Question

Dataset:6,7,8,8,8,9,9,9,11,11

find Percentile rank of the maximum value of X with explain with rule.

Answer 1

Variable X:

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X	(X - X̄)²
6	6.76
7	2.56
8	0.36
8	0.36
8	0.36
9	0.16
9	0.160
9	0.160
11	5.760
11	5.760

	X	(X - X̄)²
total sum	86	22.40
n	10	10

mean =    ΣX/n =    86.000   /   10   =   8.6000
                      
sample variance =    Σ(X - X̄)²/(n-1)=   22.4000   /   9   =   2.489
                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (22.4/9)   =       1.5776

range=max-min =    11   -   6   =   5
mid range=(max + min)/2= (   11   +   6   ) /2 =    8.5

mode= highest frequency data =    8

coefficient of variation,CV=σ/µ=   0.183444

skewness using pearson coefficient of skewness,PC      
PC=3(mean-median)/std dev=       0.190160

IQR = Q3-Q1 =    1.75
  
1.5IQR =    2.625
  
lower bound=Q1-1.5IQR=   5.125
  
upper bound=Q3+1.5IQR=   12.125
  
outlier =values outside lower bound and upper bound  
total outlier below lower bound=   0
total outlier above upper bound=   0
total outlier =    0

Z score of mean value = 0

Percentile Rank of maximum value = 1