mai took a survey of students in her class to find out how many hours they spend each week. here are some…

Explanation:

Step1: Recall outlier - IQR rule

The inter - quartile range (IQR) is calculated as $IQR = Q3 - Q1$. Here, $Q1 = 5$ hours and $Q3=11$ hours, so $IQR=11 - 5=6$ hours. The lower fence for outliers is $Q1-1.5\times IQR$ and the upper fence is $Q3 + 1.5\times IQR$.

Step2: Calculate lower and upper fences

The lower fence is $5-1.5\times6=5 - 9=- 4$ hours. The upper fence is $11 + 1.5\times6=11 + 9 = 20$ hours.

Step3: Determine median

Since we are not given the number of data - points, assume the data is arranged in ascending order. If $n$ is the number of data - points, when $n$ is odd, the median is the $\left(\frac{n + 1}{2}\right)$-th value; when $n$ is even, the median is the average of the $\frac{n}{2}$-th and $\left(\frac{n}{2}+1\right)$-th values. Here, we know the median is 7 hours.

Step4: Answer part a

An example of a number of hours larger than the median that would be an outlier is any number greater than 20 hours. For example, 25 hours. Reasoning: Using the IQR rule, values greater than $Q3+1.5\times IQR = 20$ hours are considered outliers.

Step5: Answer part b

There are no outliers below the median. Reasoning: The lower fence for outliers is - 4 hours. Since the number of hours (a non - negative quantity in this context) cannot be less than 0, and all non - negative values greater than or equal to 0 are greater than the lower fence of - 4 hours, there are no outliers below the median.

Answer:

a. An example is 25 hours. Reason: Values greater than $Q3 + 1.5\times IQR=20$ hours are outliers. b. No. Reason: The lower fence is - 4 hours and since hours cannot be negative, all non - negative values are above the lower fence.