Business Statistics - Calculation of Quartiles (Formulas)

 

Calculation of Quartiles

–      Formulas

 

There are 3 measures of quartiles – first quartile (Q1), second quartile (Q2) and third quartile (Q3). Actually, Q2 is same as the Median.

 

Formulas of Quartiles

For simple distribution

Step 1:

Arrange the data in ascending order.

 

Step 2:

Q1 = Value of [(n +1)/4] ^Th observation.

Q2 = Value of [(n +1)/2] ^Th observation.

Q3 = Value of [3(n +1)/4] ^Th observation.

 

For simple frequency distribution

Step 1:

Construct a cumulative frequency distribution table (“less than” type)

 

Step 2:

Q1 = Value of [(N +1)/4] ^Th observation.

Q2 = Value of [(N +1)/2] ^Th observation.

Q3 = Value of [3(N +1)/4] ^Th observation.

 

For grouped frequency distribution

Step 1:

If the class intervals are given in ‘limits’, convert the class limits into class boundaries

 

Step 2:

Construct a cumulative frequency distribution table (“less than” type)

 

Step 3:

Q1 = L1 + [(L2 – L1)/f]*(m – c)

 

[Here,

L1 = Lower boundary of the Q1 class

L2 = Upper boundary of the Q1 class

f = Frequency of the Q1 class

m = N/4

N = Total frequency

c = Cumulative frequency of the class interval immediately preceding the Q1 class

Q1 class = the class interval in which the

                 (N/4) ^Th observation lies

 

Q2 = L1 + [(L2 – L1)/f]*(m – c)

 

[Here,

L1 = Lower boundary of the Q2 class

L2 = Upper boundary of the Q2 class

f = Frequency of the Q2 class

m = N/2

N = Total frequency

c = Cumulative frequency of the class interval immediately preceding the Q2 class

Q2 class = the class interval in which the

                 (N/2) ^Th observation lies

 

Q3 = L1 + [(L2 – L1)/f]*(m – c)

 

[Here,

L1 = Lower boundary of the Q3 class

L2 = Upper boundary of the Q3 class

f = Frequency of the Q3 class

m = 3N/4

N = Total frequency

c = Cumulative frequency of the class interval immediately preceding the Q3 class

Q3 class = the class interval in which the

                 (3N/4) ^Th observation lies