Question

the following 10 scores were input in the grade - book for prof. barness class. 19, 75, 78, 82, 91, 94, 96, 97, 97, 188. 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: Arrange data in ascending order

$19,75,78,82,91,94,96,97,97,188$

Step2: Calculate the first quartile ($Q_1$)

The position of $Q_1$ is $\frac{n + 1}{4}=\frac{10+1}{4}=2.75$. So $Q_1=75+(78 - 75)\times0.75 = 77.25$

Step3: Calculate the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$. So $Q_3=97+(97 - 97)\times0.25=97$

Step4: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=97 - 77.25 = 19.75$

Step5: Determine the lower and upper bounds for non - outliers

Lower bound: $Q_1-1.5\times IQR=77.25-1.5\times19.75=77.25 - 29.625 = 47.625$
Upper bound: $Q_3+1.5\times IQR=97+1.5\times19.75=97 + 29.625 = 126.625$

Step6: Identify outliers

Values less than the lower bound or greater than the upper bound are outliers. The value $19$ is less than $47.625$ and the value $188$ is greater than $126.625$.

Answer:

$19,188$