Class Intervals20−2930−3940−4950−5960−6970−7980−89Frequencies (fi)50697090524011Cumulative Frequencies50119189279331371382∑fi=382
The percentile coefficient of Kurtosis, denoted as Kp, is defined in terms of quartiles and percentiles as
Kp=2(P90−P10)Q3−Q1
Q1=L1+[f1∑fi×1/4−Cf]⋅C1
∑fi×1/4=382×1/4=95.5,L1=30,Cf=50,C1=10,f1=69
Q1=30+[6995.5−50]⋅10=36.5942
Q3=L3+[f3∑fi×3/4−Cf]⋅C3
∑fi×3/4=382×3/4=286.5,L3=60,Cf=279,C3=10,f3=52
Q3=60+[52286.5−279]⋅10=61.4423
Pk=L1+[fk∑fi×(k/100)−Cf]⋅Ck
k=90,∑fi×(k/100)=382×(90/100)=343.8,L1=70,Cf=331,C90=10,f90=40
P90=70+[40343.8−331]⋅10=73.20
k=10,∑fi×(k/100)=382×(10/100)=38.2,L1=20,Cf=0,C10=10,f10=50
P10=10+[5038.2−0]⋅10=17.64 The percentile coefficient of Kurtosis
Kp=2(73.20−17.64)61.4423−36.5942=0.2236 Since Kp=0.2236<0.263, the curve is leptokurtic or thin.
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