Questions: Which data set has an outlier? 6,13,13,15,15,18,18,22 4,4,4,8,9,9,11,18 2,3,5,7,8,8,9,10,12,17 3,6,7,7,8,8,9,9,9,10

Transcript text: Which data set has an outlier? $6,13,13,15,15,18,18,22$ $4,4,4,8,9,9,11,18$ $2,3,5,7,8,8,9,10,12,17$ $3,6,7,7,8,8,9,9,9,10$

Solution

To determine which data set has an outlier, we can use the Interquartile Range (IQR) method. The steps are as follows:

Calculate the first quartile (Q1) and third quartile (Q3) of each data set.
Compute the IQR as Q3 - Q1.
Determine the lower bound as Q1 - 1.5 * IQR and the upper bound as Q3 + 1.5 * IQR.
Identify any data points that fall outside these bounds as outliers.

Step 1: Calculate Quartiles and IQR for Each Data Set

For each data set, we calculate the first quartile ($Q1$) and the third quartile ($Q3$), and then compute the interquartile range (IQR) as $Q3 - Q1$.

Data Set 1: $[6, 13, 13, 15, 15, 18, 18, 22]$

Data Set 2: $[4, 4, 4, 8, 9, 9, 11, 18]$

Data Set 3: $[2, 3, 5, 7, 8, 8, 9, 10, 12, 17]$

Data Set 4: $[3, 6, 7, 7, 8, 8, 9, 9, 9, 10]$

Step 2: Determine Outlier Bounds

Using the IQR, we determine the lower and upper bounds for outliers as follows:

Data Set 1:

Data Set 2:

Data Set 3:

Data Set 4:

Step 3: Identify Outliers

We identify any data points that fall outside the lower and upper bounds as outliers.

Data Set 1:

Data Set 2:

Data Set 3:

Data Set 4:

$\boxed{\text{Data Set 2 has an outlier: } 18}$
$\boxed{\text{Data Set 3 has an outlier: } 17}$
$\boxed{\text{Data Set 4 has an outlier: } 3}$

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