2.13.1.17 quantiles
Brief Information
Compute quantiles on worksheet columns
Command Line Usage
1. quantiles ix:=Col(1);
2. quantiles ix:=Col(1) median:=mymedian;
X-Function Execution Options
Please refer to the page for additional option switches when accessing the x-function from script
Variables
Display Name
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Variable Name
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I/O and Type
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Default Value
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Description
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Input
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ix
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Input
vector
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<active>
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This variable specifies the range of input data for which quantiles will be calculated.
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Minimum
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min
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Output
double
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<unassigned>
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This variable specifies the output for the minimum value of the data set.
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Q1
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q1
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Output
double
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<unassigned>
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This variable specifies the output for the 1st quartile, that is, the value in a dataset that demarcates the lowest 25% of the values in an ordered set.
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Median
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median
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Output
double
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<unassigned>
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This variable specifies the output for the median or 2nd quartile, that is, the value in a dataset that demarcates the lowest 50% of the values in an ordered set.
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Q3
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q3
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Output
double
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<unassigned>
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This variable specifies the output for the 3rd quartile, that is, the value in a dataset that demarcates the lowest 75% of the values in an ordered set.
|
Maximum
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max
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Output
double
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<unassigned>
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This variable specifies the output for the maximum value.
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Interquartile Range
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iqr
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Output
double
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<unassigned>
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This variable specifies the output for the interquartile range (IQR), that is, Q3 -Q1.
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Index of Minimum
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i1
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Output
double
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<unassigned>
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This variable specifies the output for the row index of the minimum value in the dataset.
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Index of Maximum
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i2
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Output
double
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<unassigned>
|
This variable specifies the output for the row index of the maximum value in the dataset.
|
Description
quantiles are values from the data below which lie a given proportion of the data points in a given set. For example, 25% of data points in any set of data lay below the first quartile, and 50% of data points in a set lay below the second quartile, or median. When data is divided into 100 parts, percentiles can be calculated.
This analysis can give the basic information of the data, such as the minimum, maximum, 1st quartile, median, 3rd quartile and the interquartile range.
Examples
Example 1
- Highlight the 1st column of the active dataset
- Right click the mouse and select fill column with: normal random numbers.
- Type
quantiles
in the command window. Press Enter.
- Then you can run
quantiles.=
to get the basic information about the data you specified, such as minimum, maximum, 1st quantile, median, 3rd quantile and interquantile range.
Example 2
The following script will get the minimum and maximum values and the corresponding row indices.
win -t wks;
string fn$=system.path.program$ + "Samples\graphing\group.dat";
impasc fname:=fn$;
quantiles ix:=Col(1) max:=mymax min:=mymin i1:=a1 i2:=a2;
mymax=;
mymin=;
a1=;
a2=;
Algorithm
Sort given data first. Denote the sorted data range as ,
1. The 1st quartile is computed as , where is the integer part, and is the fractional part of equation
2. The median, or 2nd quartile, is computed as , where is the integer part, and is the fractional part of equation
3. 3rd quartile is computed as , where is the integer part, and is the fractional part of equation
4. The interquartile range, or IQR, is calculated as
References
David, H. A. 1981. Order Statistics. 2nd ed. Wiley, New York.
Tukey, J.W. Exploratory Data Analysis. Addison-Wesley, 1977.
Related X-Functions
stats, moments, rowquantiles, rowstats, mquantiles
Keywords:minimum, maximum, median, q1, q3
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