The mean and median sales prices of new homes sold in the U.S. in November 2010 were $213,000 and $268,000. Which of these numbers is the mean and which is the median? Explain how you know.
I'm assuming the median is $213,000 and the mean is $268,000. However, I'm just guessing. I'm not sure how to know this without data.
I would say you are correct! Outliers can skew the mean higher; thus the mean will be higher than the median.
Outliers could also skew the mean lower as well.
To determine which number is the mean and which is the median, we need to understand the definitions of these two statistical terms and their relationship to the data.
1. Mean: The mean is calculated by summing up all the values in a dataset and dividing by the total number of values. It represents the average value of the dataset.
2. Median: The median is the middle value of a dataset when it is arranged in ascending or descending order. It divides the dataset into two equal halves.
Now, let's analyze the given information: the mean sales price is $213,000, and the median sales price is $268,000.
If the mean is greater than the median, it suggests that there are some higher values in the dataset that are pulling the average upward. On the other hand, if the median is greater than the mean, it suggests that there are some lower values in the dataset that are pulling the average downward.
Comparing $213,000 (mean) to $268,000 (median), we can observe that the median is greater than the mean. Therefore, your initial assumption is incorrect. The correct interpretation would be:
- The median sales price of new homes sold in the U.S. in November 2010 is $268,000.
- The mean sales price of new homes sold in the U.S. in November 2010 is $213,000.
Remember, this conclusion is made by comparing the values provided, and it is not based on any additional data or analysis.