Question

In a survey of 20-year-olds in China, Germany, and the United States, people were asked the number of foreign countries they had visited in their lifetime. The following box plots display the results.

a. In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected.

b. Have more Americans or more Germans surveyed been to over eight foreign countries?

c. Compare the three box plots. What do they imply about the foreign travel of 20-year-old residents of the three countries when compared to each other

Short answer

a) China's data is skewed to the right, Germany's data is skewed to the left, and the United States' data is skewed to the right.

b) Because the box plot for Germany shows that at least 50% of Germans surveyed have been to eight or more foreign countries, while the box plot for the United States shows that fewer than25% of US participants have been to eight or more foreign countries, more Germans surveyed have been to more than eight foreign countries.

c) The box plots reveal that Chinese 20-year-olds rarely travel outside of the nation. Germans travel extensively, with 50% of Germans visiting at least 8 foreign countries. The most variation is found in the United States, where 25% of individuals have never gone outside the country but 25% have visited at least 5 foreign countries.

Step-by-step solution

Part (a) - Step 1: To determine

What each box plot's form tells us about the distribution of the data collected.

Part (a) - Step 2: Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot. These values are used to see how similar other data values are to them.

A box plot can be used to determine how skewed the data is. If the median is roughly in the middle of the box, the data is symmetric. The data is rightskewed if the longer part of the box is to the right of the median. The data is left-skewed if the longer part of the box is to the left of the median.

Seventy-five percent of Chinese participants have never visited a foreign nation, according to the box plots. Because the only variation occurs in the top 25% of the population, this data is skewed to the right.

The lower 50 %of data for Germans is more spread out than the top 50%, so the German box plot is skewed to the left.

The data for U.S. participants is skewed to the right.

Part (a) - Step 3: Final answer

China's data is skewed to the right, Germany's data is skewed to the left, and the data for the United States is skewed to the right.

Part (b) - Step 4: To determine

Whether more Americans or more Germans surveyed have been to over eight foreign countries.

Part (b) - Step 5: Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot. These values are used to see how similar other data values are to them.

The median is 8 in the box plot for Germany, indicating that at least 50% of Germans surveyed have visited eight or more foreign countries, whereas the third quartile is 5 in the box plot for the United States, indicating that fewer than 25% of US participants have visited eight or more foreign countries.

Part (b) - Step 6: Final answer

More Germans surveyed have been to over eight foreign countries.

Part (c) - Step 7: To compare

The three box plots and determine what they imply about the foreign travel of 20 -year-old residents of three countries when compared to each other.

Part (c) - Step 8: Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot. These values are used to see how similar other data values are to them.

When comparing the box plots, it is evident that Chinese 20-year-olds rarely go outside of their home country. Germans travel extensively. A total of 50% of Germans have visited at least 8 countries. The most variation may be found in the United States, where 25% of participants have never been outside the country but 25% have visited at least 5 foreign countries and 50% have visited at least 2 foreign countries.