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

14. mai took a survey of students in her class to find out how many hours they spend reading each week. here are some summary statistics for the data that mai gathered: mean: 8.5 hours, standard deviation: 5.3 hours, median: 7 hours, q1: 5 hours, q3: 11 hours. a. give an example of a number of hours larger than the median which would be an outlier. explain your reasoning. b. are there any outliers below the median? explain your reasoning.

14. mai took a survey of students in her class to find out how many hours they spend reading each week. here are some summary statistics for the data that mai gathered: mean: 8.5 hours, standard deviation: 5.3 hours, median: 7 hours, q1: 5 hours, q3: 11 hours. a. give an example of a number of hours larger than the median which would be an outlier. explain your reasoning. b. are there any outliers below the median? explain your reasoning.

Answer

Explanation:

Step1: Calculate the inter - quartile range (IQR)

$IQR = Q3 - Q1$ $IQR=11 - 5=6$

Step2: Determine the upper fence for outliers

The upper fence for outliers is $Q3+1.5\times IQR$ $Q3 + 1.5\times IQR=11+1.5\times6=11 + 9=20$ Any value larger than 20 is an outlier. A number larger than the median (7) that is an outlier could be 21. Since $21>20$, it is an outlier.

Step3: Determine the lower fence for outliers

The lower fence for outliers is $Q1 - 1.5\times IQR$ $Q1-1.5\times IQR=5-1.5\times6=5 - 9=- 4$ Since the number of hours cannot be negative, the lowest non - negative value we consider. The median is 7. All non - negative values above the lower fence ($0$ is the lowest non - negative value in the context of hours) and below the median are not outliers. So there are no outliers below the median.

Answer:

a. 21. Reason: The upper fence for outliers is $Q3 + 1.5\times IQR=20$, and $21>20$. b. No. Reason: The lower fence for outliers is $Q1-1.5\times IQR=-4$, and since hours cannot be negative, all non - negative values below the median (7) are within the acceptable range.