Question

The geyser Old Faithful in Yellowstone National Park alternates period of eruption, which typically last from 1.5 to 4 minutes, with periods of dormancy, which ar considerably longer. The following data set represents the durations, in minutes, of a random sample of 16 eruptions. Find the five-number summary. Round to the nearest tenth, if necessary. 91,88,89,92,93,99,84,94,89,101,59,86,93,66,103,99

Answer 1

The five-number summary for the durations of Old Faithful's eruptions is 59, 87, 91.5, 93.5, 103, representing the minimum, first quartile, median, third quartile, and maximum of the data set.

Step-by-step explanation:

To find the five-number summary of the durations of eruptions of Old Faithful, we first need to arrange the data in ascending order and then calculate the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.

1. Arrange the data in ascending order: 59, 66, 84, 86, 88, 89, 89, 91, 92, 93, 93, 94, 99, 99, 101, 103.
2. Minimum: The lowest value is 59.
3. Q1: The first quartile is the median of the first half of the data (in this case, the average of the 4th and 5th values), which is (86+88)/2 = 87.
4. Median (Q2): The median is the middle value, which is the average of the 8th and 9th values, giving us (91+92)/2 = 91.5.
5. Q3: The third quartile is the median of the second half of the data, which is the average of the 12th and 13th values, which is (93+94)/2 = 93.5.
6. Maximum: The highest value is 103.

So, the five-number summary is 59, 87, 91.5, 93.5, 103.