What Is Lowest Quartile?

Author: Roslyn

Published: 16 Aug 2022

Table of Content

The Quarticile: A Measure of Central Trend
The median of the lower half in a large sample
The symmetries of the two-dimensional $mathcal N=2$ superconformal field theory
On the number of cumulative percents in a given bin
Outliers in the data set: a way to find them
How tall are you?
Streaming Algorithms for Piecewise Constant and Linear Interpolation
Q Index

The Quarticile: A Measure of Central Trend

A quartile is a term that describes a division of observations into four defined intervals based on the values of the datand how they compare to the entire set of observations. The median is a measure of central tendency and it is important to understand the quartile. The middle value of a set of numbers is the median in statistics.

Half of the data is below and the other half above the central value. The median is a robust location estimate but it doesn't say how the data on either side of the value is spread or dispersed. The quartile steps in.

The median of the lower half in a large sample

The first quarter is the median of the lower half. The third quarter is the median of the upper half. The average of the middle 2 values in the data set is the median.

The symmetries of the two-dimensional $mathcal N=2$ superconformal field theory

There are four different levels of the same thing. The data is divided into four quarters. Four quarters and four quartiles are what they are. They are labeled Q1, Q2, Q3 and Q4.

On the number of cumulative percents in a given bin

If there are values with cumulative percents 25, 50, 75, then equal numbers can be provided in each of the 4 bins. No such values exist. You have to do approximations. The only alternative to assigning observations with the same value to different bins is statistically indefensible.

Outliers in the data set: a way to find them

If the data set has outliers, the middle 50% of the data can be useful. There are probably some outliers in the data set if the minimum or maximum values are far away.

How tall are you?

Have you ever heard someone say that they have trouble shopping for clothes because they are too tall or short or fat? Stores don't stock the whole range of clothes sizes to fit everyone. Stores will stock the sizes that match their customers' sizes so they can make a profit and not carry too much stock.

Streaming Algorithms for Piecewise Constant and Linear Interpolation

The first three are piecewise constant, changing abruptly at each data point, while the last five use linear interpolation between data points, and differ only in how the index used to choose the point along the piecewise linear interpolation curve. Both methods belong to the family of data sketches that are subsets of Streaming Algorithms with useful properties. Partitioning the sketch for a large amount of values can be done in parallel using trivially parallel processes.

quantiles are less susceptible than long-tailed distributions and outliers. If the data is not distributed according to an assumed distribution, quantiles may be more useful than means and other moment-related statistics. The subject of least absolute deviations is a method of regression that is more robust to outliers than is least squares, and in which the sum of the absolute value of the observed errors is used in place of the squared error.