Question

identifying an outlier
the data set below represents the number of televisions repaired in a service shop over an 11 - week period.
1, 48, 50, 25, 21, 19, 26, 30, 18, 17, 3
the outlier of the data set is.

Explanation:

Step1: Sort the data

Sort the data set \(1,48,50,25,21,19,26,30,18,17,3\) in ascending order: \(1,3,17,18,19,21,25,26,30,48,50\).

Step2: Calculate the inter - quartile range (IQR)

Find the median (second quartile \(Q_2\)). Since \(n = 11\), \(Q_2\) is the 6th value. So \(Q_2=21\).
The lower half of the data is \(1,3,17,18,19\). The median of the lower half (\(Q_1\)) is the 3rd value, so \(Q_1 = 17\).
The upper half of the data is \(25,26,30,48,50\). The median of the upper half (\(Q_3\)) is the 3rd value of the upper half, so \(Q_3=30\).
The inter - quartile range \(IQR=Q_3 - Q_1=30 - 17 = 13\).

Step3: Determine the outlier boundaries

The lower boundary is \(Q_1-1.5\times IQR=17-1.5\times13=17 - 19.5=- 2.5\).
The upper boundary is \(Q_3 + 1.5\times IQR=30+1.5\times13=30 + 19.5 = 49.5\).

Answer:

48 and 50