For the data set below, find the outlier(s). $$\begin{array} { l l l l l l l l l l }
210 & 172 & 252 & 183 & 183 & 179 & 191 & 197 & 169 & 202
\end{array}$$
A) 202
B) 252
C) 202 and 210
D) None are outliers.

Question

For the data set below, find the outlier(s). $$\begin{array} { l l l l l l l l l l } 
210 & 172 & 252 & 183 & 183 & 179 & 191 & 197 & 169 & 202
\end{array}$$
A) 202
B) 252
C) 202 and 210
D) None are outliers.

Quizplus · Accepted Answer

To find if there are any outliers, we first need to compute the five-number summary: minimum, maximum, median, and first and third quartiles. The minimum of the data set is 169, the maximum is 252, and the median is the average of the fifth and sixth values, which is (179 + 191)/2 = 185. The first quartile is the median of the data to the left of the median, which is (172 + 183)/2 = 177.5, and the third quartile is the median of the data to the right of the median, which is (197 + 202)/2 = 199.5.

To identify outliers, we can use the interquartile range (IQR), which is the distance between the first and third quartiles. The IQR is 199.5 - 177.5 = 22. Any values below the first quartile minus 1.5 times the IQR or above the third quartile plus 1.5 times the IQR are considered outliers.

Using this formula, the lowest value that would be considered an outlier is 177.5 - 1.5(22) = 146.5 and the highest value is 199.5 + 1.5(22) = 230.5. In this data set, there are no values that fall outside this range except for 252, which is greater than the upper limit of 230.5. Therefore, 252 is the only outlier in the data set.

For the Data Set Below, Find the Outlier(s) 210172252183183179191197169202\begin{array} { l l l l l l l l l l } 210 & 172 & 252 & 183 & 183 & 179 & 191 & 197 & 169 & 202\end{array}210​172​252​183​183​179​191​197​169​202​

For the Data Set Below, Find the Outlier(s) $\begin{array} { l l l l l l l l l l } 210 & 172 & 252 & 183 & 183 & 179 & 191 & 197 & 169 & 202\end{array}$