Question

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 q1: 5 hours median: 7 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.

Explanation:

Step1: Calculate the inter - quartile range (IQR)

IQR = Q3 - Q1. Given Q1 = 5 hours and Q3 = 11 hours, so IQR=11 - 5=6 hours.

Step2: Determine the upper - fence for outliers

The upper - fence for outliers is Q3+1.5×IQR. Substitute the values: 11 + 1.5×6=11 + 9 = 20 hours. Any value larger than 20 hours is an outlier. A number larger than the median (7 hours) and an outlier could be 21 hours. Since 21>20, it is an outlier.

Step3: Determine the lower - fence for outliers

The lower - fence for outliers is Q1 - 1.5×IQR. Substitute the values: 5-1.5×6=5 - 9=-4 hours. Since the number of hours spent reading cannot be negative, the lowest non - negative value we consider is 0. All non - negative values greater than or equal to 0 and less than the median (7 hours) are not outliers because they are greater than the lower - fence (-4 hours).

Answer:

a. 21 hours. Reason: The upper - fence for outliers is Q3 + 1.5×IQR=20 hours, and 21>20.
b. No. Reason: The lower - fence for outliers is Q1 - 1.5×IQR=-4 hours, and since the number of hours cannot be negative, all non - negative values less than the median are not outliers.