某学生记录了连续5天每天完成数学作业所用的时间(单位:分钟):35,40,30,45,35。这5天完成作业所用时间的众数和中位数分别是多少?
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本题综合考查了数据的收集、整理与描述(平均数、中位数)、实数运算、一次函数(二元一次方程组应用)以及不等式比较。解题关键在于:首先通过统计方法确定‘高峰阈值’,这需要准确计算平均数和中位数并比较大小;其次利用两个已知点建立一次函数模型,通过解二元一次方程组求出函数表达式;最后代入具体数值求解并做出逻辑判断。题目情境真实,融合了统计与函数知识,要求学生具备较强的综合分析与计算能力,符合困难难度要求。
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[{"id":410,"content":"在一次环保活动中,某班学生收集了可回收垃圾和不可回收垃圾共120千克。已知可回收垃圾比不可回收垃圾多40千克,那么不可回收垃圾有多少千克?","type":"选择题","subject":"数学","grade":"初一","stage":"初中","difficulty":"简单","answer":"A","explanation":"设不可回收垃圾为x千克,则可回收垃圾为(x + 40)千克。根据题意,两者之和为120千克,列出方程:x + (x + 40) = 120。化简得:2x + 40 = 120,移项得:2x = 80,解得:x = 40。因此,不可回收垃圾有40千克。本题考查一元一次方程的实际应用,属于简单难度,符合七年级数学课程要求。","options":[{"id":"A","content":"40千克"},{"id":"B","content":"50千克"},{"id":"C","content":"60千克"},{"id":"D","content":"80千克"}]},{"id":17,"content":"工业革命首先发生在哪个国家?","type":"选择题","subject":"历史","grade":"初二","stage":"初中","difficulty":"简单","answer":"A","explanation":"工业革命首先发生在18世纪的英国。","options":[{"id":"A","content":"英国"},{"id":"B","content":"法国"},{"id":"C","content":"德国"},{"id":"D","content":"美国"}]},{"id":707,"content":"某学生在调查班级同学最喜欢的运动项目时,共收集了30份有效问卷,其中喜欢篮球的有12人,喜欢足球的有8人,喜欢跳绳的有5人,其余同学喜欢乒乓球。那么喜欢乒乓球的同学占全班人数的____(填最简分数)。","type":"填空题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"1\/6","explanation":"总人数为30人,喜欢篮球、足球和跳绳的人数分别为12人、8人和5人,合计为12 + 8 + 5 = 25人。因此喜欢乒乓球的人数为30 - 25 = 5人。喜欢乒乓球的人数占全班人数的比例为5\/30,约分后得到最简分数1\/6。","options":[]},{"id":334,"content":"90°","type":"选择题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"答案待完善","explanation":"解析待完善","options":[]},{"id":691,"content":"某学生测量了家中客厅地面的长和宽,发现长为 4.5 米,宽为 3.2 米。若用边长为 0.3 米的正方形地砖铺满整个地面(不考虑损耗),则至少需要 ___ 块地砖。","type":"填空题","subject":"数学","grade":"初一","stage":"初中","difficulty":"简单","answer":"160","explanation":"首先计算客厅地面的面积:4.5 × 3.2 = 14.4(平方米)。然后计算每块地砖的面积:0.3 × 0.3 = 0.09(平方米)。最后用总面积除以单块地砖面积:14.4 ÷ 0.09 = 160。因为题目要求‘至少需要’且‘铺满’,所以结果为整数 160 块。本题综合考查了有理数的乘除运算和实际问题中的面积计算,属于简单难度。","options":[]},{"id":851,"content":"某学生在绘制班级同学最喜爱的课外活动统计图时,将数据整理成如下表格:阅读占20%,运动占35%,音乐占15%,绘画占___%,其余为其他活动。已知喜欢绘画的人数比喜欢音乐的人数多6人,且班级总人数为60人,那么绘画所占的百分比是____。","type":"填空题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"25","explanation":"首先,根据题意,班级总人数为60人。喜欢音乐的人占15%,即 60 × 15% = 9 人。喜欢绘画的人数比音乐多6人,所以绘画人数为 9 + 6 = 15 人。那么绘画所占的百分比为 (15 ÷ 60) × 100% = 25%。因此,空白处应填写25。","options":[]},{"id":751,"content":"在一次校园环保活动中,某学生收集了若干千克废纸。若每千克废纸可生产再生纸0.8千克,则该学生收集的废纸共可生产再生纸____千克。已知他最终生产出的再生纸比收集的废纸少6千克,则他最初收集的废纸是____千克。","type":"填空题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"0.8x, 30","explanation":"设该学生收集的废纸为x千克。根据题意,每千克废纸可生产0.8千克再生纸,因此可生产的再生纸为0.8x千克。又知再生纸比废纸少6千克,即x - 0.8x = 6,解得0.2x = 6,x = 30。因此,第一空填0.8x(表示再生纸质量与废纸质量的关系),第二空填30(表示收集的废纸质量)。本题综合考查了一元一次方程的建立与求解,以及有理数的运算,符合七年级数学课程要求。","options":[]},{"id":18,"content":"世界上面积最大的洲是?","type":"选择题","subject":"地理","grade":"初一","stage":"初中","difficulty":"简单","answer":"A","explanation":"亚洲是世界上面积最大、人口最多的大洲。","options":[{"id":"A","content":"亚洲"},{"id":"B","content":"非洲"},{"id":"C","content":"北美洲"},{"id":"D","content":"南美洲"}]},{"id":1928,"content":"在平面直角坐标系中,点A(2, 3)绕原点逆时针旋转90°后得到点B,再将点B向右平移4个单位,得到点C。若点C的坐标为(a, b),则a + b的值为____。","type":"填空题","subject":"数学","grade":"七年级","stage":"初中","difficulty":"困难","answer":"5","explanation":"点A(2,3)绕原点逆时针旋转90°得B(-3,2),再向右平移4个单位得C(1,2),故a=1, b=2,a+b=3。","options":[]},{"id":484,"content":"众数 < 中位数 < 平均数","type":"选择题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"待完善","explanation":"解析待完善","options":[]}]