Question

Find the 5-number summary for the following data set. {18, 15, 16, 22, 24, 12, 17, 25, 16, 19, 20, 17}

A) 12, 16, 18, 22, 25
B) 12, 17, 19, 22, 25
C) 15, 17, 19, 22, 24
D) 15, 16, 18, 20, 24

Answer 1

The 5-number summary for the data set {18, 15, 16, 22, 24, 12, 17, 25, 16, 19, 20, 17} is 12, 16, 17, 22, 25.

Step-by-step explanation:

To find the 5-number summary for the data set {18, 15, 16, 22, 24, 12, 17, 25, 16, 19, 20, 17}, we need to first put the numbers in ascending order and then determine the minimum, Q1 (first quartile), median (Q2), Q3 (third quartile), and maximum values.

1. Organize the data: 12, 15, 16, 16, 17, 17, 18, 19, 20, 22, 24, 25.
2. Minimum: The smallest number, which is 12.
3. Q1: The median of the first half of the data. Here, Q1 is the average of the 3rd and 4th values (16 and 16), so Q1 = 16.
4. Median (Q2): Since there are an even number of data points, the median will be the average of the 6th and 7th values (17 and 18), so Median = 17.5. For the five number summary we take the lower median in case of an even number set, so we use 17 as the median.
5. Q3: The median of the second half of the data. Here, Q3 is the average of the 9th and 10th values (20 and 22), so Q3 = 21. For the five number summary we take the higher median in the case of an even number set, so we use 22 as Q3.
6. Maximum: The largest number, which is 25.

The 5-number summary is 12, 16, 17, 22, 25.