GMAT数学常用概念
<p> 1.<span word="mode">mode</span>(众数) 1.<span word="mode">mode</span>(众数) 1.<span word="mode">mode</span>(众数) 一堆数中出现频率最高的一个或几个数 ( <span word="e">e</span>.<span word="g">g</span>. <span word="mode">mode</span> <span word="of">of</span> 1,1,1,2,3,0,0,0,5 <span word="is">is</span> 1 <span word="and">and</span> 0 ) 2.<span word="range">range</span>(值域) 一堆数中最大和最小数之差 ( <span word="e">e</span>.<span word="g">g</span>. <span word="range">range</span> <span word="of">of</span> 1,1,2,3,5 <span word="is">is</span> 5-1=4 ) 3.<span word="mean">mean</span>(平均数) <span word="arithmatic">arithmatic</span> <span word="mean">mean</span>(算术平均数) (不用解释了吧?) <span word="geometric">geometric</span> <span word="mean">mean</span> (几何平均数) <span word="n">n</span>个数之积的<span word="n">n</span>次方根 4.<span word="median">median</span>(中数) 将一堆数排序之后，正中间的一个数(奇数个数字)， 或者中间两个数的平均数(偶数个数字)( <span word="e">e</span>.<span word="g">g</span>. <span word="median">median</span> <span word="of">of</span> 1,7,4,9,2,2,2,2,2,5,8 <span word="is">is</span> 2 // <span word="median">median</span> <span word="of">of</span> 1,7,4,9,2,5 <span word="is">is</span> (5+7)/2=6 ) 5.<span word="standard">standard</span> <span word="error">error</span>(标准偏差) 一堆数中，每个数与平均数的差的绝对值之和，除以这堆数的个数(<span word="n">n</span>)<span word="e">e</span>.<span word="g">g</span>. <span word="standard">standard</span> <span word="error">error</span> <span word="of">of</span> 0,2,5,7,6 <span word="is">is</span>: (|0-4|+|2-4|+|5-4|+|7-4|+|6-4|)/5=2.4 ) 6.<span word="standard">standard</span> <span word="variation">variation</span> 一堆数中，每个数与平均数之差的平方之和，再除以<span word="ne">ne</span>.<span word="g">g</span>. <span word="standard">standard</span> <span word="variation">variation</span> <span word="of">of</span> 0,2,5,7,6 <span word="is">is</span>:_ 2 2 2 2 2_|_(0-4) +(2-4)+(5-4)+(7-4)+(6-4)_|/5=6.8</p><p> 7.<span word="standard">standard</span> <span word="deviation">deviation</span> 就是<span word="standard">standard</span> <span word="variation">variation</span>的平方根 标准方差的公式：<span word="d">d</span>^2=[(<span word="a">a</span>1-<span word="a">a</span>)^2+(<span word="a">a</span>2-<span word="a">a</span>)^2+....+(<span word="an">an</span>-<span word="a">a</span>)^2 ]/<span word="n">n</span> <span word="d">d</span> 为标准方差 8. 三角形 余玄定理<span word="C">C</span>^2=<span word="A">A</span>^2+<span word="B">B</span>^2-2<span word="ABCOSt">ABCOSt</span> <span word="t">t</span>为<span word="AB">AB</span>两条线间的夹角 9. <span word="Y">Y</span>=<span word="k">k</span>1<span word="X">X</span>+<span word="B">B</span>1,<span word="Y">Y</span>=<span word="k">k</span>2<span word="X">X</span>+<span word="B">B</span>2，两线垂直的条件为<span word="K">K</span>1<span word="K">K</span>2=-1 10. 熟悉一下根号2、3、5的值 <span word="sqrt">sqrt</span>(2)=1.414 <span word="sqrt">sqrt</span>(3)=1.732 <span word="sqrt">sqrt</span>(5)=2.236 <span word="sqrt">sqrt</span>(10)=3.162 11. <span word="a">a</span> <span word="if">if</span> <span word="only">only</span> <span word="b">b</span>: <span word="b">b</span>-<span word="a">a</span> 12.概率<span word="P">P</span>=满足某个条件的所有可能情况数量/所有可能情况数量性质 0=1 <span word="a">a</span>1,<span word="a">a</span>2为两两不相容的事件(即发生了<span word="a">a</span>1，就不会发生<span word="a">a</span>2) <span word="P">P</span>(<span word="a">a</span>1或<span word="a">a</span>2)=<span word="P">P</span>(<span word="a">a</span>1)+<span word="P">P</span>(<span word="a">a</span>2) <span word="a">a</span>1,<span word="a">a</span>2不是两两不相容的事件，分别用集合<span word="A">A</span>和集合<span word="B">B</span>来表示 即集合<span word="A">A</span>与集合<span word="B">B</span>有交集，表示为<span word="A">A</span>*<span word="B">B</span> (<span word="a">a</span>1发生且<span word="a">a</span>2发生) 集合<span word="A">A</span>与集合<span word="B">B</span>的并集，表示为<span word="A">A</span> <span word="U">U</span> <span word="B">B</span> (<span word="a">a</span>1发生或<span word="a">a</span>2发生) 则 <span word="P">P</span>(<span word="A">A</span> <span word="U">U</span> <span word="B">B</span>)= <span word="P">P</span>(<span word="A">A</span>)+<span word="P">P</span>(<span word="B">B</span>)-<span word="P">P</span>(<span word="A">A</span>*<span word="B">B</span>).........公式2 还有就是条件概率： 考虑的是事件<span word="A">A</span>已发生的条件下事件<span word="B">B</span>发生的概率 定义：设<span word="A">A</span>，<span word="B">B</span>是两个事件，且<span word="P">P</span>(<span word="A">A</span>)0,称 <span word="P">P</span>(<span word="B">B</span>|<span word="A">A</span>)=<span word="P">P</span>(<span word="A">A</span>*<span word="B">B</span>)/<span word="P">P</span>(<span word="A">A</span>) 一堆数中出现频率最高的一个或几个数 ( <span word="e">e</span>.<span word="g">g</span>. <span word="mode">mode</span> <span word="of">of</span> 1,1,1,2,3,0,0,0,5 <span word="is">is</span> 1 <span word="and">and</span> 0 ) 2.<span word="range">range</span>(值域) 一堆数中最大和最小数之差 ( <span word="e">e</span>.<span word="g">g</span>. <span word="range">range</span> <span word="of">of</span> 1,1,2,3,5 <span word="is">is</span> 5-1=4 ) 3.<span word="mean">mean</span>(平均数) <span word="arithmatic">arithmatic</span> <span word="mean">mean</span>(算术平均数) (不用解释了吧?) <span word="geometric">geometric</span> <span word="mean">mean</span> (几何平均数) <span word="n">n</span>个数之积的<span word="n">n</span>次方根 4.<span word="median">median</span>(中数) 将一堆数排序之后，正中间的一个数(奇数个数字)， 或者中间两个数的平均数(偶数个数字)( <span word="e">e</span>.<span word="g">g</span>. <span word="median">median</span> <span word="of">of</span> 1,7,4,9,2,2,2,2,2,5,8 <span word="is">is</span> 2 // <span word="median">median</span> <span word="of">of</span> 1,7,4,9,2,5 <span word="is">is</span> (5+7)/2=6 ) 5.<span word="standard">standard</span> <span word="error">error</span>(标准偏差) 一堆数中，每个数与平均数的差的绝对值之和，除以这堆数的个数(<span word="n">n</span>)<span word="e">e</span>.<span word="g">g</span>. <span word="standard">standard</span> <span word="error">error</span> <span word="of">of</span> 0,2,5,7,6 <span word="is">is</span>: (|0-4|+|2-4|+|5-4|+|7-4|+|6-4|)/5=2.4 ) 6.<span word="standard">standard</span> <span word="variation">variation</span> 一堆数中，每个数与平均数之差的平方之和，再除以<span word="ne">ne</span>.<span word="g">g</span>. <span word="standard">standard</span> <span word="variation">variation</span> <span word="of">of</span> 0,2,5,7,6 <span word="is">is</span>:_ 2 2 2 2 2_|_(0-4) +(2-4)+(5-4)+(7-4)+(6-4)_|/5=6.8 7.<span word="standard">standard</span> <span word="deviation">deviation</span> 就是<span word="standard">standard</span> <span word="variation">variation</span>的平方根 标准方差的公式：<span word="d">d</span>^2=[(<span word="a">a</span>1-<span word="a">a</span>)^2+(<span word="a">a</span>2-<span word="a">a</span>)^2+....+(<span word="an">an</span>-<span word="a">a</span>)^2 ]/<span word="n">n</span> <span word="d">d</span> 为标准方差 8. 三角形 余玄定理<span word="C">C</span>^2=<span word="A">A</span>^2+<span word="B">B</span>^2-2<span word="ABCOSt">ABCOSt</span> <span word="t">t</span>为<span word="AB">AB</span>两条线间的夹角 9. <span word="Y">Y</span>=<span word="k">k</span>1<span word="X">X</span>+<span word="B">B</span>1,<span word="Y">Y</span>=<span word="k">k</span>2<span word="X">X</span>+<span word="B">B</span>2，两线垂直的条件为<span word="K">K</span>1<span word="K">K</span>2=-1 10. 熟悉一下根号2、3、5的值 <span word="sqrt">sqrt</span>(2)=1.414 <span word="sqrt">sqrt</span>(3)=1.732 <span word="sqrt">sqrt</span>(5)=2.236 <span word="sqrt">sqrt</span>(10)=3.162 11. <span word="a">a</span> <span word="if">if</span> <span word="only">only</span> <span word="b">b</span>: <span word="b">b</span>-<span word="a">a</span> 12.概率<span word="P">P</span>=满足某个条件的所有可能情况数量/所有可能情况数量性质 0=1 <span word="a">a</span>1,<span word="a">a</span>2为两两不相容的事件(即发生了<span word="a">a</span>1，就不会发生<span word="a">a</span>2) <span word="P">P</span>(<span word="a">a</span>1或<span word="a">a</span>2)=<span word="P">P</span>(<span word="a">a</span>1)+<span word="P">P</span>(<span word="a">a</span>2) <span word="a">a</span>1,<span word="a">a</span>2不是两两不相容的事件，分别用集合<span word="A">A</span>和集合<span word="B">B</span>来表示 即集合<span word="A">A</span>与集合<span word="B">B</span>有交集，表示为<span word="A">A</span>*<span word="B">B</span> (<span word="a">a</span>1发生且<span word="a">a</span>2发生) 集合<span word="A">A</span>与集合<span word="B">B</span>的并集，表示为<span word="A">A</span> <span word="U">U</span> <span word="B">B</span> (<span word="a">a</span>1发生或<span word="a">a</span>2发生) 则 <span word="P">P</span>(<span word="A">A</span> <span word="U">U</span> <span word="B">B</span>)= <span word="P">P</span>(<span word="A">A</span>)+<span word="P">P</span>(<span word="B">B</span>)-<span word="P">P</span>(<span word="A">A</span>*<span word="B">B</span>).........公式2 还有就是条件概率： 考虑的是事件<span word="A">A</span>已发生的条件下事件<span word="B">B</span>发生的概率 定义：设<span word="A">A</span>，<span word="B">B</span>是两个事件，且<span word="P">P</span>(<span word="A">A</span>)0,称 <span word="P">P</span>(<span word="B">B</span>|<span word="A">A</span>)=<span word="P">P</span>(<span word="A">A</span>*<span word="B">B</span>)/<span word="P">P</span>(<span word="A">A</span>)</p>
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