Quartile Deviation Formula

Quartile Deviation Formula

The quartile deviation formula is used to calculate the deviation of each data point from the median of the data set. The quartile deviation is then used to create a quartile range, which is the range of data points that are between the first and third quartiles.

Importance of Quartile Deviation

A quartile deviation is a measure of the dispersion of values in a dataset. It is calculated by taking the difference between the third quartile and the first quartile, and then dividing that number by the interquartile range. The quartile deviation used to measure the variability of a dataset and to identify outliers.

Quartile Formula

The quartile formula used to calculate the quartile of a given set of data. The quartile is the value that divides the data set into four equal parts. The first quartile is the value that is greater than or equal to 25% of the data set, and the third quartile is the value that is greater than or equal to 75% of the data set.

About Quartile Deviation

Quartile deviation is a measure of how spread out a set of data is. It calculated by finding the quartiles of a data set and then subtracting the lower quartile from the upper quartile. This gives you the range of the data. The quartile deviation then calculated by dividing this range by the number of data points in the set.

Quartile Deviation Definition: The Quartile Deviation (QD) is the measure of dispersion of a distribution. It defined as the difference between the upper and lower quartiles. The lower quartile is the value below which 25% of the observations lie and the upper quartile is the value above which 25% of the observations lie.

Quartile Deviation Formula:

QD = UQ – LQ

Where,

QD = Quartile Deviation

UQ = Upper Quartile

LQ = Lower Quartile

Quartile Deviation Example:

Consider the data set given below:

11, 13, 15, 17, 18, 20, 26, 30

Step 1: The data ordered or arranged in ascending order.

11, 13, 15, 17, 18, 20, 26, 30

Step 2: The lower quartile (LQ) is the value below which 25% of the observations lie which given by the formula:

LQ = n/4

Where,

n = number of observations

= 8/4

= 2

Hence, LQ = 13

Step 3: The upper quartile (UQ) is the value above which 25% of the observations lie which given by the formula:

UQ = 3n/4

Where,

n = number of observations

= 8*3/4

= 6

Hence, UQ = 20

Step 4: The quartile deviation (QD) is the difference between the upper and lower quartiles.

QD = UQ – LQ

= 20 – 13

= 7

Thus, the quartile deviation is 7.