Questions: Find the mean and the median of the trade deficits without trade deficit to country A. Which measure of central tendency, the mean or the median, was affected more by the elimination of trade deficits to country A? The mean of the trade deficits is billion Data table Trade Deficits (in billions of dollars) Country A 2761 Country L 67.4 Country B 1951 Country M 45.8 Country C 499 Country N 29.5 Country D 28.0 Country O 29.0 Country E 425 Country P 39.9 Country F 101.5 Country Q 29.8 Country G 28.9 Country R 15.4 Country H 14.4 Country S 11.7 Country I 25.3 Country J 14.0 Country K 53.6

Solution Steps

To find the mean and median of the trade deficits without the trade deficit to Country A, we first need to exclude the trade deficit value for Country A from the dataset. Then, we calculate the mean by summing the remaining trade deficits and dividing by the number of countries. For the median, we sort the remaining trade deficits and find the middle value. Finally, we compare the mean and median before and after the exclusion to determine which measure was affected more.

We start by excluding the trade deficit for Country A, which is \(2761\) billion dollars, from the dataset. The remaining trade deficits are:

\[ \{1951, 499, 28.0, 425, 101.5, 28.9, 14.4, 25.3, 14.0, 53.6, 67.4, 45.8, 29.5, 29.0, 39.9, 29.8, 15.4, 11.7\} \]

The mean of the trade deficits is calculated by summing all the values and dividing by the number of countries:

\[ \text{Mean} = \frac{1951 + 499 + 28.0 + 425 + 101.5 + 28.9 + 14.4 + 25.3 + 14.0 + 53.6 + 67.4 + 45.8 + 29.5 + 29.0 + 39.9 + 29.8 + 15.4 + 11.7}{18} \]

\[ \text{Mean} \approx 189.4 \]

To find the median, we first sort the trade deficits:

\[ \{11.7, 14.0, 14.4, 15.4, 25.3, 28.0, 28.9, 29.0, 29.5, 29.8, 39.9, 45.8, 53.6, 67.4, 101.5, 425, 499, 1951\} \]

Since there are 18 values, the median is the average of the 9th and 10th values:

\[ \text{Median} = \frac{29.5 + 29.8}{2} = 29.65 \]

The mean of the trade deficits is \(189.4\) billion dollars, and the median is \(29.65\) billion dollars. The mean is significantly higher than the median, indicating that the mean is more affected by the elimination of the trade deficit to Country A, which was a large outlier.

Final Answer