Question

in a survey, 11 people gave the following ratings for a local politician (on a scale of 0 to 100).
40, 42, 43, 45, 46, 49, 50, 52, 54, 54, 89
identify 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: Find the median

The data set has 11 values. The median is the 6th value.
$$40,42,43,45,46,\mathbf{49},50,52,54,54,89$$
Median ($Q_2$) = $49$

Step2: Find $Q_1$ and $Q_3$

For $Q_1$ (lower half: $40,42,43,45,46$), the median of the lower half is the 3rd value.
$$Q_1 = 43$$
For $Q_3$ (upper half: $50,52,54,54,89$), the median of the upper half is the 3rd value.
$$Q_3 = 54$$

Step3: Calculate the inter - quartile range (IQR)

$$IQR=Q_3 - Q_1=54 - 43 = 11$$

Step4: Determine the outlier boundaries

Lower boundary: $Q_1-1.5\times IQR=43-1.5\times11=43 - 16.5 = 26.5$
Upper boundary: $Q_3 + 1.5\times IQR=54+1.5\times11=54 + 16.5 = 70.5$

Step5: Check for outliers

Any value less than $26.5$ or greater than $70.5$ is an outlier.
The value $89>70.5$

Answer:

$89$