lienore the 96 symbo when entering your arewer For example, if the answer in 12. Allo enter 12.4) 12 Center, spread, and shape of distributions.advanced You might need: Cakulator The area in thousands of square kilometers of 19 countries in East and Southeast Asia are shown in the dot plot. Each value is rounded to the nearest 250 thousand square kilometers China, which has an area of 9,597 thousand square kilometers, was excluded from the data. If China were included, then which of the following changes would NOT occur? Choose 1 answer: The mean area would increase. The median area would increase. The range of the areas would increase.

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12-06-2024
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lienore the 96 symbo when entering your arewer For example, if the answer in 12. Allo enter 12.4) 12 Center, spread, and shape of distributions.advanced You might need: Cakulator The area in thousands of square kilometers of 19 countries in East and Southeast Asia are shown in the dot plot. Each value is rounded to the nearest 250 thousand square kilometers China, which has an area of 9,597 thousand square kilometers, was excluded from the data. If China were included, then which of the following changes would NOT occur? Choose 1 answer: The mean area would increase. The median area would increase. The range of the areas would increase.

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Answer:

To address this problem, let's first understand what happens when we include an additional data point that is significantly larger than the other data points.

Given that the area of China is 9,597 thousand square kilometers, which is substantially larger than the areas of the other 19 countries, adding China to the dataset will impact the mean, median, and range.

Explanation:Mean

The mean (average) of a set of numbers is calculated by adding all the numbers together and dividing by the number of numbers. Adding a large value like China will definitely increase the sum of all the areas, and since the number of countries increases by one, the mean will increase.

Median

The median is the middle value of a data set when it is ordered from smallest to largest. Since China's area is much larger than the other values, adding it will increase the total count of data points to 20, making the median the average of the 10th and 11th values in the ordered list. Because China's value is much larger, it will not affect the middle of the ordered list significantly, but it could still cause a slight increase in the median, depending on the distribution of the existing values.

Range

The range is the difference between the largest and smallest values in a dataset. Adding China, which has an area of 9,597 thousand square kilometers, will increase the maximum value in the dataset and, thus, will definitely increase the range.

Conclusion

Based on this analysis:

The mean area would increase because adding a large value will increase the overall sum and the count of data points.

The median area could potentially increase slightly because adding a large value affects the positioning of the middle values.

The range of the areas would increase since adding a very large value will increase the maximum value in the dataset.

Therefore, the correct answer is:

The median area would increase. This is the change that might not occur as drastically as the others. However, without the exact distribution of the 19 countries' areas, it's impossible to be absolutely certain, but generally, the median is less sensitive to extreme values compared to the mean and range.

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