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.

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 given by $Q3+1.5\times IQR$
$Q3 + 1.5\times IQR=11+1.5\times6$
$=11 + 9=20$
Any value greater than 20 is an outlier. Since the median is 7 hours, 21 hours is a number larger than the median which is an outlier.

Answer:

21 hours. The upper fence for outliers is calculated as $Q3 + 1.5\times IQR$. With $Q1 = 5$, $Q3 = 11$, $IQR=6$, and the upper fence is 20. So any value greater than 20 is an outlier. 21 is greater than the median (7) and also an outlier.