Question

Given the following data.

154 173 119 122 178 246 116 125 113 142

145 119 126 117 124 116 115 124 146 118

a) Put the raw data in a data array.

b) Give the Five Number summary.

c) Compute the InterQuartileRange, Upper Fence, Lower Fence.

d) List outlier, if any

e) Find the percentile rank of 122

f) Find the score corresponding to 90th percentile.

Answer 1

a)

X
154
173
119
122
178
246
116
125
113
142
145
119
126
117
124
116
115
124
146
118

b) five number summary = 113 , 117.25 , 124 , 145.75 , 178

c)

quartile , Q1 = 0.25(n+1)th value=   5.25th value of sorted data=   117.25
      
Quartile , Q3 = 0.75(n+1)th value=   15.75th value of sorted data=   145.75
      
IQR = Q3-Q1 =    145.75-117.25=   28.5
      
1.5IQR =    42.75  
      
lower bound=Q1-1.5IQR=   74.50  
upper bound=Q3+1.5IQR=   188.50  

d)

outlier =values outside lower bound and upper bound  

so, outlier is 246

e)

90th percentile = 177.5