Question

which values in the ordered data set would be considered outliers? 21, 26, 38, 43, 56, 61, 64, 65, 66, 68, 72, 76, 79, 80, 80, 95, 109, 118

• identify each value listed below as an outlier or not an outlier by pressing the appropriate hotspot.
• press the answer box after each selection to save your responses.

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Explanation:

Step1: Find the median (Q2)

For $n = 18$ data points, $Q_2=\frac{66 + 68}{2}=67$.

Step2: Find Q1

Median of first 9 values is $Q_1 = 56$.

Step3: Find Q3

Median of last 9 values is $Q_3=80$.

Step4: Calculate IQR

$IQR=Q_3 - Q_1=80 - 56=24$.

Step5: Determine outlier boundaries

Lower: $Q_1-1.5\times IQR = 20$, Upper: $Q_3+1.5\times IQR=116$.

Step6: Identify outliers

109 and 118 are outliers, others are not.

Answer:

To determine outliers, we first need to find the first quartile ($Q_1$), the third quartile ($Q_3$), and the inter - quartile range (IQR).

1. Find the median (Q2):

• There are $n = 18$ data points. The median is the average of the 9th and 10th ordered values.
• The 9th value is 66 and the 10th value is 68. So, $Q_2=\frac{66 + 68}{2}=67$.

1. Find Q1:

• The lower half of the data consists of the first 9 values: $21,26,38,43,56,61,64,65,66$.
• Since there are 9 values, the median of the lower half (Q1) is the 5th value. So, $Q_1 = 56$.

1. Find Q3:

• The upper half of the data consists of the last 9 values: $68,72,76,79,80,80,95,109,118$.
• Since there are 9 values, the median of the upper half (Q3) is the 5th value. So, $Q_3=80$.

1. Calculate the IQR:

• $IQR=Q_3 - Q_1=80 - 56 = 24$.

1. Determine the outlier boundaries:

• The lower boundary for non - outliers is $Q_1-1.5\times IQR=56-1.5\times24=56 - 36=20$.
• The upper boundary for non - outliers is $Q_3 + 1.5\times IQR=80+1.5\times24=80 + 36 = 116$.

Values less than 20 or greater than 116 are outliers. So, 109 and 118 are outliers, and the rest of the values are not outliers.