Solved Examples on Decile

Example 1: Given the following grouped data representing the scores of students in a class:

Find the first decile for this data.

Solution:

First we will calculate the cumulative Frequency

Total number of observations (N) = 5 + 8 + 12 + 15 + 10 = 50

Position of Decile D₁ = N/10

= 50/10 = 5

Now, cumulative frequency just greater than D₁ is corresponding to the score range 11-20

Now we know, that for ungrouped data

D(n) = L + [Tex]\left( \frac{\left(\frac{n}{10} \times N \right) – F}{f} \right) \times c[/Tex]

where,

• L is Lower boundary of the score range containing D₁ (11 in this case)
• F is Cumulative frequency of the score range before D₁ (5)
• f is Frequency of the score range containing D₁ (8)
• w is Width of the score range (10 – 0 = 10)

Putting the values in the formula we get,

D₁ = 11 + [Tex]\left( \frac{5 – 5}{8} \right)[/Tex] × 10

D₁ = 11 + (0/8) × 10

D₁ = 11 + 0 × 10

∴ D₁ = 11

Example 2: Given the following ungrouped data representing the ages of ten individuals: 22,25,30,33,35,40,45,50,55,60. Find the deciles for this data.

Solution:

First, we will arrange the given data in ascending order: 22, 25, 30, 33, 35, 40, 45, 50, 55, 60.

Now using the formula of calculating decile; D(n) = N × (n +1) /10 we will find the deciles. Where, N is the total frequency, and n ranges from 1 to 9

First Decile D(1) = 1 × (9 +1) /10 = 10/10 =1

Second Decile D(2) = 2 × (9 +1) /10 = 20/10 = 2

Third Decile D(3) = 3 × (9 +1) /10 = 30/10 = 3

Fourth Decile D(4) = 4 × (9 +1) /10 = 40/10 = 4

Fifth Decile D(5) = 5 × (9 +1) /10 = 50/10 = 5

Sixth Decile D(6) = 6 × (9 +1) /10 = 60/10 = 6

Seventh Decile D(7) = 7 × (9 +1) /10 = 70/10 = 7

Eighth Decile D(8) = 8 × (9 +1) /10 = 80/10 = 8

Ninth Decile D(9) = 9 × (9 +1) /10 = 90/10 = 9

Decile is a statistical measure that divides a dataset into ten equal parts, and each part contains 10% of the data. It is different from percentage as in percentage there are 100 parts. In this article, we will learn in detail about what is decile, the formulas of decile (grouped data and ungrouped data)