Question

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

Explanation:

Step1: Identify quartiles

From the box - plot, the first quartile $Q_1$ is around 40, the third quartile $Q_3$ is around 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

The minimum value in the box - plot is around 20 (within the lower bound of 10) and the maximum value is around 100 (outside the upper bound of 90).

Answer:

Yes, there are outliers. The upper bound for non - outliers is 90 pounds, and since the maximum value in the data set (from the box - plot) is 100 pounds which is greater than 90 pounds, there is at least one outlier.