Question

Below is the five-number summary for 144 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of time to complete the 212-mile hike from Yosemite Valley across the high Sierras to the top of Mount Whitney. Five-number summary: Minimum: 9 days Q1: 18 days Median: 21 days Q3: 28 days Maximum: 56 days If we use the 1.5 * IQR rule to determine whether there are any outliers, what is the left boundary?

Answer 1

Answer:

The IQR is given by:

$IQR = Q_3 -Q_1 = 28-18= 10$

If we want to find any possible outliers we can use the following formulas for the limits:

$Lower= Q_1 - 1.5 IQR$

$Upper= Q_3 + 1.5 IQR$

And if we find the lower limt we got:

$Lower= Q_1 - 1.5 IQR= 18-1.5*10 = 3$

$Upper= Q_3 + 1.5 IQR= 28+1.5*10= 43$

So then the left boundary for this case would be 3 days

Step-by-step explanation:

For this case we have the following 5 number summary from the data of 144 values:

Minimum: 9 days

Q1: 18 days

Median: 21 days

Q3: 28 days

Maximum: 56 days

The IQR is given by:

$IQR = Q_3 -Q_1 = 28-18= 10$

If we want to find any possible outliers we can use the following formulas for the limits:

$Lower= Q_1 - 1.5 IQR$

$Upper= Q_3 + 1.5 IQR$

And if we find the lower limt we got:

$Lower= Q_1 - 1.5 IQR= 18-1.5*10 = 3$

$Upper= Q_3 + 1.5 IQR= 28+1.5*10= 43$

So then the left boundary for this case would be 3 days