Question

identify the outlier in the set of data, if it exists: 92, 88, 106, 109, 76, 72, 67, 10, 115, 73, 111, 102

Explanation:

Step1: Sort the data

Sort the data set: \(10,67,72,73,76,88,92,102,106,109,111,115\)

Step2: Find quartiles

Find the first quartile \(Q_1\) (median of the lower half). The lower half is \(10,67,72,73,76,88\). \(Q_1=\frac{72 + 73}{2}=72.5\)
Find the third quartile \(Q_3\) (median of the upper half). The upper half is \(92,102,106,109,111,115\). \(Q_3=\frac{106+109}{2} = 107.5\)

Step3: Calculate IQR

Calculate the inter - quartile range \(IQR=Q_3 - Q_1=107.5-72.5 = 35\)

Step4: Determine bounds

Determine the lower bound \(Q_1-1.5\times IQR=72.5-1.5\times35=72.5 - 52.5=20\)
Determine the upper bound \(Q_3 + 1.5\times IQR=107.5+1.5\times35=107.5 + 52.5=160\)

Step5: Identify outlier

Check for values outside the bounds. The value \(10<20\)

Answer:

The outlier is \(10\)