# Quartile Deviation – How to find, Formulas, and Example Problems

Quartile Deviation – Quartile Deviation or called Semi Inter-Quartile Range is half of the quartile range. For more details, see our discussion of Quartile Deviation Material starting from How to Find Quartile Deviation, Quartile Deviation Formulas, and Examples of Quartile Deviation Problems below.

## Definition of Quartile Deviation

Quartile Deviation, also known as Semi-Inter-Quartile Range is half of the quartile range.

K3 – K1. or with JAK (interquartile range), K3 = 3rd quartile, K1 = 1st quartile.

Standard Value Suppose you have a sample of size n (the number of data = n), and from the data x1, x2, x3,…,xn. Then the average = x. And the standard deviation is = s.

New data is formed: z1, z2, z3…, zn by using Coefficient of Variation. Coefficient of Variation KV = JAK = K3 – K1 Semi Inter-Quartile Range = 1/2 (K3 – K1) Quartile Notation : q

## Forms of Quartile Deviations

Quartile has 4 equal parts in dividing the data (n).——|—— Q1 Q2 Q3.

Where :

• Q1 = Lower Quartile (1/4n )
• Q2 = Middle Quartile (Median) (1/2n)
• Q3 = upper quartile (1/4n ) In the data that is not grouped first look for middle quartile (median) then the lower quartile and the upper quartile.

## How to find the quartile deviation

Quartile is a measure that divides the data into four equal parts. As explained above, the quartile consists of the lower quartile (Q₁), the middle quartile (Q₂/median) and the upper quartile (Q₃).

The quartile deviation is half of the difference between the upper and lower quartile.

Quartile deviation = (Q₃ – Q₁)

If we want to determine the quartile value, the data must be sorted first from smallest to largest.

If the number of data n is odd

Q₁ = data ke (n + 1)
Q₂ = data ke (n + 1)
Q₃ = data ke (n + 1)

If the number of data n is even

Q₁ = data ke (n + 2)
Q₂ = (data ke n + data ke (½ n + 1))
Q₃ = data to (3n + 2)

Discussion

In determining the quartile deviation, you have to find the 1st quartile and 3rd quartile first, then we just need to enter it into the formula, namely:

Quartile deviation = (Q₃ – Q₁)

Let’s take an example, the quartile deviation of the following data is ….

Value 4 5 6 8 10

Frequency 2 4 7 6 1

In finding the quartiles of the table, we also construct the cumulative frequency

Cumulative frequency value

Pay attention to the following table!

 4 2 2 5 4 2 + 4=6 6 7 6 + 7=13 8 6 13 + 6=19 10 1 19 + 1=20

From the table, based on the cumulative frequency, the meaning is:
Value 4 is data to 1 to 2
Value 5 is the data to 3 to 6
Value 6 is data to 7 to 13
The value 8 is the data to 14 to 19
The value 10 is the data to 20

Since n = 20 is an even number, then:

Q₁ = data ke (n + 2)

Q₁ = data ke (20 + 2)

Q₁ = data ke 5,5

Q₁ = (data ke 5 + data ke 6)

Q₁ = ½ (5 + 5)

Q₁ = ½ (10)

Q₁ = 5

Q₃ = data to (3n + 2)

Q₃ = data ke (3(20) + 2)

Q₃ = data ke (60 + 2)

Q₃ = data ke (62)

Q₃ = data ke 15,5

Q₃ = (data ke 15 + data ke 16)

Q₃ = ½ (8 + 8)

Q₃ = ½ (16)

Q₃ = 8

So the quartile deviation of the data is:

= ½ (Q₃ – Q₁)

= ½ (8 – 5)

= ½ (3)

= 1,5

### Problems example

The following is an example of a quartile deviation

Determine the interquartile range and quartile deviation of the data below:

20  35 50 45  30  30  25  40  45  30  35

The first thing you have to do is sort the data to find the upper and lower quartile, look at the picture below.

So, the lower quartile (Q1) and the upper quartile (Q3), from the two data, are 30 and 45, then:

QR = Q3 – Q1

QR = 45 – 30

QR = 15

The quartile deviations are:

Qd = ½QR

Qd = ½.15

Qd = 7,5

So the answer: the interquartile range and the quartile deviation of the data is 15 & 7,5.

What is quartile deviation?

Quartile Deviation or called the Semi-Inter-Quartile Range is half of the quartile range.

Quartile deviation formula

Qd = (1/2)(Q3 – Q1)

Information :

Qd = Quartile deviation
Q1 = Lower quartile or 1st quartile
Q3 = Upper quartile or 3rd quartile

Thus our discussion of the Quartile Deviation Material. May be useful.

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