Formula of Discrete Series Quartile Deviation

Quartile deviation is a measure of dispersion that determines the spread of data in a given dataset. It is calculated by finding the difference between the upper quartile (Q3) and the lower quartile (Q1). In the case of a discrete series, where the data is presented in the form of individual values, the quartile deviation can be calculated using the following formula:

Quartile Deviation (QD) = (Q3 - Q1) / 2

Where:
- Q1 represents the first quartile, which is the median of the lower half of the dataset.
- Q3 represents the third quartile, which is the median of the upper half of the dataset.

Explanation:

To calculate the quartile deviation for a discrete series, you need to follow these steps:

Step 1: Arrange the data in ascending order
- Start by arranging the given data in ascending order. This will help in determining the first quartile (Q1), third quartile (Q3), and the median (Q2) of the dataset.

Step 2: Find the median (Q2)
- Calculate the median of the dataset, which is the value that divides the data into two equal halves. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values.

Step 3: Determine Q1 and Q3
- Divide the dataset into two halves at the median (Q2). The lower half of the dataset consists of values below or equal to the median, and the upper half consists of values above or equal to the median.
- Calculate the median of the lower half, which represents the first quartile (Q1).
- Calculate the median of the upper half, which represents the third quartile (Q3).

Step 4: Calculate the Quartile Deviation (QD)
- Subtract the first quartile (Q1) from the third quartile (Q3).
- Divide the result by 2 to obtain the quartile deviation (QD).

The quartile deviation provides information about the spread of the data in the dataset. It indicates how far away the middle 50% of the data points are from the median. A smaller quartile deviation implies that the data is more concentrated and less dispersed, while a larger quartile deviation indicates a wider spread of the data points.