Question

the box - plot shows the statistics for the weight, in pounds, of some dogs. are there any outliers? explain how you know.

Explanation:

Step1: Identify quartiles

From the box - plot, assume the first quartile $Q_1 = 40$, the third quartile $Q_3=60$.

Step2: Calculate the inter - quartile range (IQR)

$IQR = Q_3 - Q_1=60 - 40 = 20$.

Step3: Determine the lower and upper bounds for non - outliers

The lower bound is $Q_1-1.5\times IQR=40 - 1.5\times20=40 - 30 = 10$. The upper bound is $Q_3 + 1.5\times IQR=60+1.5\times20=60 + 30=90$.

Step4: Check for outliers

Since the minimum value is greater than 10 and the maximum value is less than 90, there are no outliers.

Answer:

No, there are no outliers. The minimum and maximum values of the data set (as shown in the box - plot) are within the range calculated by $Q_1-1.5\times IQR$ and $Q_3 + 1.5\times IQR$.