Quartile Deviation of Continuous Series

QUARTILE DEVIATION OF CONTINUOUS SERIES

Quartile deviation is half the difference between the third quartile and the
first quartile of a frequency distribution. It is also known as
Semi interquartile range.

Quartile Deviation (QD) = 3− 1

2

Coefficient of QD = 3− 1

3+ 1

Example:1 Find quartile deviation and its coefficient from the data:

Marks 0-10 10-20 20-30 30-40 40-50
No. of Students 2 4 3 15
Solution:

Marks(x) No. Of Cumulative frequency(cf)

Students(f)

0-10 2 2

10-20 4 6

20-30 3 9

30-40 1 10

40-50 5 15

n= 15

Q1 Class = ( ) ℎ = (15) ℎ = 3.75th class =10-20

4 4

So, l = 10, f = 4, cf = 2, i = 10

Now, Q1 = L + 4 − × = 10+ 3.75−2 × 10 = 10+4.375 =14.375
4

Similarly,

Q3 Class = (3 ) ℎ = (3×15) ℎ = 11.25th class =40-50

4 4

So, l = 40, f = 5, cf = 10, i = 10

Now, Q3 = L + 34 − × = 40+ 11.25−10 × 10 = 40+2.5 =42.5
5

Therefore, Quartile Deviation (QD) = 42.5 −14.375 =14.0625

2

Coefficient of QD = 3− 1 = 42.5 −14.375 = 28.125 = 0.49

3+ 1 42.5+14.375 56.875

Example:2 Find quartile deviation and its coefficient from the data:

Marks 0-10 0-20 0-30 0-40 0-50
No. of Students 2 6 9 10 15
Solution:

Marks(x) f Marks(x) No. Of Students(f) Cumulative
frequency(cf)
0-10 2 0-10 2
2

0-20 6 10-20 4 6

0-30 9 20-30 3 9

0-40 10 30-40 1 10

0-50 15 40-50 5 15

n= 15

Q1 Class = ( ) ℎ = (15) ℎ = 3.75th class =10-20

4 4

So, l = 10, f = 4, cf = 2, i = 10

Now, Q1 = L + 4 − × = 10+ 3.75−2 × 10 = 10+4.375 =14.375
4

Similarly,

Q3 Class = (3 ) ℎ = (3×15) ℎ = 11.25th class =40-50

4 4

So, l = 40, f = 5, cf = 10, I = 10

Now, Q3 = L + 34 − × = 40+ 11.25−10 × 10 = 40+2.5 =42.5
5

Therefore,

Quartile Deviation (QD) = 42.5 −14.375 =15.0625

2

Coefficient of QD = 3− 1 = 42.5 −14.375 = 28.125 = 0.49

3+ 1 42.5+14.375 56.875

Example:3 Find quartile deviation and its coefficient from the data:

Marks 10-19 20-29 30-39 40-49 50-59

No. of Students 2 4315
Solution:

Correction factor = 20−19 = 1 = 0.5

22

Marks(x) No. Of Students(f) Cumulative frequency(cf)

9.5-19.5 2 2

19.5-29.5 4 6

29.5-39.5 3 9

39.5-49.5 1 10

49.5-59.5 5 15

n= 15

Q1 Class = ( ) ℎ = (15) ℎ = 3.75th class =19.5-29.5

4 4

So, l = 9.5 , f = 4, cf = 2, i = 10

Now, Q1 = L + 4 − × = 9.5+ 3.75−2 × 10 = 19.5+4.375 =23.875
4

Similarly,

Q3 Class = (3 ) ℎ = (3×15) ℎ = 11.25th class =49.5-59.5

4 4

So, l = 40, f = 5, cf = 10, I = 10

Now, Q3 = L + 34 − × = 49.5+ 11.25−10 × 10 = 49.5+2.5 =52
5

Therefore,

Quartile Deviation (QD) = 52 −23.875 =14.0625

2

Coefficient of QD = 3− 1 = 52 −23.875 = 23.875 = 0.31

3+ 1 52+23.875 75.875