四分位差(quartile deviation)，也称为内距或四分间距(inter-quartile range)，它是上四分位数(QU，即位于75%)与下四分位数(QL，即位于25%)的差。计算公式.
将所有数值按大小顺序排列并分成四等份，处于三个分割点位置的得分就是四分位数。最小的四分位数称为下四分位数，所有数值中，有四分之一小于下四分位数，四分之.
把一个数组从小到大排序，中位数是中间那个数上四分位数是排在1/4的那个数下四分位数是排在3/4的那个数如果用EXCEL计算($A$1:$A$9为数列)最小值=QUARTILE.
哪位大神可以给我详细说一下4分位数的具体求法。。我举一个例子。。这里。
四分位数(Quartile)，即统计学中，把所有数值由小到大排列并分成四等份，处于三个分割点位置的得分就是四分位数。第一四分位数 (Q1)，又称“较小四分位数”，.
有一个函数是专门求四分位数的。=quartile(a1:a10,1)
四分位数和中位数是同一类的概念，将一组数据按大小顺序排列后，按数据的个数分成四份，而这三个分割点上的数值，就称四分位数，具体分别称为：第1四分位数，第2.
统计学中，把所有数值由小到大排列并分成四等份，处于三个分割点位置的数值就是四分位数。第一四分位数 (Q1)，又称“较小四分位数”，等于该样本中所有数值由.
晕死，这个貌似不是佛法，是财务方法吧。——你看这样解释对不对？——四分位法是zhidao统计学的一种分析方法。简单地说，就是将全部数据从小到大排列，正好排 列.
众数从=10中位数=10.5下四分位数=9.25上四分位数=13.5平均数=11.1667标准差=2.7579
如题，是一个数字，比如10，还是一个范围，比如2-12？怎么求中四分位范围。
四分位数是将全部数据分成相等的四部分，其中每部分包括25%的数据，处在各分位点的数值就是四分位数。  四分位数作为分位数的一种形式，在统计中有着十分重要的.
要计算过程，怎么算出来的？
从小到大排序：17,19,20,22,23,23,,24,25 下四分位数等于该样本中所有数值由小到大排列后第25%的数字，即第2个数19。上四分位数等于该样本中所有数值由小到大排列.
四分位数(Quartile)，即统计学中，把所有数值由小到大排列并分成四等份，处于三个分割点位置的数值就是四分位数。  第一四分位数 (Q1)，又称“较小四分位数”.
4分位数有两个25%和75%把一组数据按照大小的顺序排列其中前者的求法是，这个数的前面占全部数据的25%后者是这个数的前面占全部数据的75%
1/4的我知道，3/4怎么算
使用excel中quartile的函数.语法(array,quart).参数array为需要求得四分位数值的数组或数字引用区域，quart决定返回哪个四分位值.如果quart取0,1,2,3或4则函数quartile返.
四分位差是上四分位数与下四分位数之差，也称为内距或四分间距。它主要用于测度顺序数据的离散程度。当然对于数值型数据也可以计算四分位差，但它不适合于分类数.
lz你好IQR = Q3 ? Q1 四分位距通常是用来构建箱形图，以及对概率分布的简要图表概述。对一个对称性分布数据(其中位数必然等于第三四分位数与第一四分位数的算术.
75、85、87、95、99、100、101、105、113、115、125  第一个四分位数：。
75 85 87 |95 99、100、101 105 | 113 115 125 分4段，100为中点 Q1=(87+95)/2=91 Q2=100 Q3=(105+113)/2=109 四分位数：将所有数值按大小顺序排列并分成四等份，.
嗯，最好举例说一下说得明了一点，用话自己的话解释一下，容易看懂一些各。
英语是quartile？ 你要问的是lower quartile和 upper quartile？将所有的样本从小到大排列，并分成四等份，处于三个分割点位置(是一个数值)的得分就是四分位数。最小.
下四分位数怎么求啊还有upper extreme和 lower extreme 怎么求，本人在美国。
四分位数(Quartile)，即统计学中，把所有数值由小到大排列并分成四等份，处于三个分割点位置的得分就是四分位数。 第一四分位数 (Q1)，又称“较小四分位数”，.

四分位数和百分位数
 四分位数 (Quartiles)
To calculate a quartile of a sample is in theory easy, and is much like calculating the median. The difficult part is the implementation; contrary to calculating the median, there exists no single specific method that stands above the rest or can be considered the "best" method among the about twenty known methods for calculating a quartile. The "best" method will be the method that fits the purpose or - in some areas - is considered a de-facto standard.
 
 从理论上说，计算样本的四分位数很容易，并且很像计算中位数。 困难的部分是执行； 与计算中位数相反，在计算四分位数的大约二十种已知方法中，没有任何一种特定的方法可以胜过其他方法，也可以认为是“最佳”方法。 “最佳”方法将是适合目的的方法，或者在某些方面被认为是事实上的标准。 
Why, how, and when to calculate quartiles using which method is outside the scope of this article. Many articles and even books covering this have been written. However, the day you face the task to calculate a quartile using some specific method, the functions here will help you.
 
 为什么，如何以及何时 使用哪种方法来计算四分位数不在本文的讨论范围之内。 已经写了许多有关此的文章，甚至书籍。 但是，当您面对使用某种特定方法计算四分位数的任务时，此处的功能将为您提供帮助。 
 方法 (Methods)
It is quite hard to even obtain a list of known methods for calculating a quartile, not to say proven results from these. The best source, I've located (see bottom of the article), is quite old and lists 14 methods:
 
 甚至很难获得已知的计算四分位数的方法的列表，更不用说从中得出的可靠结果。 我找到的最好的资源（请参阅本文的底部）已经很旧了，并列出了14种方法： 
 
  
The additional six methods, I have located here and there. Unfortunately, the sources have vanished.
 
 我已经在这里和那里找到了另外六个方法。 不幸的是，消息来源已经消失了。 
If you are aware of any good source, please add a comment to the article.
 
 如果您知道任何好的来源，请在文章中添加评论。 
The methods have been collected as an enum including as in-line comments their names, applications, and sources, together with their basic calculation methods for the first and the third quartile (the second is always calculated as the median):
 
 这些方法已作为一个枚举收集，其中包括它们的名称，应用程序和来源以及它们在第一和第三四分位数中的基本计算方法（作为内联注释，以内嵌注释）（ 第二个始终以中位数计算）： 
' Quartile calculation methods.
' Values equal those listed in the source. See function Quartile.
'
' Common names of variables used in calculation formulas.
'
' L: Q1, Lower quartile.
' H: Q3, Higher quartile.
' M: Q2, Median (not used here).
' n: Count of elements.
' p: Calculated position of quartile.
' j: Element of dataset.
' g: Decimal part of p to be used for interpolation between j and j+1.
'
Public Enum ApQuartileMethod
    [_First] = 1
    
    ' Basic calculation methods.
    
    ' Step. Mendenhall and Sincich method.
    '   SAS #3.
    '   Round up to actual element of dataset.
    '   L:  -Int(-n/4)
    '   H: n-Int(-n/4)
    apMendenhallSincich = 1
    
    ' Average step.
    '   SAS #5, Minitab (%DESCRIBE), GLIM (percentile).    '
    '   Add bias of one on basis of n/4.
    '   L:   CLng((n+2)/2)/2
    '   H: n-Clng((n+2)/2)/2
    '   Note:
    '       Replaces these original formulas that don't return the expected values.
    '   L:   (Int((n+1)/4)+Int(n/4))/2+1
    '   H: n-(Int((n+1)/4)+Int(n/4))/2+1
    apAverage = 2
    
    ' Nearest integer to np.
    '   SAS #2.
    '   Round to nearest integer on basis of n/4.
    '   L:   CLng(n/4)
    '   H: n-CLng(n/4)
    '   Note:
    '       Replaces these original formulas that don't return the expected values.
    '   L:   Int((n+2)/4)
    '   H: n-Int((n+2)/4)
    apNearestInteger = 3
    
    ' Parzen method.
    '   Method 1 with interpolation.
    '   SAS #1.
    '   L: n/4
    '   H: 3n/4
    apParzen = 4
    
    ' Hazen method.
    '   Values midway between method 1 steps.
    '   GLIM (interpolate).
    '   Wikipedia method 3.
    '   Add bias of 2, don't round to actual element of dataset.
    '   L: (n+2)/4
    '   H: 3(n+2)/4-1
    apHazen = 5
    
    ' Weibull method.
    '   SAS #4. Minitab (DECRIBE), SPSS, BMDP, Excel exclusive.
    '   Add bias of 1, don't round to actual element of dataset.
    '   L: (n+1)/4
    '   H: 3(n+1)/4
    apWeibull = 6
    
    ' Freund, J. and Perles, B., Gumbell method.
    '   S-PLUS, R, Excel legacy, Excel inclusive, Star Office Calc.
    '   Add bias of 3, don't round to actual element of dataset.
    '   L: (n+3)/4
    '   H: (3n+1)/4
    apFreundPerlesGumbell = 7
    
    ' Median Position.
    '   Median unbiased.
    '   L: (3n+5)/12
    '   H: (9n+7)/12
    apMedianPosition = 8
    
    ' Bernard and Bos-Levenbach.
    '   L: (n/4)+0.4
    '   H: (3n/4)/+0.6
    '   Note:
    '       Reference claims L to be (n/4)+0.31.
    apBernardBosLevenbach = 9
    
    ' Blom's Plotting Position.
    '   Better approximation when the distribution is normal.
    '   L: (4n+7)/16
    '   H: (12n+9)/16
    apBlom = 10
    
    ' Moore's first method.
    '   Add bias of one half step.
    '   L: (n+0.5)/4
    '   H: n-(n+0.5)/4
    apMooreFirst = 11
    
    ' Moore's second method.
    '   Add bias of one or two steps on basis of (n+1)/4.
    '   L:   (Int((n+1)/4)+Int(n/4))/2+1
    '   H: n-(Int((n+1)/4)+Int(n/4))/2+1
    apMooreSecond = 12
    
    ' John Tukey's method.
    '   Include median from odd dataset in dataset for quartile.
    '   Wikipedia method 2.
    '   L:   (1-Int(-n/2))/2
    '   H: n-(-1-Int(-n/2))/2
    apTukey = 13
    
    ' Moore and McCabe (M & M), variation of John Tukey's method.
    '   TI-83.
    '   Wikipedia method 1.
    '   Exclude median from odd dataset in dataset for quartile.
    '   L:   (Int(n/2)+1)/2
    '   H: n-(Int(n/2)-1)/2
    apTukeyMooreMcCabe = 14
    
    ' Additional variations between Weibull's and Hazen's methods, from
    '   (i-0.000)/(n+1.00)
    ' to
    '   (i-0.500)/(n+0.00)
    
    ' Variation of Weibull.
    '   L: n(n/4-0)/(n+1)
    '   H: n(3n/4-0)/(n+1)
    apWeibullVariation = 15
    
    ' Variation of Blom.
    '   L: n(n/4-3/8)/(n+1/4)
    '   H: n(3n/4-3/8)/(n+1/4)
    apBlomVariation = 16
    
    ' Variation of Tukey.
    '   L: n(n/4-1/3)/(n+1/3)
    '   H: n(3n/4-1/3)/(n+1/3)
    apTukeyVariation = 17
    
    ' Variation of Cunnane.
    '   L: n(n/4-2/5)/(n+1/5)
    '   H: n(3n/4-2/5)/(n+1/5)
    apCunnaneVariation = 18
    
    ' Variation of Gringorten.
    '   L: n(n/4-0.44)/(n+0.12)
    '   H: n(3n/4-0.44)/(n+0.12)
    apGringortenVariation = 19
    
    ' Variation of Hazen.
    '   L: n(n/4-1/2)/n
    '   H: n(3n/4-1/2)/n
    apHazenVariation = 20
    
    [_Last] = 20
End Enum 
The actual calculation methods have been tweaked a little to fit VBA and to correct for weird results when a sample consists of very few elements.
 
 实际计算方法已进行了一些调整，以适合VBA并在样本包含很少元素的情况下纠正怪异的结果。 
 功能 (Functions)
The main function is named Quartile and has the native domain aggregate functions, DAvg etc., in mind as it takes an Expression, a Domain, and a Criteria (filter) as arguments. Other arguments are the quartile Part to return and the Method to use:
 
 主函数被命名为四分位数，并具有本机域聚合函数DAvg等，因为它需要一个表达式，一个域和一个条件 （过滤器）作为参数。 其他参数是要返回的四分位数部分和要使用的方法 ： 
Expression: Name of the field or an expression to analyse.
Domain    : Name of the source/query, or an SQL select query, to analyse.
Criteria  : Optional. A filter expression for Domain.
Part      : Optional. Which median/quartile or min/max value to return.
            Default is the median value.
Method    : Optional. Method for calculation of lower/higher quartile.
            Default is the method by Freund, Perles, and Gumbell (Excel).  
The function can be regarded to have four main parts:
 
 该功能可以认为具有四个主要部分： 
Build the SQL to retrieve the ordered samples
 构建SQL以检索有序的样本 
 
 
Calculate either the minimum or maximum value, the first or third quartile, or the median
 计算最小值或最大值，第一或第三四分位数或中位数 
 
 
Prepare for interpolation
 准备插值 
 
 
Calculate the final output
 计算最终输出 
 
Public Function Quartile( _
    ByVal Expression As String, _
    ByVal Domain As String, _
    Optional ByVal Criteria As String, _
    Optional ByVal Part As ApQuartilePart = ApQuartilePart.apMedian, _
    Optional ByVal Method As ApQuartileMethod = ApQuartileMethod.apFreundPerlesGumbell) _
    As Double
  
    ' SQL.
    Const SqlMask           As String = "Select {0} From {1} {2}"
    Const SqlLead           As String = "Select "
    Const SubMask           As String = "({0}) As T"
    Const FilterMask        As String = "Where {0} "
    Const OrderByMask       As String = "Order By {0} Asc"
    
    Dim Records     As DAO.Recordset
    
    Dim Sql         As String
    Dim SqlSub      As String
    Dim Filter      As String
    Dim Count       As Long     ' n.
    Dim Position    As Double   ' p.
    Dim Element     As Long     ' j.
    Dim Interpolate As Double   ' g.
    Dim ValueOne    As Double
    Dim ValueTwo    As Double
    Dim Value       As Double
    
    ' Return default quartile part if choice of part is
    ' outside the range of ApQuartilePart.
    If Not IsQuartilePart(Part) Then
        Part = ApQuartilePart.apMedian
    End If
    
    ' Use a default calculation method if choice of method is
    ' outside the range of ApQuartileMethod.
    If Not IsQuartileMethod(Method) Then
        Method = ApQuartileMethod.apFreundPerlesGumbell
    End If
    
    If Domain <> "" And Expression <> "" Then
        ' Build SQL to lookup values.
        If InStr(1, LTrim(Domain), SqlLead, vbTextCompare) = 1 Then
            ' Domain is an SQL expression.
            SqlSub = Replace(SubMask, "{0}", Domain)
        Else
            ' Domain is a table or query name.
            SqlSub = Domain
        End If
        If Trim(Criteria) <> "" Then
            ' Build Where clause.
            Filter = Replace(FilterMask, "{0}", Criteria)
        End If
        ' Build final SQL.
        Sql = Replace(Replace(Replace(SqlMask, "{0}", Expression), "{1}", SqlSub), "{2}", Filter) & _
            Replace(OrderByMask, "{0}", Expression)
        Set Records = CurrentDb.OpenRecordset(Sql, dbOpenSnapshot)
      
        With Records
            If Not .EOF = True Then
                If Part = ApQuartilePart.apMinimum Then
                    ' No need to count records.
                    Count = 1
                Else
                    ' Count records.
                    .MoveLast
                    Count = .RecordCount
                End If
                Select Case Part
                    Case ApQuartilePart.apMinimum
                        ' Current record is first record.
                        ' Read value of this record.
                    Case ApQuartilePart.apMaximum
                        ' Current record is last record.
                        ' Read value of this record.
                    Case ApQuartilePart.apMedian
                        ' Locate position of median.
                        Position = (Count + 1) / 2
                    Case ApQuartilePart.apLower
                        Select Case Method
                            Case ApQuartileMethod.apMendenhallSincich
                                Position = -Int(-Count / 4)
                            Case ApQuartileMethod.apAverage
                                Position = CLng((Count + 2) / 2) / 2
                            Case ApQuartileMethod.apNearestInteger
                                Position = CLng(Count / 4)
                            Case ApQuartileMethod.apParzen
                                Position = Count / 4
                            Case ApQuartileMethod.apHazen
                                Position = (Count + 2) / 4
                            Case ApQuartileMethod.apWeibull
                                Position = (Count + 1) / 4
                            Case ApQuartileMethod.apFreundPerlesGumbell
                                Position = (Count + 3) / 4
                            Case ApQuartileMethod.apMedianPosition
                                Position = (3 * Count + 5) / 12
                            Case ApQuartileMethod.apBernardBosLevenbach
                                Position = (Count / 4) + 0.4
                            Case ApQuartileMethod.apBlom
                                Position = (4 * Count + 7) / 16
                            Case ApQuartileMethod.apMooreFirst
                                Position = (Count + 0.5) / 4
                            Case ApQuartileMethod.apMooreSecond
                                Position = (Int((Count + 1) / 4) + Int(Count / 4)) / 2 + 1
                            Case ApQuartileMethod.apTukey
                                Position = (1 - Int(-Count / 2)) / 2
                            Case ApQuartileMethod.apTukeyMooreMcCabe
                                Position = (Int(Count / 2) + 1) / 2
                            Case ApQuartileMethod.apWeibullVariation
                                Position = Count * (Count / 4) / (Count + 1)
                            Case ApQuartileMethod.apBlomVariation
                                Position = Count * (Count / 4 - 3 / 8) / (Count + 1 / 4)
                            Case ApQuartileMethod.apTukeyVariation
                                Position = Count * (Count / 4 - 1 / 3) / (Count + 1 / 3)
                            Case ApQuartileMethod.apCunnaneVariation
                                Position = Count * (Count / 4 - 2 / 5) / (Count + 1 / 5)
                            Case ApQuartileMethod.apGringortenVariation
                                Position = Count * (Count / 4 - 0.44) / (Count + 0.12)
                            Case ApQuartileMethod.apHazenVariation
                                Position = Count * (Count / 4 - 1 / 2) / Count
                        End Select
                    Case ApQuartilePart.apUpper
                        ' Default position for very low counts for several methods
                        Position = Count
                        Select Case Method
                            Case ApQuartileMethod.apMendenhallSincich
                                If Count > 2 Then
                                    Position = Count - (-Int(-Count / 4))
                                End If
                            Case ApQuartileMethod.apAverage
                                If Count > 2 Then
                                    Position = Count - CLng((Count + 2) / 2) / 2
                                End If
                            Case ApQuartileMethod.apNearestInteger
                                Position = Count - CLng(Count / 4)
                            Case ApQuartileMethod.apParzen
                                Position = 3 * Count / 4
                            Case ApQuartileMethod.apHazen
                                If Count > 1 Then
                                    Position = 3 * (Count + 2) / 4 - 1
                                End If
                            Case ApQuartileMethod.apWeibull
                                If Count > 2 Then
                                    Position = 3 * (Count + 1) / 4
                                End If
                            Case ApQuartileMethod.apFreundPerlesGumbell
                                Position = (3 * Count + 1) / 4
                            Case ApQuartileMethod.apMedianPosition
                                If Count > 2 Then
                                    Position = (9 * Count + 7) / 12
                                End If
                            Case ApQuartileMethod.apBernardBosLevenbach
                                If Count > 2 Then
                                    Position = (3 * Count / 4) + 0.6
                                End If
                            Case ApQuartileMethod.apBlom
                                If Count > 2 Then
                                    Position = (12 * Count + 9) / 16
                                End If
                            Case ApQuartileMethod.apMooreFirst
                                Position = Count - (Count + 0.5) / 4
                            Case ApQuartileMethod.apMooreSecond
                                ' Basic calculation method. Will fail for 2 or 3 elements.
                                '   Position = Count - (Int((Count + 1) / 4) + Int(Count / 4)) / 2 + 1
                                ' Calculation method adjusted to accept 2 or 3 elements.
                                Position = Count - (Int((Count + Int((Count * 2) / (Count + 4))) / 4) + Int(Count / 4)) / 2 + 1
                            Case ApQuartileMethod.apTukey
                                Position = Count - (-1 - Int(-Count / 2)) / 2
                            Case ApQuartileMethod.apTukeyMooreMcCabe
                                If Count > 1 Then
                                    Position = Count - (Int(Count / 2) - 1) / 2
                                End If
                            Case ApQuartileMethod.apWeibullVariation
                                Position = Count * (3 * Count / 4) / (Count + 1)
                            Case ApQuartileMethod.apBlomVariation
                                Position = Count * (3 * Count / 4 - 3 / 8) / (Count + 1 / 4)
                            Case ApQuartileMethod.apTukeyVariation
                                Position = Count * (3 * Count / 4 - 1 / 3) / (Count + 1 / 3)
                            Case ApQuartileMethod.apCunnaneVariation
                                Position = Count * (3 * Count / 4 - 2 / 5) / (Count + 1 / 5)
                            Case ApQuartileMethod.apGringortenVariation
                                Position = Count * (3 * Count / 4 - 0.44) / (Count + 0.12)
                            Case ApQuartileMethod.apHazenVariation
                                Position = Count * (3 * Count / 4 - 1 / 2) / Count
                        End Select
                End Select
                Select Case Part
                    Case ApQuartilePart.apMinimum, ApQuartilePart.apMaximum
                        ' Read current row.
                    Case Else
                        .MoveFirst
                        ' Find position of first observation to retrieve.
                        ' If Element is 0, then upper position is first record.
                        ' If Element is not 0 and position is not an integer, then
                        ' read the next observation too.
                        Element = Fix(Position)
                        Interpolate = Position - Element
                        If Count = 1 Then
                            ' Nowhere else to move.
                            If Interpolate < 0 Then
                                ' Prevent values to be created by extrapolation beyond zero from observation one
                                ' for these methods:
                                '   ApQuartileMethod.apBlomVariation
                                '   ApQuartileMethod.apTukeyVariation
                                '   ApQuartileMethod.apCunnaneVariation
                                '   ApQuartileMethod.apGringortenVariation
                                '   ApQuartileMethod.apHazenVariation
                                '
                                ' Comment this line out, if reading by extrapolation *is* requested.
                                Interpolate = 0
                            End If
                        ElseIf Element > 1 Then
                            ' Move to the record to read.
                            .Move Element - 1
                            ' Special case for apMooreSecond and upper quartile for 2 and 3 elements.
                            If .EOF Then
                                .MoveLast
                            End If
                        End If
                End Select
                ' Retrieve value from first observation.
                ValueOne = .Fields(0).Value
          
                Select Case Part
                    Case ApQuartilePart.apMinimum, ApQuartilePart.apMaximum
                        Value = ValueOne
                    Case Else
                        If Interpolate = 0 Then
                            ' Only one observation to read.
                            If Element = 0 Then
                                ' Return 0.
                            Else
                                Value = ValueOne
                            End If
                        Else
                            If Element = 0 Or Element = Count Then
                                ' No first/last observation to retrieve.
                                ValueTwo = ValueOne
                                If ValueOne > 0 Then
                                    ' Use 0 as other observation.
                                    ValueOne = 0
                                Else
                                    ValueOne = 2 * ValueOne
                                End If
                            Else
                                ' Move to next observation.
                                .MoveNext
                                ' Retrieve value from second observation.
                                ValueTwo = .Fields(0).Value
                            End If
                            ' For positive values interpolate between 0 and ValueOne.
                            ' For negative values interpolate between 2 * ValueOne and ValueOne.
                            ' Calculate quartile using linear interpolation.
                            Value = ValueOne + Interpolate * CDec(ValueTwo - ValueOne)
                        End If
                End Select
            End If
            .Close
        End With
    End If
      
    Quartile = Value

End Function 
Two important features are, that the Domain argument can be an SQL select query, and the samples in the passed records do not have to be sorted. The function will itself take care of sorting the samples. 
 
 两个重要功能是，Domain参数可以是SQL select查询 ，并且传递记录中的样本不必排序 。 该函数本身将负责对样本进行排序。 
Thus, typical usages can be as listed here where the resulting SQL has been included for better understanding of the parsing of the Domain argument done by the function:
 
 因此，典型用法可以列在此处，其中包括了生成SQL，以更好地理解函数完成的Domain参数的解析： 
' Example calls and the internally generated SQL:
'
'   With fieldname as expression, table (or query) as domain, no filter, and default sorting:
'       Q1 = Quartile("Data", "Observation", , apFirst, apFreundPerlesGumbell)
'       Select Data From Observation Order By Data Asc
'
'   With two fieldnames as expression, table (or query) as domain, no filter, and sorting on two fields:
'       Q1 = Quartile("Data, Step", "Observation", , apFirst, apFreundPerlesGumbell)
'       Select Data, Step From Observation Order By Data, Step Asc
'
'   With fieldname as expression, SQL as domain, no filter, and default sorting:
'       Q1 = Quartile("Data", "Select Data From Observation", , apFirst, apFreundPerlesGumbell)
'       Select Data From (Select Data From Observation) As T Order By Data Asc
'
'   With fieldname as expression, SQL as domain, simple filter, and sorting on one field:
'       Q1 = Quartile("Data", "Select Data, Step From Observation", "Step = 10", apFirst, apFreundPerlesGumbell)
'       Select Data From (Select Data, Step From Observation) As T Where Step = 10 Order By Data Asc
'
'   With calculated expression, SQL as domain, extended filter, and sorting on one field:
'       Q1 = Quartile("Data * 10", "Select Data, Step From Observation", "Step = 10 And Data <= 40", apFirst, apFreundPerlesGumbell)
'       Select Data * 10 From (Select Data, Step From Observation) As T Where Step = 10 And Data <= 40 Order By Data * 10 Asc
'
'   With filtered SQL domain, additional filter, and sorting on one field:
'       Q1 = Quartile("Data", "Select Data, Step From Observation Where Step = 10", "Data <= 40", apFirst, apFreundPerlesGumbell)
'       Select Data From (Select Data, Step From Observation Where Step = 10) As T Where Data <= 40 Order By Data Asc
'
'   With filtered SQL domain, additional filter, and sorting on two fields:
'       Q1 = Quartile("Step, Data", "Select Data, Step From Observation Where Step = 10", "Data <= 40", apFirst, apFreundPerlesGumbell)
'       Select Step, Data From (Select Data, Step From Observation Where Step = 10) As T Where Data <= 40 Order By Step, Data Asc 
Note please, that the function is heavily in-line documented as the code otherwise would be uncomprehensive.
 
 请注意，该函数已大量内联文档，否则代码将不完整。 
 域功能 (Domain functions)
To ease the use, indeed in queries, two domain functions supplement the main function:
 
 为了简化在查询中的使用，两个域函数补充了主要功能： 
DMedian
 
 DMedian 
DQuartile
 
 四分位数 
These mimic the native Dxxx domain aggregate functions and take only the arguments needed, using default values - for DMedian, for the part to return and, for DQuartile, for the calculation method to use; that method has been chosen to be the original method used by Excel (formulas QUARTILE and QUARTILE.INCL):
 
 它们模仿本地的Dxxx域聚合函数，并使用默认值仅接受所需的参数-对于DMedian，用于返回的部分，对于DQuartile，用于使用的计算方法； 该方法已被选为Excel所使用的原始方法（公式QUARTILE和QUARTILE.INCL）： 
' Returns the median of a field of a table/query.
'
' Parameters:
'   Expression: Name of the field or an expression to analyse.
'   Domain    : Name of the source/query, or an SQL select query, to analyse.
'   Criteria  : Optional. A filter expression for Domain.
'
' Reference and examples: See function Quartile.
'
' Data must be in ascending order by Field.
'
' 2019-08-15. Gustav Brock, Cactus Data ApS, CPH.
'
Public Function DMedian( _
    ByVal Expression As String, _
    ByVal Domain As String, _
    Optional ByVal Criteria As String) _
    As Double
    
    Dim Value       As Double
    
    Value = Quartile(Expression, Domain, Criteria)
    
    DMedian = Value

End Function 
' Returns the upper or lower quartile or the median or the
' minimum or maximum value of a field of a table/query
' using the method by Freund, Perles, and Gumbell (Excel).
'
' Parameters:
'   Expression: Name of the field or an expression to analyse.
'   Domain    : Name of the source/query, or an SQL select query, to analyse.
'   Criteria  : Optional. A filter expression for Domain.
'   Part      : Optional. Which median/quartile or min/max value to return.
'               Default is the median value.
'
' Reference and examples: See function Quartile.
'
' 2019-08-15. Gustav Brock, Cactus Data ApS, CPH.
'
Public Function DQuartile( _
    ByVal Expression As String, _
    ByVal Domain As String, _
    Optional ByVal Criteria As String, _
    Optional ByVal Part As ApQuartilePart = ApQuartilePart.apMedian) _
    As Double
    
    Dim Value       As Double
    
    Value = Quartile(Expression, Domain, Criteria, Part)
    
    DQuartile = Value

End Function 
 结果 (Results)
An example workbook with generated results from the Excel formulas is attached for reference. 
 
 随附一个示例工作簿，其中包含从Excel公式生成的结果，以供参考。 
It displays like this:
 
 它显示如下： 
 
  
The output from the function ListExcelQuartile, found in the attached Access example file, lists identical values.
 
 在附件的Access示例文件中找到的ListExcelQuartile函数的输出列出了相同的值。 
The two methods are our methods 7 and 6, or the enum elements apFreundPerlesGumbell and apWeibull:
 
 这两种方法是我们的​​方法7和6，或者是枚举元素apFreundPerlesGumbell和apWeibull ： 
               100           99            98            97            96            95 
INCLUDE (LEGACY)
 7            25,75         25,50         25,25         25,00         24,75         24,50         
 7            50,50         50,00         49,50         49,00         48,50         48,00         
 7            75,25         74,50         73,75         73,00         72,25         71,50         

EXCLUDE
 6            25,25         25,00         24,75         24,50         24,25         24,00         
 6            50,50         50,00         49,50         49,00         48,50         48,00         
 6            75,75         75,00         74,25         73,50         72,75         72,00  
Likewise, the function ListFirstQuartile returns an output similar to the results from the main source (table H-4 at top):
 
 同样，函数ListFirstQuartile返回的输出类似于主源的结果（顶部的表H-4）： 
               40            50            60            70 
 1            10,00         20,00         20,00         20,00         
 2            15,00         20,00         20,00         20,00         
 3            10,00         10,00         20,00         20,00         
 4            10,00         12,50         15,00         17,50         
 5            15,00         17,50         20,00         22,50         
 6            12,50         15,00         17,50         20,00         
 7            17,50         20,00         22,50         25,00         
 8            14,17         16,67         19,17         21,67         
 9            14,00         16,50         19,00         21,50         
 10           14,38         16,88         19,38         21,88         
 11           11,25         13,75         16,25         18,75         
 12           20,00         20,00         20,00         25,00         
 13           15,00         20,00         20,00         25,00         
 14           15,00         15,00         20,00         20,00         
 15           8,00          10,42         12,86         15,31         
 16           5,88          8,33          10,80         13,28         
 17           6,15          8,59          11,05         13,52         
 18           5,71          8,17          10,65         13,13         
 19           5,44          7,91          10,39         12,88         
 20           5,00          7,50          10,00         12,50         

               100           99            98            97            96            95 
 1            25,00         25,00         25,00         25,00         24,00         24,00         
 2            25,50         25,00         25,00         25,00         24,50         24,00         
 3            25,00         25,00         24,00         24,00         24,00         24,00         
 4            25,00         24,75         24,50         24,25         24,00         23,75         
 5            25,50         25,25         25,00         24,75         24,50         24,25         
 6            25,25         25,00         24,75         24,50         24,25         24,00         
 7            25,75         25,50         25,25         25,00         24,75         24,50         
 8            25,42         25,17         24,92         24,67         24,42         24,17         
 9            25,40         25,15         24,90         24,65         24,40         24,15         
 10           25,44         25,19         24,94         24,69         24,44         24,19         
 11           25,13         24,88         24,63         24,38         24,13         23,88         
 12           26,00         25,50         25,00         25,00         25,00         24,50         
 13           25,50         25,50         25,00         25,00         24,50         24,50         
 14           25,50         25,00         25,00         24,50         24,50         24,00         
 15           24,75         24,50         24,25         24,00         23,75         23,50         
 16           24,56         24,31         24,06         23,81         23,56         23,31         
 17           24,58         24,33         24,08         23,83         23,58         23,33         
 18           24,55         24,30         24,05         23,80         23,55         23,30         
 19           24,53         24,28         24,03         23,78         23,53         23,28         
 20           24,50         24,25         24,00         23,75         23,50         23,25          
Note please, that column 100-96 here contain the correct values, while in Table H-4 they hold the values for samples 99-95.
 
 请注意，此处的100-96列包含正确的值，而在表H-4中，它们保留了样本99-95的值。 
The two small examples found on Wikipedia display the results using three different methods which equal our methods 14, 13, and 5 respectively, or the enum elements apTukeyMooreMcCabe, apTukey, and apHazen:
 
 维基百科上发现的两个小的例子显示使用，它们分别等于我们的方法14，图13，和图5三种不同的方法，或枚举元素apTukeyMooreMcCabe，apTukey和 apHazen结果： 
 例子1 
 (Example 1 )
 例子2 (Example 2)
 
  
These can be reproduced by the function ListWikipediaSamples:
 
 这些可以由功能ListWikipediaSamples复制 ： 
              Method 1      Method 2      Method 3
              
Q1             15            25,5          20,25 
Q2             40            40            40 
Q3             43            42,5          42,75 

Q1             15            15            15 
Q2             37,5          37,5          37,5 
Q3             40            40            40  
Also, a query, FirstQuartileAllMethods, is included which will list the results for all sets of samples between 1 and 100 for all 20 methods for the lower quartile. Here's a snip:
 
 此外，还包含一个查询FirstQuartileAllMethods ，它将针对下四分位数的所有20种方法列出1至100之间的所有样本集的结果。 这是一个片段： 
 
  
Finally, a form is included which lets you select any method and then have the results for all three quartiles for every sample between 1 and 100 listed:
 
 最后，包含一个表格，您可以选择任何方法，然后列出列出的1至100之间的每个样本的所有三个四分位数的结果： 
 
  

(
)
 实作 (Implementation)
To be able to calculate quartiles, import the module QuartileCode in your application. That's all.
 
 为了能够计算四分位数，请在您的应用程序中导入模块QuartileCode 。 就这样。 
The other module, QuartileDemo, is only needed for testing and for the demo form (also named QuartileDemo) to display.
 
 其他模块QuartileDemo仅用于测试和显示的演示表单（也称为QuartileDemo）。 
Bonus tip: Study the form's code to see how to right-align numbers in a Listbox column.
 
 温馨提示： 研究表单的代码以查看如何在“列表框”列中将数字右对齐。 
 结论 (Conclusion)
From the sparse sources to be located, a function has been created that for just about any practical purpose will allow for the quartiles of a sample of records to be calculated by twenty different methods.
 
 从要定位的稀疏源中创建了一个函数，该函数几乎可以用于任何实际目的，从而可以通过二十种不同的方法来计算记录样本的四分位数。 
In addition, simplified functions intended to supplement the native domain aggregate functions have been presented. Also, a collection of functions and a query for testing and demonstration have been included.
 
 另外，已经提出了旨在补充本地域聚合功能的简化功能。 此外，还包括功能集合以及用于测试和演示的查询。 
 资料来源 (Sources)
Original source (now off-line) by David A. Heiser: http://www.daheiser.info/excel/notes/NOTE%20N.pdf
 
 David A. Heiser的原始资源（现已离线）： http ://www.daheiser.info/excel/notes/NOTE%20N.pdf 
Archived source at The Internet Archive: NOTE 20
 Internet存档中的存档源： NOTE 20 
Notes: 
 
 笔记： 
Table H-4, p. 4, has correct data for the dataset for 1-96 while the datasets for 1-100 to 1-97 actually are the datasets for 1-99 to 1-96 shifted one column left. Thus, the dataset for 1-100 is missing, and that for 1-96 is listed twice.
 表H-4，第6页。 4，具有1-96数据集的正确数据，而1-100到1-97的数据集实际上是1-99到1-96的数据集向左移动了一列。 因此，缺少1-100的数据集，并且两次列出了1-96的数据集。 
 
 
Method 3b is not implemented as no one seems to use it. Neither is no example data given. Thus method 3a has here been labeled method
 方法3b未实现，因为似乎没有人使用它。 没有给出示例数据。 因此，方法3a在这里被标记为方法 
 
Further notes on quartiles and methods can be found here:
 
 有关四分位数和方法的更多说明，请参见： 
Wikipedia
 
 维基百科 
Math Forum
 
 数学论坛 
HaiWeb
 
 海网 
murdoch.edu.au (archived)
 
 murdoch.edu.au（已归档） 
Should you be aware of any good source that can supplement or improve this article, please do not hesitate posting a link as comment.
 
 如果您知道可以补充或改进本文的任何好的资源，请不要犹豫发布链接作为评论。 
 下载 (Download)
The full and current code is available for download at GitHub: VBA.Quartiles
 
 完整和当前的代码可从GitHub下载： VBA.Quartiles 
Also, code and a demo application is here: Quartiles 1.0.1.zip 
 
 另外，代码和演示应用程序也在这里： Quartiles 1.0.1.zip 
An Excel workbook with the presented example: Quartiles.xlsx
 
 一个带有示例的Excel工作簿： Quartiles.xlsx 
I hope you found this article useful. You are encouraged to ask questions, report any bugs or make any other comments about it below.
 
 希望本文对您有所帮助。 鼓励您在下面提出问题，报告任何错误或对此作出任何其他评论。 
Note: If you need further "Support" about this topic, please consider using the Ask a Question feature of Experts Exchange. I monitor questions asked and would be pleased to provide any additional support required in questions asked in this manner, along with other EE experts.
 
 注意 ：如果您需要有关此主题的更多“支持”，请考虑使用Experts Exchange 的“提问”功能。 我会监督提出的问题，并很高兴与其他电子工程师一起为以这种方式提出的问题提供所需的任何其他支持。 
Please do not forget to press the "Thumbs Up" button if you think this article was helpful and valuable for EE members.
 
 如果您认为本文对EE成员有用且有价值，请不要忘记按下“竖起大拇指”按钮。 

                  
  
翻译自: https://www.experts-exchange.com/articles/33718/20-Varieties-of-Quartiles.html
四分位数和百分位数

箱线图学习笔记


四分位数（Quartile）也称四分位点，是指在统计学中把所有数值由小到大排列并分成四等份，处于三个分割点位置的数值。多应用于统计学中的箱线图绘制。它是一组数据排序后处于25%和75%位置上的值。四分位数是通过3个点将全部数据等分为4部分，其中每部分包含25%的数据。很显然，中间的四分位数就是中位数，因此通常所说的四分位数是指处在25%位置上的数值(称为下四分位数)和处在75%位置上的数值(称为上四分位数)。与中位数的计算方法类似，根据未分组数据计算四分位数时，首先对数据进行排序，然后确定四分位数所在的位置，该位置上的数值就是四分位数。与中位数不同的是，四分位数位置的确定方法有几种，每种方法得到的结果会有一定差异，但差异不会很大。
箱形图（Box-plot）又称为盒须图、盒式图或箱线图，是一种用作显示一组数据分散情况资料的统计图。因形状如箱子而得名。在各种领域也经常被使用，常见于品质管理。它主要用于反映原始数据分布的特征，还可以进行多组数据分布特征的比 较。箱线图的绘制方法是：先找出一组数据的上边缘、下边缘、中位数和两个四分位数；然后， 连接两个四分位数画出箱体；再将上边缘和下边缘与箱体相连接，中位数在箱体中间。
参考自：百度百科

编辑
本词条缺少概述、信息栏、名片图，补充相关内容使词条更完整，还能快速升级，赶紧来编辑吧！
简介编辑
四分位数间距：由P25、P50、P75将一组变量值等分为四部分，P25称下四分位数，P75称上四分位数，将P75与P25之差定义为四分位数间距。是上四分位数与下四分位数之差,用四分位数间距可反映变异程度的大小.
即：Q3 --Q1
四分位数求法编辑
第一步
确定四分位数的位置
四分位数是将数列等分成四个部分的数，一个数列有三个四分位数，设下四分位数、中位数和上四分位数分别为Q1、Q2、Q3，则：Q1、Q2、Q3的位置可由下述公式确定：
Q1的位置 1(n+1)/4
Q2的位置 2 (n+1) /4
Q3的位置 3(n+1)/4
式中n表示资料的项数
第二步
根据第一步所确定的四分位数的位置，确定其相应的四分位数。
例1
例如：某车间某月份的工人生产某产品的数量分别为13、13.5、13.8、13.9、14、14.6、14.8、15、15.2、15.4、15.7公斤，则三个四分位数的位置分别为：
Q1的位置 (n+1)/4 =(11+1)/4=3
Q2的位置 (n+1) /2=(11+1)/2=6
Q3的位置 3(n+1)/4=3(11+1)/4=9
即变量数列中的第三个、第六个、第九个工人的某种产品产量分别为下四分位数、中位数和上四分位数。即：
Q1 = 13.8公斤、Q2 = 14.6公斤、Q3 = 15.2公斤
例2
上例中(n+1)恰好为4的倍数，所以确定四分数较简单，如果(n+1)不为4的整数倍数，按上述分式计算出来的四分位数位置就带有小数，这时，有关的四分位数就应该是与该小数相邻的两个整数位置上的标志值的平均数，权数的大小取决于两个整数位置距离的远近，距离越近，权数越大，距离越远，权数越小，权数之和等于1。
例如：某车间某月份的工人生产某产品的数量分别为13、13.5、13.8、13.9、14、14.6、14.8、15、15.2、15.4公斤，则三个四分位数的位置分别为：
Q1的位置 (n+1)/4 =(10+1)/4=2.75
Q2的位置(n+1) /2=(10+1)/2=5.5
Q3的位置3(n+1)/4=3(10+1)/4=8.25
即变量数列中的第2.75项、第5.5项、第8.25项工人的某种产品产量分别为下四分位数、中位数和上四分位数。即：
Q1=0.25×第二项+0.75×第三项=0.25×13.5+0.75×13.8=13.73(公斤)
Q2=0.5×第五项+0.5×第六项=0.5×14+0.5×14.6=14.3(公斤)
Q3=0.75×第八项+0.25×第九项=0.75×15+0.25×15.2=15.05(公斤)
在实际资料中，由于标志值序列中的相邻标志值往往是相同的，因而不一定要通过计算才能得到有关的四分位数。
利用Excel求四分位编辑
在Excel表中可以使用公式QUARTILE(array,quart)来很方便求得，
例如：=QUARTILE(A3:A30,1)即为Q1，
=QUARTILE(A3:A30,3)即为Q3。
转载本文请联系原作者获取授权，同时请注明本文来自贺小星科学网博客。
链接地址：http://blog.sciencenet.cn/blog-2985083-957668.html
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