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


The extent to which the values of a distribution differ from the typical of that distribution is called Dispersion. The measures of dispersion might be both absolute or relative. The Measures of Absolute Dispersion include Vary, Quartile Deviation, Imply Deviation, Normal 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 method 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’t use it for evaluating the variability of two or extra distributions when they’re expressed in several items. Due to this fact, with a purpose to evaluate the variability of two or extra collection with totally 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 collection. The method 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 Completely different Collection

1. Particular person Collection:

Instance:

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

Information Table

 

Resolution:

Quartile Deviation Table

 

Q1Size~of~[frac{N+1}{4}]^{th}~item=Size~of~[frac{7+1}{4}]^{th}~item=Size~of~2^{nd}~item

Q1 = 140

Q3Size~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 Collection:

Instance:

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

Information Table

 

Resolution:

Quartile Deviation Table

 

Q1Size~of~[frac{N+1}{4}]^{th}~item=Size~of~[frac{199+1}{4}]^{th}~item=Size~of~50^{th}~item

Q1 = 68

Q3Size~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 Collection:

Instance:

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

Information Table

 

Resolution:

Quartile Deviation Table

 

Q1Size~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

Q3Size~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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