The median is the measure of center that is most affected by outliers. The reason for this is that the median is the middle value when the data set is arranged in order, and outliers can increase or decrease the value of the middle point.
For example, consider the following data set:
2, 3, 4, 5, 6, 7, 8, 9, 10, 200
The mean of this data set is 34.4, the mode is not relevant as there are no repeating values, and the median is 6.5. The outlier, 200, in this case greatly affects the median, pulling it towards the right end of the data set. If we were to remove the outlier and recalculate the median, it would be 5.5. This shows how one extreme value can have a significant impact on the median, making it the measure of center that is most affected by outliers.
Of the mean, median, and mode, which measure of center is most affected by outliers? Explain your reasoning including an example with at least 10 data points.(4 points)
4 answers
stan dont listen to the bot he is wrong i just did this and he gave me wrong answer
I apologize if my response was not helpful or incorrect. Can you please clarify which part of my response you believe is incorrect, so I can provide a more accurate answer?
The bot is wrong use this as and example
Did you know that of the mean, median, and mode, the measure of center most affected by outliers is the mean? The mean is calculated by summing all the data points and then dividing by the total number of data points. Outliers, which are extreme values that differ significantly from the majority of the data, can have a substantial impact on the mean because they directly influence the sum. For example, let's consider a data set of 10 ages: 18, 20, 21, 22, 23, 24, 25, 26, 27, and 100. The median of this data set is 24, as it represents the middle value. The mode is 18 since it is the most frequently occurring age. However, when calculating the mean, we add up all the ages and divide by 10, resulting in a mean of 29.6. Now, observe the outlier of 100, representing an older age than the rest of the data set. If we replace the outlier with a more reasonable value, such as 30, the mean would decrease to 24.8. This example demonstrates how outliers, or extreme values, can significantly impact the mean
Did you know that of the mean, median, and mode, the measure of center most affected by outliers is the mean? The mean is calculated by summing all the data points and then dividing by the total number of data points. Outliers, which are extreme values that differ significantly from the majority of the data, can have a substantial impact on the mean because they directly influence the sum. For example, let's consider a data set of 10 ages: 18, 20, 21, 22, 23, 24, 25, 26, 27, and 100. The median of this data set is 24, as it represents the middle value. The mode is 18 since it is the most frequently occurring age. However, when calculating the mean, we add up all the ages and divide by 10, resulting in a mean of 29.6. Now, observe the outlier of 100, representing an older age than the rest of the data set. If we replace the outlier with a more reasonable value, such as 30, the mean would decrease to 24.8. This example demonstrates how outliers, or extreme values, can significantly impact the mean