2.13.1.18 rowquantiles
Brief Information
Compute quantiles on worksheet rows
Command Line Usage
1. rowquantiles irng:=col(1):col(5)
2. rowquantiles irng:=Col(A):Col(F) median:=Col(G)
Variables
Display Name

Variable Name

I/O and Type

Default Value

Description

Input

irng

Input
Range

<active>

This variable specifies the range of input data for which quantiles will be calculated.

Minimum

min

Output
vector

<new>

This variable specifies the output column for the minimum value of the data set.

1st Quartile(Q1)

q1

Output
vector

<optional>

This variable specifies the output column for the 1st quartile, that is, the value in a dataset that demarcates the lowest 25% of the values in an ordered set.

Median

median

Output
vector

<new>

This variable specifies the output column 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.

3rd Quartile(Q3)

q3

Output
vector

<optional>

This variable specifies the output column for the 3rd quartile, that is, the value in a dataset that demarcates the lowest 75% of the values in an ordered set.

Maximum

max

Output
vector

<new>

This variable specifies the output column for the maximum value.

Description
This function computes the quantiles for each row within a specific rectangular range.
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, and 75% of data in a set lay below the third quartile. When data is divided into 100 parts, percentiles can be calculated.
Examples
Suppose you only want to investigate the general information about health status of the students, such as the minimum, median and maximum. You collected 40 students and recorded the name, gender, age, height and weight. (Import body_row.dat on \Samples\Statistics)
Operation:
1. Highlight the two rows of the data, which is the Hight and Weight row respectively.
2. Type rowquantiles in Command Window.
3. Click Enter.
Then you can obtain the minimum, median and maximum of the 40 students's height and weight.

Algorithm
Sort given data first. Denote the sorted data range as ,
1. The 1^{st} quartile is computed as , where is the integer part, and is the fractional part of equation
2. The median, or 2^{nd} quartile, is computed as , where is the integer part, and is the fractional part of equation
3. 3^{rd} quartile is computed as , where is the integer part, and is the fractional part of equation
References
David, H. A. 1981. Order Statistics. 2nd ed. Wiley, New York.
Tukey, J.W. Exploratory Data Analysis. AddisonWesley, 1977.
Related XFunctions
quantiles, moments, stats, rowstats
Keywords:minimum, maximum, median, q1, q3
