Question

in a survey, 11 people gave the following ratings for a local politician (on a scale of 0 to 100).41, 42, 44, 46, 47, 49, 49, 49, 50, 51, 54, 55identify all values that are outliers.if there is more than one outlier, separate them with commas.if there are no outliers, click on
one\.

Explanation:

Step1: Sort the data

First, sort the data set \(41,42,44,46,47,49,49,50,51,54,55\) in ascending order (it is already sorted).

Step2: Calculate the quartiles

The number of data points \(n = 11\).
The first quartile \(Q_1\):
The position of \(Q_1=\frac{n + 1}{4}=\frac{11+1}{4}=3\). So \(Q_1 = 44\).
The third quartile \(Q_3\):
The position of \(Q_3=\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9\). So \(Q_3=51\).
The inter - quartile range \(IQR=Q_3 - Q_1=51 - 44 = 7\).

Step3: Determine the outlier boundaries

The lower boundary \(=Q_1-1.5\times IQR=44-1.5\times7=44 - 10.5 = 33.5\).
The upper boundary \(=Q_3 + 1.5\times IQR=51+1.5\times7=51 + 10.5=61.5\).
Since all the data points \(41,42,44,46,47,49,49,50,51,54,55\) lie within the range \([33.5,61.5]\), there are no outliers.

Answer:

None