Revision: 11th Std >> Measures of Dispersion MAH-MHT CET (PCM/PCB) Measures of Dispersion

The observations which divide the whole set of observations into four equal parts are known as quartiles.

Before finding quartiles, the given data must always be arranged in ascending order of magnitude.

The difference between the largest and smallest values in a data set is called the range.

Range = Largest value − Smallest value

Inter-quartile range:

The difference between the upper quartile (Q₃) and the lower quartile (Q₁) is called the inter-quartile range.

Inter-quartile range = Q₃ − Q₁

• It is always positive, since Q₃ > Q₁.

Semi-interquartile range:

Half of the inter-quartile range is called the semi-interquartile range.

Semi-interquartile range = `1/2` (Q₃ − Q₁)

Case I: When n is ODD

• Lower Quartile, Q₁ = (n + 1) / 4 th term

• Upper Quartile, Q₃ = 3(n + 1) / 4 th term

Case II: When n is EVEN

• Lower Quartile, Q₁ = n / 4 th term

• Upper Quartile, Q₃ = 3n / 4 th term

Types of Quartiles

1. Lower Quartile (Q₁)
   The observation lies midway between the lowest value and the median.

2. Middle Quartile (Q₂)
   The median of the data.

3. Upper Quartile (Q₃)
   The observation lies midway between the median and the highest value.