认为这样的调查结果能很好地反映该市市民的意愿吗?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018791": { + "id": "018791", + "content": "在 13.2 节中, 厂家为考察某一新型 LED 灯管的使用寿命, 从首批生产的$200$根灯管中抽取$10$根灯管进行加速寿命试验. 试用随机数表法进行抽取.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018792": { + "id": "018792", + "content": "下列抽取样本的方法是简单随机抽样吗? 判断并简要说明理由.\\\\\n(1) 某公司年会时将所有员工的姓名写在纸条上, 放进抽奖箱, 混合均匀后抽取$10$名员工进行奖励;\\\\\n(2) 课堂上, 教师抽取班上学号尾号为$0$的学生回答问题.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018793": { + "id": "018793", + "content": "下列抽样实验中, 最适合用抽签法的是\\bracket{20}.\n\\onech{从某厂生产的$30000$件产品中抽取$600$件进行质量检验}{从某班级$30$名学生中抽取$5$名学生参加一个座谈会}{从某校高中一年级$320$名学生中抽取$30$名学生了解体育运动情况}{从某厂生产的$30000$件产品中抽取$10$件进行质量检验}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018794": { + "id": "018794", + "content": "北京时间$2021$年$6$月$17$日9 时$22$分, 搭载神舟十二号载人飞船的长征二号F遥十二运载火箭, 在酒泉卫星发射中心点火发射. 某中学为此举行了``讲好航天故事''演讲比赛. 现从报名的$80$位学生中利用下面的随机数表抽取$10$位同学参加演讲比赛, 将$80$位学生按$01$、$02$、$\\cdots$、$80$进行编号, 假设从随机数表第$1$行的第$3$个数字开始由左到右依次选取两个数字, 重复的跳过, 则选出来的第$7$个号码所对应的学生编号为\n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n$0627$ & $4313$ & $2636$ & $1547$ & $0941$ & $2512$ & $6317$ & $6323$ & $2616$ & $8045$ & $6011$ \\\\ \n$1410$ & $9577$ & $7424$ & $6762$ & $4281$ & $1457$ & $2042$ & $5332$ & $3732$ & $2707$ & $3607$ \\\\ \n$5124$ & $5179$ & $3014$ & $2310$ & $2118$ & $2191$ & $3726$ & $3890$ & $0140$ & $0523$ & $2617$ \n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018795": { + "id": "018795", + "content": "已知某校合唱队有男生$32$名、女生$28$名, 为举办校新春晩会, 需要从该合唱队中抽取$10$名男生、$8$名女生参加节目. 请设计一个抽取样本的方法, 并写出具体的操作步骤.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018796": { + "id": "018796", + "content": "某校共有$100$名教师, 为了支援教育薄弱地区, 现要从中随机抽出$12$名教师组成讲师团在暑假期间前往支教. 请设计一个抽取样本的方法, 并写出具体操作步骤.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018797": { + "id": "018797", + "content": "某高中一年级共有学生$425$名, 其中男生$204$名, 女生$221$名, 为了解该校高一年级学生的身高情况, 现从中抽取$50$名学生测量身高. 问: 应当如何抽取? 男女生各要抽取多少名?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018798": { + "id": "018798", + "content": "生命在于运动. 为了增强体质, 树立``健康第一''的教育理念, 某高中在全校师生中积极开展阳光体育活动, 现计划举办以``每天健身一小时, 健康生活一辈子''为主题的教职工趣味运动会. 已知该校共有教职工$152$名, 其中$40$岁及以下共$87$名, 40 岁以上共$65$名. 计划从教职工中抽取$20$名参加趣味运动会. 那么, 两个年龄段的教职工各要抽取多少名?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018799": { + "id": "018799", + "content": "下列问题中, 采用怎样的抽样方法较为合理?\\\\\n(1) 某餐厅从一桌正在就餐的$12$名客人中抽取$2$名客人进行服务满意度调查;\\\\\n(2) 植物根据植株的高度及分枝部位等可以分为乔木、灌木和草本三大类. 某植物园需要对其园中的不同植物的干重(烘干后测定的质量)进行调查.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018800": { + "id": "018800", + "content": "下列问题中, 采用怎样的抽样方法较为合理?\\\\\n(1) 从$10$名学生中抽取$3$名参加座谈会;\\\\\n(2) 从某工厂生产的$700$个零件中抽取$30$个样本进行测试;\\\\\n(3) 近几年来移动支付越来越普遍, 不同年龄段的人对移动支付的熟知程度不同. 某学校兴趣小组为了了解学校所在社区不同年龄段的人对于移动支付的熟知度, 进行抽样调查.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018801": { + "id": "018801", + "content": "某公司在甲、乙、丙、丁四会地区分别有$150$个、$120$个、$180$个、$150$个销售点, 公司为了了解相关情况, 现要完成下列两项抽样调查: \n\\textcircled{1} 从这$600$个销售点中抽取一个容量为$100$的样本; \\textcircled{2} 在甲地区有$20$个大型销售点, 从中抽取$7$个大型销售点调查其销量及售后服务等情况. 请问较为合理的抽样方法是\\bracket{20}.\n\\twoch{\\textcircled{1}采用简单随机抽样, \\textcircled{2}采用分层随机抽样}{\\textcircled{1}采用分层随机抽样, \\textcircled{2}采用简单随机抽样}{\\textcircled{1}和\\textcircled{2}都采用分层随机抽样}{\\textcircled{1}和\\textcircled{2}都采用简单随机抽样}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018802": { + "id": "018802", + "content": "某工厂生产$A$、$B$、$C$三种不同型号的产品, 产品的数量之比依次为$3: 4: 7$, 现在用分层随机抽样的方法抽出容量为$n$的样本, 样本中$A$型号产品有$15$件, 那么样本容量$n$为\\blank{50}.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018803": { + "id": "018803", + "content": "某高中为了了解学生收看空中课堂的具体情况, 利用分层随机抽样的方法从高中三个年级的学生中随机抽取了$150$名进行问卷调查, 其中从高一年级的学生中抽取了$40$名, 从高二年级的学生中抽取了$50$名, 若高三年级共有学生$420$名, 则该高中共有学生\\blank{50}名.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018804": { + "id": "018804", + "content": "我国古代数学名著《九章算术》中有一抽样问题: ``今有北乡若干人, 西乡七千四百八十八人, 南乡六千九百一十二人, 凡三乡, 发役三百人, 而北乡需遣一百零八人, 问北乡人数几何? ''根据分层随机抽样的方法, 则北乡共有\\blank{50}人.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018805": { + "id": "018805", + "content": "某高中一年级有$271$名学生, 为了培养良好的阅读习惯, 要求学生从四大名著中选且仅选一本阅读. 其中有$84$名学生选《三国演义》, $43$名学生选 《水游传》, $68$名学生选《西游记》, $76$名学生选《红楼梦》, 现从中抽取$20$名学生分享他们的读后感, 问: 应当如何抽取? 从阅读《三国演义》、《水游传》、《西游记》、《红楼梦》的学生中各抽取多少人?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018806": { + "id": "018806", + "content": "某单位有管理人员、业务人员、后勤人员共$m$人, 其中业务人员有$120$人, 现采用分层抽样的方法从管理人员、业务人员、后勤人员中抽取部分职工了解他们的健康状况, 若抽取的管理人员有$6$人, 且抽取的管理人员与业务人员的比为$1: 4$, 抽取的后勤人员比业务人员少$20$人, 则$m$的值可以为\\bracket{20}.\n\\fourch{$170$}{$200$}{$150$}{$120$}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018807": { + "id": "018807", + "content": "某单位最近组织了一次健身活动, 活动分为登山和游泳, 且每个职工参加且仅参加其中一项. 在参加活动的职工中, 青年人占$42.5 \\%$, 中年人占$47.5 \\%$, 老年人占$10 \\%$. 登山的职工占参加活动总人数的$\\dfrac{1}{4}$, 且登山的职工中, 青年人占$50 \\%$, 中年人占$40 \\%$, 老年人占$10 \\%$. 为了了解各组不同年龄层次的职工对本次活动的满意程度, 现用分层抽样方法从参加活动的全体职工中抽取一个容量为$200$的样本. 试求:\\\\\n(1) 参加游泳的职工中, 青年人、中年人、老年人所占的比例分别为多少?\\\\\n(2) 参加游泳的职工中, 青年人、中年人、老年人应分别抽取多少人?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018808": { + "id": "018808", + "content": "某区通过分层随机抽样得到$400$名高三年级学生的身高(单位: $\\text{cm}$) 数据, 制作了如下的频数分布表. 请根据频数分布表制作频率分布表, 并绘制频率分布直方图.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline 身高 & 频数 & 累积频数 & 身高 & 频数 & 累积频数 \\\\\n\\hline 150 & 1 & 1 & 169 & 10 & 120 \\\\\n\\hline 151 & 0 & 1 & 170 & 15 & 135 \\\\\n\\hline 152 & 2 & 3 & 171 & 19 & 154 \\\\\n\\hline 153 & 3 & 6 & 172 & 23 & 177 \\\\\n\\hline 154 & 2 & 8 & 173 & 21 & 198 \\\\\n\\hline 155 & 4 & 12 & 174 & 25 & 223 \\\\\n\\hline 156 & 5 & 17 & 175 & 29 & 252 \\\\\n\\hline 157 & 5 & 22 & 176 & 27 & 279 \\\\\n\\hline 158 & 5 & 27 & 177 & 28 & 307 \\\\\n\\hline 159 & 8 & 35 & 178 & 23 & 330 \\\\\n\\hline 160 & 3 & 38 & 179 & 15 & 345 \\\\\n\\hline 161 & 5 & 43 & 180 & 15 & 360 \\\\\n\\hline 162 & 8 & 51 & 181 & 9 & 369 \\\\\n\\hline 163 & 3 & 54 & 182 & 13 & 382 \\\\\n\\hline 164 & 9 & 63 & 183 & 9 & 391 \\\\\n\\hline 165 & 13 & 76 & 184 & 5 & 396 \\\\\n\\hline 166 & 11 & 87 & 185 & 3 & 399 \\\\\n\\hline 167 & 11 & 98 & 186 & 0 & 399 \\\\\n\\hline 168 & 12 & 110 & 187 & 1 & 400 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018809": { + "id": "018809", + "content": "收集数据并制作一份你所在班级学生的体重频率分布直方图, 并根据频率分布直方图分析班级学生的体重分布情况.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018810": { + "id": "018810", + "content": "请尝试设计并绘制一份可以反映教材 P138 表 13-2 中高一年级男女生体重分布的差异性的统计图.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018811": { + "id": "018811", + "content": "根据表中的数据, 分别绘制女生和男生的体重分布茎叶图, 并比较女生和男生的体重分布.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline 性别 & 身高$\\text{cm}$& 体重$/ \\mathrm{kg}$& 性别 & 身高$/ \\text{cm}$& 体重$/ \\mathrm{kg}$& 性别 & 身高$\\text{cm}$& 体重$/ \\mathrm{kg}$\\\\\n\\hline 女 & 152 & 46 & 女 & 164 & 52 & 男 & 172 & 92 \\\\\n\\hline 女 & 153 & 47 & 男 & 165 & 54 & 男 & 172 & 64 \\\\\n\\hline 女 & 154 & 63 & 男 & 165 & 60 & 女 & 172 & 69 \\\\\n\\hline 女 & 155 & 50 & 男 & 165 & 48 & 男 & 173 & 75 \\\\\n\\hline 女 & 156 & 48 & 女 & 165 & 51 & 男 & 173 & 72 \\\\\n\\hline 女 & 156 & 50 & 女 & 165 & 55 & 男 & 174 & 55 \\\\\n\\hline 女 & 156 & 51 & 女 & 165 & 58 & 男 & 174 & 56 \\\\\n\\hline 女 & 157 & 51 & 女 & 165 & 63 & 男 & 174 & 63 \\\\\n\\hline 女 & 157 & 50 & 男 & 166 & 64 & 男 & 174 & 74 \\\\\n\\hline 女 & 159 & 49 & 男 & 167 & 54 & 男 & 175 & 53 \\\\\n\\hline 女 & 159 & 51 & 男 & 167 & 52 & 男 & 176 & 64 \\\\\n\\hline 女 & 160 & 47 & 男 & 167 & 53 & 男 & 176 & 60 \\\\\n\\hline 女 & 160 & 62 & 女 & 167 & 69 & 男 & 177 & 63 \\\\\n\\hline 女 & 160 & 50 & 女 & 167 & 61 & 男 & 177 & 75 \\\\\n\\hline 女 & 160 & 63 & 男 & 168 & 97 & 男 & 178 & 62 \\\\\n\\hline 女 & 161 & 53 & 女 & 168 & 60 & 男 & 178 & 60 \\\\\n\\hline 女 & 162 & 84 & 女 & 168 & 44 & 男 & 178 & 73 \\\\\n\\hline 女 & 163 & 66 & 男 & 170 & 53 & 男 & 178 & 68 \\\\\n\\hline 女 & 163 & 53 & 男 & 170 & 54 & 男 & 179 & 78 \\\\\n\\hline 女 & 164 & 63 & 男 & 170 & 57 & 男 & 181 & 80 \\\\\n\\hline 女 & 164 & 68 & 男 & 170 & 47 & 男 & 182 & 92 \\\\\n\\hline 女 & 164 & 52 & 男 & 170 & 69 & 男 & 184 & 78 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018812": { + "id": "018812", + "content": "某宝石店经理随机选取了$20$颗钻石, 将它们的价格(单位: 千元)、质量(单位: 克拉) 以及颜色记录在表中.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline 序号 & 价格/千元 & 质量/克拉 & 颜色 \\\\\n\\hline 1 & 11 & 0.9 & 3 \\\\\n\\hline 2 & 11 & 1.21 & 5 \\\\\n\\hline 3 & 12.9 & 1 & 5 \\\\\n\\hline 4 & 13.2 & 1.14 & 4 \\\\\n\\hline 5 & 15.5 & 1.3 & 6 \\\\\n\\hline 6 & 15.9 & 1.17 & 4 \\\\\n\\hline 7 & 16.6 & 1.33 & 7 \\\\\n\\hline 8 & 17.6 & 1.1 & 5 \\\\\n\\hline 9 & 18.9 & 1.11 & 4 \\\\\n\\hline 10 & 20.6 & 1.45 & 5 \\\\\n\\hline 11 & 20.8 & 1.3 & 2 \\\\\n\\hline 12 & 21.6 & 1.5 & 9 \\\\\n\\hline 13 & 22.5 & 1.6 & 2 \\\\\n\\hline 14 & 22.8 & 1.5 & 6 \\\\\n\\hline 15 & 28.8 & 1.12 & 2 \\\\\n\\hline 16 & 29.5 & 1.7 & 8 \\\\\n\\hline 17 & 29.8 & 1.9 & 5 \\\\\n\\hline 18 & 33 & 2.13 & 8 \\\\\n\\hline 19 & 36.6 & 1.77 & 3 \\\\\n\\hline 20 & 40 & 1.82 & 4 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 将该宝石店$20$颗钻石的价格按四舍五入精确到整数, 试就取整数后的$20$颗钻石的价格绘制茎叶图, 并分析这些钻石价格的分布特点;\\\\\n(2) 试分别绘制质量与价格的散点图, 以及颜色与价格的散点图, 并观察随着钻石的质量和颜色数值的增加, 钻石的价格是如何变化的.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018813": { + "id": "018813", + "content": "请调查你所在学校本年级学生每天户外活动的平均时间和视力情况, 用合适的统计图表呈现出来, 并尝试寻找这两组数据之间的关系.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018814": { + "id": "018814", + "content": "某营养学研究人员用随机抽样的方法获得了某高校$100$名女大学生平均每日摄取的热量 (单位: 千卡, $1$千大卡= $1000$千卡), 其数据如下:\n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$1.42$ & $1.44$ & $1.45$ & $1.46$ & $1.48$ & $1.50$ & $1.51$ & $1.51$ & $1.53$ & $1.54$ \\\\ \n$1.56$ & $1.56$ & $1.57$ & $1.59$ & $1.60$ & $1.60$ & $1.60$ & $1.61$ & $1.62$ & $1.63$ \\\\ \n$1.63$ & $1.64$ & $1.66$ & $1.67$ & $1.67$ & $1.68$ & $1.69$ & $1.70$ & $1.71$ & $1.71$ \\\\ \n$1.71$ & $1.71$ & $1.72$ & $1.73$ & $1.73$ & $1.74$ & $1.74$ & $1.75$ & $1.75$ & $1.75$ \\\\ \n$1.76$ & $1.76$ & $1.79$ & $1.79$ & $1.80$ & $1.80$ & $1.82$ & $1.82$ & $1.83$ & $1.83$ \\\\ \n$1.83$ & $1.84$ & $1.84$ & $1.84$ & $1.85$ & $1.85$ & $1.86$ & $1.86$ & $1.87$ & $1.87$ \\\\ \n$1.87$ & $1.88$ & $1.88$ & $1.88$ & $1.89$ & $1.90$ & $1.90$ & $1.91$ & $1.91$ & $1.92$ \\\\ \n$1.93$ & $1.94$ & $1.94$ & $1.95$ & $1.95$ & $1.96$ & $1.96$ & $1.97$ & $1.97$ & $1.97$ \\\\ \n$1.99$ & $2.00$ & $2.01$ & $2.03$ & $2.04$ & $2.07$ & $2.07$ & $2.09$ & $2.09$ & $2.10$ \\\\ \n$2.13$ & $2.14$ & $2.14$ & $2.15$ & $2.17$ & $2.19$ & $2.23$ & $2.25$ & $2.28$ & $2.29$ \n\\end{tabular}\n\\end{center}\n(1) 试估计该校全体女大学生每日摄取热量的分布情况;\\\\\n(2) 健康的成年女性每天需要摄取$1.80 \\sim 1.90$千大卡(不含$1.90$千大卡) 的热量, 试估计该校有多少比例的女大学生摄取的热量在此范围之内.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018815": { + "id": "018815", + "content": "某市$2021$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? 请自行上网查阅空气质量分级标准, 设计适当的频率分布直方图展示这组数据, 并结合该标准分析数据.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018816": { + "id": "018816", + "content": "统计你们班所有同学的鞋号, 选择合适的统计图进行描述, 并分析鞋号的分布有什么特点. 能用你们班同学鞋号的分布估计你所在学校全体高中生鞋号的分布吗? 估计全国高中学生的鞋号分布呢?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018817": { + "id": "018817", + "content": "请与$2\\sim 4$位同学组成合作小组, 从一本英语书中随机抽取$100$句句子, 数出每句句子中的单词数, 作出这$100$个数据的频率分布表, 并由此作出你们小组觉得有意义的统计估计.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018818": { + "id": "018818", + "content": "为了解某体校学生跑步的情况, 观察随机抽取的$20$名学生一周内跑步的累计距离(单位: $\\text{km}$), 在各区间内的频数记录如下表所示.\n\\begin{center}\n\\begin{tabular}{|c|c|}\n\\hline 周跑步累计距离分组区间 & 频数 \\\\\n\\hline$[5.5,10.5)$& 1 \\\\\n\\hline$[10.5,15.5)$& 2 \\\\\n\\hline$[15.5,20.5)$& 3 \\\\\n\\hline$[20.5,25.5)$& 5 \\\\\n\\hline$[25.5,30.5)$& 4 \\\\\n\\hline$[30.5,35.5)$& 3 \\\\\n\\hline$[35.5,40.5)$& 2 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n试估计一周内该校学生平均跑步累计距离.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018819": { + "id": "018819", + "content": "A 校抽取了66名高一年级学生, 测量他们的身高数据. 现在假设由于某种原因这些原始样本数据不可查得, 但已知按照分层随机抽样原则抽取了样本, 其中男生$34$名, 身高的样本平均数为$173.1 \\text{cm}$, 方差为$25.9$; 女生$32$名, 身高的样本平均数为$161.3 \\text{cm}$, 方差为 $23.3$. 试用这些已知的数据求该$66$名高一年级学生身高的样本平均数和方差, 并估计高一年级学生身高的总体方差. (结果精确到$0.01$)", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018820": { + "id": "018820", + "content": "某果园种植了$120$棵苹果树, 为调查苹果产量, 从中随机抽取了$10$棵苹果树, 测得其产量 (单位: $\\mathrm{kg}$) 分别为$24$、$25$、$28$、$32$、$20$、$26$、$33$、$26$、$27$、$30$. 试预估该果园的苹果产量.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018821": { + "id": "018821", + "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$s_y^2$, $b$、$k$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$y_1=k x_1$、$y_2=k x_2$、$\\cdots$、$y_n=k x_n$, 那么$s_y^2=k^2 s_x^2$.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018822": { + "id": "018822", + "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$8$个评分的平均分. 那么, 这两位选手的最终得分是多少? 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": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018823": { + "id": "018823", + "content": "下表是$13\\sim 17$岁未成年人的身高的主要百分位数(单位: $\\text{cm}$). 小明今年$16$岁, 他的身高为$176 \\text{cm}$, 他所在城市男性同龄人约有$6.4$万人. 试估计小明的身高至少高于他所在城市多少男性同龄人.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline \\multicolumn{2}{|c|}{} & P1 & P5 & P10 & P25 & P50 & P75 & P90 & P95 & P99 \\\\\n\\hline \\multirow{2}{*}{$13 -15$岁} & 男 & 141 & 147 & 151 & 157 & 164 & 169 & 174 & 177 & 182 \\\\\n\\cline {2 - 11} & 女 & 143 & 147 & 150 & 153 & 157 & 161 & 165 & 167 & 171 \\\\\n\\hline \\multirow{2}{*}{$16-17$岁} & 男 & 155 & 160 & 163 & 167 & 171 & 175 & 179 & 181 & 186 \\\\\n\\cline {2 - 11} & 女 & 147 & 150 & 152 & 155 & 159 & 163 & 166 & 169 & 172 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n{\\it 数据来源: 《中国未成年人人体尺寸》(标准号: GB/T 26158-2010).}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018824": { + "id": "018824", + "content": "为了实现绿色发展, 避免能源浪费, 有关部门计划对居民用电阶梯式收费办法作相关调研, 为此在某市随机调查了六月份$200$户居民的用电量(单位: $\\mathrm{kW} \\cdot \\mathrm{h})$. 数据如下:\n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$107$ & $101$ & $78$ & $99$ & $208$ & $127$ & $74$ & $223$ & $31$ & $131$ \\\\ \n$214$ & $135$ & $89$ & $66$ & $60$ & $115$ & $189$ & $135$ & $146$ & $127$ \\\\ \n$203$ & $97$ & $96$ & $62$ & $65$ & $111$ & $56$ & $151$ & $106$ & $8$ \\\\ \n$162$ & $91$ & $67$ & $93$ & $212$ & $159$ & $61$ & $63$ & $178$ & $194$ \\\\ \n$194$ & $216$ & $101$ & $98$ & $139$ & $78$ & $110$ & $192$ & $105$ & $96$ \\\\ \n$22$ & $50$ & $138$ & $251$ & $120$ & $112$ & $100$ & $201$ & $98$ & $84$ \\\\ \n$137$ & $203$ & $260$ & $134$ & $156$ & $61$ & $70$ & $100$ & $72$ & $164$ \\\\ \n$174$ & $131$ & $93$ & $100$ & $163$ & $80$ & $76$ & $95$ & $152$ & $182$ \\\\ \n$88$ & $247$ & $191$ & $70$ & $130$ & $49$ & $114$ & $110$ & $163$ & $202$ \\\\ \n$265$ & $18$ & $94$ & $146$ & $149$ & $147$ & $177$ & $339$ & $57$ & $109$ \\\\ \n$107$ & $182$ & $101$ & $148$ & $274$ & $289$ & $82$ & $213$ & $165$ & $224$ \\\\ \n$142$ & $61$ & $108$ & $137$ & $90$ & $254$ & $201$ & $83$ & $253$ & $113$ \\\\ \n$130$ & $82$ & $170$ & $110$ & $108$ & $63$ & $250$ & $237$ & $120$ & $84$ \\\\ \n$154$ & $288$ & $170$ & $123$ & $172$ & $319$ & $62$ & $133$ & $130$ & $127$ \\\\ \n$107$ & $71$ & $96$ & $140$ & $77$ & $106$ & $132$ & $106$ & $135$ & $132$ \\\\ \n$167$ & $82$ & $258$ & $542$ & $51$ & $107$ & $69$ & $98$ & $72$ & $48$ \\\\ \n$109$ & $134$ & $250$ & $42$ & $320$ & $113$ & $180$ & $144$ & $116$ & $530$ \\\\ \n$200$ & $174$ & $135$ & $160$ & $462$ & $139$ & $133$ & $304$ & $191$ & $283$ \\\\ \n$121$ & $132$ & $118$ & $134$ & $124$ & $178$ & $206$ & $626$ & $120$ & $274$ \\\\ \n$141$ & $80$ & $187$ & $88$ & $324$ & $136$ & $498$ & $169$ & $77$ & $57$ \n\\end{tabular}\n\\end{center}\n根据以上数据, 应当如何确定阶梯电价的电量临界值?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018825": { + "id": "018825", + "content": "为了解 A 校高一年级的男生身高情况, 下面是随机抽取的$23$名男生的身高 (单位: $\\text{cm}$) 数据:\n\\begin{center}\n\\begin{tabular}{cccccccccccc}\n$173$ & $174$ & $166$ & $172$ & $170$ & $165$ & $165$ & $168$ & $164$ & $173$ & $172$ & $173$ \\\\ \n$175$ & $168$ & $170$ & $172$ & $176$ & $175$ & $168$ & $173$ & $167$ & $170$ & $175$ \n\\end{tabular}\n\\end{center}\n请估计 A 校高一年级男生身高的第$25$、$50$、$75$百分位数.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018826": { + "id": "018826", + "content": "已知$3.2$、$3.4$、$3.8$、$4.2$、$4.3$、$4.5$、$6.6$与$x$这八个数据的第$65$百分位数是$4.5$, 则实数$x$的取值范围是\\bracket{20}.\n\\fourch{$[4.5,+\\infty)$}{$[4.5,6.6)$}{$(4.5,+\\infty)$}{$(4.5,6.6]$}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018827": { + "id": "018827", + "content": "从某珍珠公司生产的产品中, 任意抽取$12$颗珍珠, 得到它们的质量 (单位: g) 如下: $7.9$、$9.0$、$8.9$、$8.6$、$8.4$、$8.5$、$8.5$、$8.5$、$9.9$、$7.8$、$8.3$、$8.0$.\\\\\n(1) 分别求出这组数据的第$25$、$50$、$95$百分位数;\\\\\n(2) 请找出珍珠质量较小的前$15 \\%$的珍珠质量;\\\\\n(3) 若用第$25$、$50$、$95$百分位数把公司生产的珍珠的等级划分为次品、合格品、优等品和特优品, 依照这个样本的数据, 给出该公司珍珠等级的划分标准.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018828": { + "id": "018828", + "content": "我国是世界上严重缺水的国家之一, 城市缺水问题较为突出. 某市政府为了减少水资源浪费, 计划对居民生活用水费用实施阶梯式水价制度, 即确定一户居民月用水量(单位: $\\mathrm{t}$) 标准为$a$, 用水量不超过$a$的部分按平价收费, 超出$a$的部分按议价收费. 通过抽样调查, 获得$100$户居民某年的月均用水量(单位: $\\mathrm{t}$) 如下:\n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$9.0$ & $13.6$ & $14.9$ & $5.9$ & $4.0$ & $7.1$ & $6.4$ & $5.4$ & $19.4$ & $2.0$ \\\\ \n$2.2$ & $8.6$ & $13.8$ & $5.4$ & $10.2$ & $4.9$ & $6.8$ & $14.0$ & $2.0$ & $10.5$ \\\\ \n$2.1$ & $5.7$ & $5.1$ & $16.8$ & $6.0$ & $11.1$ & $1.3$ & $11.2$ & $7.7$ & $4.9$ \\\\ \n$2.3$ & $10.0$ & $16.7$ & $12.0$ & $12.4$ & $7.8$ & $5.2$ & $13.6$ & $2.6$ & $22.4$ \\\\ \n$3.6$ & $7.1$ & $8.8$ & $25.6$ & $3.2$ & $18.3$ & $5.1$ & $2.0$ & $3.0$ & $12.0$ \\\\ \n$22.2$ & $10.8$ & $5.5$ & $2.0$ & $24.3$ & $9.9$ & $3.6$ & $5.6$ & $4.4$ & $7.9$ \\\\ \n$5.1$ & $24.5$ & $6.4$ & $7.5$ & $4.7$ & $20.5$ & $5.5$ & $15.7$ & $2.6$ & $5.7$ \\\\ \n$5.5$ & $6.0$ & $16.0$ & $2.4$ & $9.5$ & $3.7$ & $17.0$ & $3.8$ & $4.1$ & $2.3$ \\\\ \n$5.3$ & $7.8$ & $8.1$ & $4.3$ & $13.3$ & $6.8$ & $1.3$ & $7.0$ & $4.9$ & $1.8$ \\\\ \n$7.1$ & $28.0$ & $10.2$ & $13.8$ & $17.9$ & $10.1$ & $5.5$ & $4.6$ & $3.2$ & $21.6$ \\\\ \n\\end{tabular}\n\\end{center}\n如果该市政府希望使$80 \\%$的居民用户生活用水费支出按平价收费, 根据以上$100$户居民用户的月均用水量数据, 你能给市政府提出确定居民用户月均用水量标准的建议吗?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018829": { + "id": "018829", + "content": "为了实施``精准扶贫''战略, 农科院试种了甲、乙两个西红柿新品种, 从这两个品种中各任选$5$株, 测量其产量(单位: $\\mathrm{kg}$), 得到如下数据:\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|}\n\\hline 甲 & 60 & 80 & 70 & 90 & 70 \\\\\n\\hline 乙 & 80 & 60 & 70 & 80 & 75 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n利用上述数据, 现从中选出一个品种推荐给农民种植, 应该推荐哪个品种呢?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018830": { + "id": "018830", + "content": "近年来, 我国肥胖人群的规模急速增长, 肥胖人群有很大的心血管安全隐患. 目前, 国际上常用身体质量指数(BMI)来衡量人体肥胖程度以及是否健康, 其计算公式是$\\mathrm{BMI}=\\dfrac{\\text {体重}(\\text {单位: } \\mathrm{kg})}{\\text {身高}^2(\\text {单位: } \\mathrm{m}^2)}$. 中国成人的$\\mathrm{BMI}$数值标准为: $\\mathrm{BMI}<18.5$为偏瘦; $18.5 \\leq \\mathrm{BMI} \\leq 23.9$为正常; $24 \\leq \\mathrm{BMI} \\leq 27.9$为偏胖; $\\mathrm{BMI} \\geq 28$为肥胖.\n为了解某公司员工的身体肥胖情况, 研究人员从公司员工体检数据中, 采用分层随机抽样方法抽取了90名男员工、50名女员工的身高和体重数据, 计算得到他们的 BMI 值如下:\n\\begin{center}\n男员工:\\\\\n\\begin{tabular}{cccccccccc}\n$23.5$ & $21.6$ & $30.6$ & $22.1$ & $23.7$ & $20.6$ & $24.0$ & $23.9$ & $20.8$ & $21.5$ \\\\ \n$22.1$ & $21.6$ & $19.0$ & $20.2$ & $19.6$ & $17.3$ & $17.9$ & $23.4$ & $18.7$ & $23.1$ \\\\ \n$17.3$ & $22.4$ & $20.8$ & $25.1$ & $21.3$ & $27.7$ & $23.5$ & $23.6$ & $19.4$ & $23.1$ \\\\ \n$18.6$ & $24.1$ & $21.3$ & $19.5$ & $18.7$ & $21.0$ & $22.6$ & $16.0$ & $18.0$ & $17.9$ \\\\ \n$22.1$ & $19.3$ & $19.3$ & $22.8$ & $29.0$ & $21.4$ & $22.3$ & $18.8$ & $19.7$ & $27.4$ \\\\ \n$23.5$ & $23.6$ & $30.5$ & $22.3$ & $21.6$ & $17.6$ & $21.5$ & $29.1$ & $25.5$ & $18.7$ \\\\ \n$22.1$ & $18.9$ & $25.8$ & $27.8$ & $35.3$ & $17.5$ & $27.0$ & $19.9$ & $22.2$ & $24.5$ \\\\ \n$18.0$ & $19.0$ & $21.1$ & $21.3$ & $18.7$ & $23.9$ & $20.8$ & $34.2$ & $16.6$ & $19.3$ \\\\ \n$20.9$ & $23.7$ & $23.7$ & $23.0$ & $18.7$ & $27.3$ & $21.2$ & $17.3$ & $23.5$ & $30.1$ \\\\ \n\\end{tabular}\n\\\\女员工:\\\\\n\\begin{tabular}{cccccccccc}\n$21.8$ & $18.2$ & $25.2$ & $28.1$ & $21.5$ & $19.1$ & $25.7$ & $24.4$ & $17.6$ & $20.8$ \\\\ \n$20.5$ & $20.2$ & $17.4$ & $21.6$ & $18.4$ & $20.3$ & $30.8$ & $23.6$ & $23.3$ & $22.8$ \\\\ \n$20.8$ & $16.8$ & $19.0$ & $16.4$ & $18.7$ & $26.1$ & $20.2$ & $17.6$ & $15.4$ & $21.5$ \\\\ \n$19.5$ & $31.6$ & $19.1$ & $20.4$ & $13.9$ & $18.6$ & $16.6$ & $15.9$ & $18.3$ & $18.1$ \\\\ \n$29.7$ & $18.9$ & $16.9$ & $25.8$ & $19.8$ & $18.5$ & $16.0$ & $17.6$ & $19.1$ & $26.5$ \\\\ \n\\end{tabular}\n\\end{center}\n根据上面的数据, 写一份该公司员工肥胖情况的统计分析报告. 要求:\\\\\n(1) 选择合适的图表展示数据;\\\\\n(2) 比较男、女员工在肥胖状况上的差异;\\\\\n(3) 分析公司员工胖瘦程度的整体情况;\\\\\n(4) 提出控制体重的建议.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册统计例题与习题", + "edit": [ + "20230706\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "020001": { "id": "020001", "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",