Find out quartile deviation and coefficient of quartile deviation of t

1.	Find out quartile deviation and coefficient of quartile deviation of the following series: \( 28,18,20,24,30,15,47,27 \)(Ans. \( Q D=5.5 \), Coefficient of \( Q D= \)
Answer» First we arranged the data in ascending order: 15, 18, 20, 24, 27, 28, 30, 47 Now computing the quartile deviation (QD) and the formula is: QD = (Quartile 3 - Quartile 1) / 2 Computing quartile 1 and quartile 3 as: As there is even number of data (N = 8, which is even), So, Quartile 1 = 1/ 4 (n + 1)^th term = 1/4 ( 8 + 1) = 1/4 × 9 = 2.25th term Quartile 3 = 3/4 (n+1 )^th term = 3/4 (8+ 1) = 3/4 × 9 = 6.75 Computing the QD as: 2nd term is 18 and adding to this 0.25 × (20 - 18), which is 0.5, the result is 18.5 6th term is 28 and adding to this 0.75 × (30 - 28), which is 1.5. the result is 29.5 Using the QD formula as: QD = (29.5 - 18.5) / 2 = 11 / 2 = 5.5 2. Computing the coefficient of quartile deviation as: Coefficient of quartile deviation = (Quartile 3 - Quartile 1) / (Quartile 3 + Quartile 1) Putting the values of the Quartile 3 and Quartile 1 in the above formula: Coefficient of quartile deviation = (29.5 - 18.5) / (29.5 + 18.5) = 11/ 48 = 0.229

Find out quartile deviation and coefficient of quartile deviation of the following series: \( 28,18,20,24,30,15,47,27 \)(Ans. \( Q D=5.5 \), Coefficient of \( Q D= \)

Answer»

First we arranged the data in ascending order:
15, 18, 20, 24, 27, 28, 30, 47

Now computing the quartile deviation (QD) and the formula is:
QD = (Quartile 3 - Quartile 1) / 2

Computing quartile 1 and quartile 3 as:
As there is even number of data (N = 8, which is even), So,

Quartile 1 = 1/ 4 (n + 1)^th term

= 1/4 ( 8 + 1)

= 1/4 × 9

= 2.25th term

Quartile 3 = 3/4 (n+1 )^th term

= 3/4 (8+ 1)

= 3/4 × 9

= 6.75

Computing the QD as:
2nd term is 18 and adding to this 0.25 × (20 - 18), which is 0.5, the result is 18.5

6th term is 28 and adding to this 0.75 × (30 - 28), which is 1.5. the result is 29.5

Using the QD formula as:
QD = (29.5 - 18.5) / 2

= 11 / 2

= 5.5

2. Computing the coefficient of quartile deviation as:

Coefficient of quartile deviation = (Quartile 3 - Quartile 1) / (Quartile 3 + Quartile 1)

Putting the values of the Quartile 3 and Quartile 1 in the above formula:
Coefficient of quartile deviation = (29.5 - 18.5) / (29.5 + 18.5)