Computing Deciles from Frequency Distribution

From the following data, we compute the values of the deciles:

Class Intervals and Frequencies

Class Interval (C.I.)	Frequency (fi)
0-10	3
10-20	10
20-30	17
30-40	7
40-50	6
50-60	4
60-70	2
70-80	1
Total N = 50

Cumulative Frequency

Class Interval (C.I.)	Frequency (fi)	Cumulative Frequency (C.F.)
0-10	3	3
10-20	10	13
20-30	17	30
30-40	7	37
40-50	6	43
50-60	4	47
60-70	2	49
70-80	1	50

Decile Computations

Computing D₃

We have,
D₃ = ^3N⁄₁₀ = ^{3 × 50}⁄₁₀ = 15
Cumulative frequency just greater than 15 is 30, and the corresponding class is 20-30.

So, 20-30 is the third decile class such that:
l = 20, f = 17, h = 10, F = 13, N = 50

Applying the formula:
D₃ = l + ^{3N/10 – F}⁄_f × h
= 20 + ^{15 – 13}⁄₁₇ × 10
= 20 + 1.18 = 21.05

Third Decile (D₃) = 21.05

Computing D₇

We have,
D₇ = ^7N⁄₁₀ = ^{7 × 50}⁄₁₀ = 35
Cumulative frequency just greater than 35 is 37, and the corresponding class is 30-40.

So, 30-40 is the seventh decile class such that:
l = 30, f = 7, h = 10, F = 30, N = 50

Applying the formula:
D₇ = l + ^{7N/10 – F}⁄_f × h
= 30 + ^{35 – 30}⁄₇ × 10
= 30 + 7.14 = 37.14

Seventh Decile (D₇) = 37.14

PDF Presentation

decilegrouped

Video