Question

3 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 $Q3+1.5\times IQR$.
$Q3 + 1.5\times IQR=11+1.5\times6$
$=11 + 9=20$
We want a value larger than the median (7 hours) and an outlier. Any value greater than 20 hours would be an outlier. For example, 21 hours.

Answer:

21 hours. Since the upper - fence for outliers is 20 hours (calculated as $Q3 + 1.5\times IQR$ where $Q1 = 5$, $Q3 = 11$ and $IQR=Q3 - Q1 = 6$), and 21>20 and 21>7.