U.S. Trade Deficits The table at the left sho...

Question

U.S. Trade Deficits The table at the left shows the U.S. trade deficits (in billions of dollars) with 18 countries in 2020. (Source: U.S. Department of Commerce)

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a. Find the mean and the median of the trade deficits.

Accepted Answer

Hi, everyone. Let's take a look at this practice problem. This problem says the following are the numbers of books sold in thousands by 18 different bookstores in the city during 2023. And we'll give them a table, and in this table, in the first column, it is labeled store, and we have the values of A, B, C, D, E, F, G, H, and I. The next column is listed number of books sold in thousands, and we have the values of 45.2, 38.9, 27.5, 22.1, 19.8, 18.7, 16.4, 15.9, and 14.2. The next column is also labeled store, and it has the values of J, K, L, M, N, O, P, Q, and R. And the final column is the number of books sold in thousands, and it has the values of 12.8, 11.7, 10.5, 9.8, 8.3, 7.6, 6.9, 5.4, and 4.2. Calculate the mean and median number of books sold. So, the first thing we want to do is to order our data in ascending order. So, taking the number of books sold and starting at the lowest value, we will have 4.2. Then we'll have 5.4. 6.9. 7.6. 8.3 Then 9.8. Then 10.5. 11.7. 12.8 14.2 15.9. 16.4. 18.7. Then we'll have 19.8. 22.1. 27.5. 38.9. And then finally, 45.2. So, the first value that we want to calculate is going to be the mean, and recall that the mean is going to be the sum of all of our data, divided by the number of data points that we have. So, that means our mean is going to be equal to, and here in the numerator, we'll have the quantity of 4.2 plus 5.4, plus 6.9 plus 7.6. Plus 8.3. Plus 9.8 Plus 10.5. Plus 11.7. Plus 12.8. Plus, 14.2 plus 15.9 plus 16.4. Plus 18.7. Plus, 19.8 plus 22.1. Plus 27.5. Plus 38.9, and finally, plus 45.2. And that whole quantity is divided by The number of data points that we have, and if we count the number of data points that we have, we see that we have 18 data points, so we'll divide this by 18. So simplify this expression, this is going to be equal to. 295.9. Divided by 18. Which is going to be approximately equal to 16.4. So here we just rounded it to one decimal place. So that is going to be the value for a mean that we are looking for. Now, the next value that we need to find is going to be our median, and recall that the median is going to be the value that appears in the middle of our data set when we order it in ascending order. Now, since we have 18 data points, that's an even number, we're actually gonna be looking at the midpoint of the two values that are in the middle. And if we look at the values that appear up in the middle, that's going to be 12.8. And 14.2. So, recall to find the midpoint of those two values, we'll just add them together. So we'll have 12.8. Plus 14.2, and then we'll just divide that quantity by 2. In doing so, this is going to be equal to. 13.5. So that means our median, median is going to be equal to 13.5. So, our final answer for this problem is that we're going to have a mean that is equal to 16.4 000 books, and we'll have a median of 13.5 000 books. So those are the answers that we were looking for for this problem. So, I hope that this explanation has been useful, and I'll see you in the next video.

U.S. Trade Deficits The table at the left shows the U.S. trade deficits (in billions of dollars) with 18 countries in 2020. (Source: U.S. Department of Commerce)

a. Find the mean and the median of the trade deficits.

Key Concepts

Mean

Median

Trade Deficit

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