Question

The following data set represents the amount spent, in billions of dollars, each year on national defense by the u.s. government over the course of a 16-year period. find the five-number summary of this data set. round all answers to one decimal place.

296.3, 335.9, 401.2, 451.3, 479.5, 481.7, 403.2, 409.5, 366.9, 351.8, 348.5, 370.1, 472.8, 546.4, 574.6, 675.1

Answer 1

The five-number summary of the given dataset is: Minimum: 296.3, Q1: 350.15, Median: 385.65, Q3: 480.6, Maximum: 675.1

Step-by-step explanation:

To find the five-number summary of the given dataset, we need to find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.

Step 1: Sort the dataset in ascending order: 296.3, 335.9, 348.5, 351.8, 366.9, 370.1, 401.2, 403.2, 409.5, 451.3, 472.8, 479.5, 481.7, 546.4, 574.6, 675.1

Step 2: Find the minimum value, which is 296.3.

Step 3: Find the first quartile (Q1), which corresponds to the median of the lower half of the dataset. In this case, the lower half is {296.3, 335.9, 348.5, 351.8, 366.9, 370.1, 401.2, 403.2}. So, Q1 is the median of this set, which is (348.5 + 351.8) / 2 = 350.15.

Step 4: Find the median (Q2), which is the middle value of the dataset. In this case, we have an even number of values, so the median is the average of the two middle values: (370.1 + 401.2) / 2 = 385.65.

Step 5: Find the third quartile (Q3), which corresponds to the median of the upper half of the dataset. In this case, the upper half is {403.2, 409.5, 451.3, 472.8, 479.5, 481.7, 546.4, 574.6, 675.1}. So, Q3 is the median of this set, which is (479.5 + 481.7) / 2 = 480.6.

Step 6: Find the maximum value, which is 675.1.

The five-number summary of the given dataset is as follows:

Minimum: 296.3

Q1: 350.15

Median (Q2): 385.65

Q3: 480.6

Maximum: 675.1