# Finding the Median with Bowley’s Coefficient of Skewness: A Comprehensive Guide

Understanding statistical measures is crucial in many fields, from business to social sciences. One such measure is the Bowley’s Coefficient of Skewness, a non-parametric measure of the asymmetry of a probability distribution. It is a useful tool for determining the skewness of a data set, which can provide insights into the nature of the data. This article will delve into the concept of Bowley’s Coefficient of Skewness, how it is calculated, and how it can be used to find the median of a data set. We will also answer a specific question: “What is the median when Bowley’s coefficient of Skewness = -0.8; Q₁ = 44.1 and Q ₃ = 56.6?”

## Understanding Bowley’s Coefficient of Skewness

Bowley’s Coefficient of Skewness, also known as the quartile skewness, is a measure of the skewness of a distribution. It is calculated using the quartiles of the data set. The formula for Bowley’s Coefficient of Skewness is (Q3 – 2Q2 + Q1) / (Q3 – Q1), where Q1, Q2, and Q3 are the first, second (median), and third quartiles, respectively.

## Interpreting Bowley’s Coefficient of Skewness

The value of Bowley’s Coefficient of Skewness ranges from -1 to 1. A positive value indicates that the distribution is skewed to the right, meaning that the right tail of the distribution is longer or fatter than the left. Conversely, a negative value indicates that the distribution is skewed to the left, meaning that the left tail of the distribution is longer or fatter than the right. A value of zero indicates a symmetric distribution.

## Finding the Median with Bowley’s Coefficient of Skewness

Given the values of Bowley’s Coefficient of Skewness and the first and third quartiles, we can rearrange the formula to solve for the median (Q2). The rearranged formula is Q2 = ((Q3 – Q1) * Skewness + Q1 + Q3) / 2.