Question

1. 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.

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 IQR = 6 and Q3 = 11 into the formula: 11+1.5×6=11 + 9=20 hours. Any value greater than 20 hours is an outlier. So, 21 hours is an example of a number larger than the median (7 hours) that is an outlier.

Step3: Determine the lower - fence for outliers

The lower - fence for outliers is Q1 - 1.5×IQR. Substitute IQR = 6 and Q1 = 5 into the formula: 5-1.5×6=5 - 9=-4 hours. Since the number of hours spent reading cannot be negative, the minimum possible non - negative value is 0. All non - negative values greater than or equal to 0 and less than the median (7 hours) are within the normal range. So, there are no outliers below the median.

Answer:

a. 21 hours. Reason: IQR = Q3 - Q1=11 - 5 = 6 hours. Upper - fence=Q3+1.5×IQR=11 + 9=20 hours. 21>20 and 21>7.
b. No. Reason: Lower - fence=Q1 - 1.5×IQR=5 - 9=-4 hours. Since the number of hours cannot be negative, and all non - negative values less than the median (7 hours) are within the normal range (greater than or equal to 0), there are no outliers below the median.