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Partition values or fractiles or quantiles

(1) Quartiles (Q_r), where r = 1,2,3

Q₁ = first quartile or lower quartile, Q₂ = middle quartile or secound quartile, Q₃ = third quartile or upper quartile.

Quartile divide whole data into four equal parts and each part covers 25% of the total value.

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(2) Deciles (D_r), where r = 1,2,3.......,9

Decile divide whole data into 10 equal parts and each part covers 10% 0f the total value.

D₁ = called first decile, D₂ = called as secound decile, D₃ = called as third decile,............. D₉ = called as nineth decile.

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(3) Percentiles (P_r) , where r = 1,2,3.........,99.

Percentile divide whole data into 100 equal parts and each part covers 1% of the total value.

P₁ = first percentile, P₂ = 2nd percentile, P₃ = 3rd percentile, P₉₉ = 99th percentile,

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Important:

(i) M_d = Q ₂ = D₅ = P₅₀

(ii) D₁ = P₁₀, D₂ = P₂₀, D₃ = P₃₀,.........,D₉ = P₉₀

(iii) Q₁ = P₂₅, Q₃ = P₇₅

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Formulas of Quartiles :

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N = ∑f = Total no.of observations.

L₁ = Lower limit of desired class .

p.c.f = Previous class cumulative frequency to desired class.

f = frequency of desired class.

h = L₂ - L₁ = upper limit - lower limit.