Question

Below is the five-number summary for 136 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 Which one of the following statements about the distribution is most accurate? Most people finished the JMT within 9 to 56 days, but some took a little longer. There were less hikers between Q1 and the median than there were between the median and Q3. Exactly 36 hikers had times ranging from 18 to 21 days. At least 36 hikers completed the JMT within 28 to 56 days.

Answer 1

Answer:

Option B) There were less hikers between Q1 and the median than there were between the median and Q3

Step-by-step explanation:

The given five-number summary is:

Minimum     :     9

Q1                :     18  

Median        :     21  

Q3               :     28  

Maximum    :     56  

Now based on these numbers we will evaluate the given options:

Option A)

Most people finished the JMT within 9 to 56 days, but some took a little longer.

This statement is false because minimum time is 9 days and maximum time is 56 days. This means all of the people finished JMT within 9 to 56 days. As 56 is the maximum, no one took longer than this to finish JMT. Hence, this option is Wrong.

Option B)

There were less hikers between Q1 and the median than there were between the median and Q3

Difference between median and Q1 = 21 - 18 = 3

Difference between Q3 and median = 28 - 21 = 7

So, the given statement is true as there are 3 hikers between Q1 and the median and 7 hikers between the median and Q3. Thus this statement is Correct.

Option C)

Exactly 36 hikers had times ranging from 18 to 21 days

18 days is the Q1 and 21 days represent median. Remember that Q1 is the 25th percentile and Median is the 50th percentile. So 25% of the hikers will have time ranging from 18(25th percentile) to 21 days(50th percentile).

Since, total number of hikers is 136, and 25% of 136 is 34. This means, 34 hikers had times ranging from 18 to 21 days. Thus, this statement is Wrong.

Option D)

At least 36 hikers completed the JMT within 28 to 56 days.

28 days represent Q3, the 3rd quartile or 75th percentile and 56 days represent the maximum value. So there are 25% of the hikers will finish between 28 days and 56 days.

25% of 136 is 34. This means 34 hikers completed the JMT within 28 to 56 days. Therefore, this statement is also wrong.

Hence, option B gives the most accurate description about the given five-number summary.