Quartile Deviation and Coefficient of Quartile Deviation: Which means, Formulation, Calculation, and Examples

February 7, 2023

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The extent to which the values of a distribution differ from the common of that distribution is named Dispersion. The measures of dispersion could be both absolute or relative. The Measures of Absolute Dispersion include Vary, Quartile Deviation, Imply Deviation, Commonplace Deviation, and Lorenz Curve.

What’s Quartile Deviation?

Quartile Deviation or Semi-Interquartile Vary is the half of distinction between the Higher Quartile (Q₃) and the Decrease Quartile (Q₁). In easy phrases, QD is the half of inter-quartile vary. Therefore, the system for figuring out Quartile Deviation is as follows:

$Quartile~Deviation=frac{Q_3-Q_1}{2}$

The place,

Q₃ = Higher Quartile (Measurement of $3[frac{N+1}{4}]^{th}$ merchandise)

Q₁ = Decrease Quartile (Measurement of $[frac{N+1}{4}]^{th}$ merchandise)

What’s Coefficient of Quartile Deviation?

As Quartile Deviation is an absolute measure of dispersion, one can not use it for evaluating the variability of two or extra distributions when they’re expressed in several items. Subsequently, so as to examine the variability of two or extra sequence with completely different items it’s important to find out the relative measure of Quartile Deviation, which is often known as the Coefficient of Quartile Deviation. It’s studied to make the comparability between the diploma of variation in several sequence. The system for figuring out Coefficient of Quartile Deviation is as follows:

$Coefficient~of~Quartile~Deviation=frac{Q_3-Q_1}{Q_3+Q_1}$

The place,

Q₃ = Higher Quartile (Measurement of $3[frac{N+1}{4}]^{th}$ merchandise)

Q₁ = Decrease Quartile (Measurement of $[frac{N+1}{4}]^{th}$ merchandise)

Calculation of Quartile Deviation in Totally different Sequence

1. Particular person Sequence:

Instance:

With the assistance of the information given beneath, discover the interquartile vary, quartile deviation, and coefficient of quartile deviation.

Resolution:

Q₁ = $Size~of~[frac{N+1}{4}]^{th}~item=Size~of~[frac{7+1}{4}]^{th}~item=Size~of~2^{nd}~item$

Q₁ = 140

Q₃ = $Size~of~3[frac{N+1}{4}]^{th}~item=Size~of~3[frac{7+1}{4}]^{th}~item=Size~of~6^{th}~item$

Q₃ = 268

Interquartile Vary = Q₃ – Q₁ = 268 – 140 = 128

Quartile Deviation = $frac{Q_3-Q_1}{2}=frac{268-140}{2}=64$

Coefficient of Quartile Deviation = $frac{Q_3-Q_1}{Q_3+Q_1}=frac{268-140}{268+140}=frac{128}{408}=0.31$

Interquartile Vary = 128

Quartile Deviation = 64

Coefficient of Quartile Deviation = 0.31

2. Discrete Sequence:

Instance:

From the next desk giving marks of scholars, calculate the interquartile vary, quartile deviation, and coefficient of quartile deviation.

Resolution:

Q₁ = $Size~of~[frac{N+1}{4}]^{th}~item=Size~of~[frac{199+1}{4}]^{th}~item=Size~of~50^{th}~item$

Q₁ = 68

Q₃ = $Size~of~3[frac{N+1}{4}]^{th}~item=Size~of~3[frac{199+1}{4}]^{th}~item=Size~of~150^{th}~item$

Q₃ = 88

Interquartile Vary = Q₃ – Q₁ = 88 – 68 = 20

Quartile Deviation = $frac{Q_3-Q_1}{2}=frac{88-68}{2}=10$

Coefficient of Quartile Deviation = $frac{Q_3-Q_1}{Q_3+Q_1}=frac{88-68}{88+68}=frac{20}{156}=0.12$

Interquartile Vary = 20

Quartile Deviation = 10

Coefficient of Quartile Deviation = 0.12

3. Steady Sequence:

Instance:

Calculate interquartile vary, quartile deviation, and coefficient of quartile deviation from the next figures:

Resolution:

Q₁ = $Size~of~[frac{N}{4}]^{th}~item=Size~of~[frac{100}{4}]^{th}~item=Size~of~25^{th}~item$

Q₁ lies within the group 20-30

l₁ = 20, c.f. = 24, f = 29, i = 10

$Q_1=l_1+frac{frac{N}{4}-c.f.}{f}times{i}=20+frac{25-24}{29}times{10}=20+0.34$

Q₁ = 20.34

Q₃ = $Size~of~[frac{3N}{4}]^{th}~item=Size~of~[frac{3times100}{4}]^{th}~item=Size~of~75^{th}~item$

Q₃ lies within the group 30-40

l₁ = 30, c.f. = 53, f = 24, i = 10

$Q_1=l_1+frac{frac{3N}{4}-c.f.}{f}times{i}=30+frac{75-53}{24}times{10}=30+9.16$

Q₃ = 39.16

Interquartile Vary = Q₃ – Q₁ = 39.16 – 20.34 = 18.82

Quartile Deviation = $frac{Q_3-Q_1}{2}=frac{39.16-20.34}{2}=9.41$

Coefficient of Quartile Deviation = $frac{Q_3-Q_1}{Q_3+Q_1}=frac{39.16-20.34}{39.16+20.34}=frac{18.82}{59.5}=0.31$

Interquartile Vary = 18.82

Quartile Deviation = 9.41

Coefficient of Quartile Deviation = 0.31

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Quartile Deviation and Coefficient of Quartile Deviation: Which means, Formulation, Calculation, and Examples

What’s Quartile Deviation?

What’s Coefficient of Quartile Deviation?

Calculation of Quartile Deviation in Totally different Sequence

1. Particular person Sequence:

Instance:

Resolution:

2. Discrete Sequence:

Instance:

Resolution:

3. Steady Sequence:

Instance:

Resolution:

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