Question

the five - number summary of a dataset was found to be: 1, 10, 13, 19, 20. an observation is considered a low outlier if it is below: an observation is considered a high outlier if it is above: question help: written example message instructor

Explanation:

Step1: Recall outlier rules

For a dataset, to find the boundaries for outliers we first need to find the first quartile ($Q_1$), third quartile ($Q_3$) and the inter - quartile range ($IQR = Q_3 - Q_1$). A low outlier is below $Q_1- 1.5\times IQR$ and a high outlier is above $Q_3 + 1.5\times IQR$. First, we need to order the data. The ordered data is 1, 10, 13, 19, 20.

Step2: Calculate quartiles

Since $n = 5$ (odd number of data points), the median ($Q_2$) is the middle value. So $Q_2=13$. The lower half of the data is 1, 10, so $Q_1=\frac{1 + 10}{2}=5.5$. The upper half of the data is 19, 20, so $Q_3=\frac{19+20}{2}=19.5$.

Step3: Calculate IQR

$IQR=Q_3 - Q_1=19.5 - 5.5 = 14$.

Step4: Find low - outlier boundary

The boundary for low outliers is $Q_1-1.5\times IQR=5.5-1.5\times14=5.5 - 21=- 15.5$.

Step5: Find high - outlier boundary

The boundary for high outliers is $Q_3 + 1.5\times IQR=19.5+1.5\times14=19.5 + 21 = 40.5$.

Answer:

A low outlier is below - 15.5 and a high outlier is above 40.5.