Below is the five-number summary for 136 hikers who recently completed the John
ID: 2923374 • Letter: B
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 fewer hikers between Q1 and the median than there were between the median and Q3.
Most people took more than 28 days to complete the JMT.
At least 34 hikers completed the JMT within 28 to 56 days.
Explanation / Answer
The range of hiking is 9 days to 56 days. So everyone has completed within 9 days to 56 days.
Q1 = 18 days , Median = 21 days, Q3 = 28 days.
So,
# Everyone completed between 9 days to 56 days and none left. first one is false
# There is an equal number of people who completed between 18 to 21 days and from 21 days to 28 days. Second one is also false.
# exactly half the number of the people took 28 days to complete JMT as this is median. Hence the third one is also false.
# Since 136/4 = 34 and Q1, Median(Q2) and Q3 divides the entire dataset( ordered increasingly) into 4 equal parts so there are at least 136/4 = 34 people between 28 days to 56 days. The last one is TRUE.
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