Question

Consider Dataset A for answering the questions that follows below. a. Calculate the measures of central tendencies for Variable X and Variable Y. i. Mean ii. Median iii. Mode iv. Midrange v. What can you say about the skewness of X and Y variables? b. Calculate the measures of variations for Variable X and Variable Y. i. Range ii. Variance iii. Standard Deviation iv. Coefficient of Variation v. Which is more variable, X or Y? Why? c. Calculate the measures of position for Variable X. i. Z-score of the mean value of X ii. Percentile rank of the maximum value of X iii. Check for any outliers in variable X

variable X:6,7,8,8,8,9,9,9,11,11

variableY: -2.77,-0.23,-0.29,-0.05,0.33,0.43,0.51,0.63,0.85,1.12

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

Variable Y

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	X	(X - X̄)²
total sum	0.53	10.71
n	10	10

mean =    ΣX/n =    0.530   /   10   =   0.0530
                      
sample variance =    Σ(X - X̄)²/(n-1)=   10.7120   /   9   =   1.190
                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (10.712/9)   =       1.0910

range=max-min =    1.12   -   -2.77   =   3.89
mid range=(max + min)/2= (   1.12   +   -2.77   ) /2 =    -0.825
Skewness=   -2.1904              

coefficient of variation,CV=σ/µ=   20.584407

lower bound=Q1-1.5IQR=   -1.64
  
upper bound=Q3+1.5IQR=   2.08
  
outlier =values outside lower bound and upper bound  
total outlier below lower bound=   1
total outlier above upper bound=   0
total outlier =    1

Thanks in advance!

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