For the data set below, find the upper outlier boundary. $$\begin{array} { l l l l l l l l l l }
166 & 174 & 175 & 183 & 188 & 190 & 197 & 204 & 209 & 253
\end{array}$$
A) 232.5
B) 247.5
C) 131.5
D) 253

Question

For the data set below, find the upper outlier boundary. $$\begin{array} { l l l l l l l l l l } 
166 & 174 & 175 & 183 & 188 & 190 & 197 & 204 & 209 & 253
\end{array}$$
A) 232.5
B) 247.5
C) 131.5
D) 253

Quizplus · Accepted Answer

To find the upper outlier boundary, we need to first calculate the interquartile range (IQR). To do this, we first need to find the median. Since there are 10 numbers, the median is the average of the 5th and 6th numbers, which is (190+197)/2 = 193.5. Then, we find the first quartile (Q1) and third quartile (Q3) by finding the medians of the lower and upper halves of the data, respectively. 
Q1 = median of {166, 174, 175, 183, 188} = (174+175)/2 = 174.5 
Q3 = median of {197, 204, 209, 253} = (204+209)/2 = 206.5 
IQR = Q3 - Q1 = 206.5 - 174.5 = 32 
To find the upper outlier boundary, we add 1.5 times the IQR to Q3: 
Upper outlier boundary = Q3 + 1.5(IQR) = 206.5 + 1.5(32) = 247 
Therefore, the best choice is B, 247.5.

For the Data Set Below, Find the Upper Outlier Boundary 166174175183188190197204209253\begin{array} { l l l l l l l l l l } 166 & 174 & 175 & 183 & 188 & 190 & 197 & 204 & 209 & 253\end{array}166​174​175​183​188​190​197​204​209​253​

For the Data Set Below, Find the Upper Outlier Boundary $\begin{array} { l l l l l l l l l l } 166 & 174 & 175 & 183 & 188 & 190 & 197 & 204 & 209 & 253\end{array}$