A set of data has a mean of 25 and an outlier of 5. You find the mean without the outlier. Which of the following best describes your new mean?
A. The new mean is the same as the original mean.
B The new mean is the as the meadian
C. The new mean is greater than the original mean.
D. The new mean is less then the original mean.
Since the mean is greatly effected by outliers, removing the outlier from below the mean will cause its value to increase (D).
You need to proofread your questions before you post them. If B indicates that the mean will have the same value as the median, without outliers, the mean is the same value as the median in a normal distribution.
A set of data has a mean of 35 and an outlier of 100. You find the mean without the outlier. Which of the following best describes your new mean?
To find the new mean without the outlier, you'll need to remove the outlier from your data set and recalculate the mean.
In this case, the original mean is 25, and the outlier is 5. By removing the outlier, you can calculate the mean with the remaining data points. Without any further information about the remaining data points, we can't determine the exact new mean value.
However, we can make some general statements about the possible relationship between the original mean and the new mean. Recall that the mean is sensitive to extreme values, such as outliers. Removing an outlier tends to move the mean closer to the rest of the data.
Based on this observation, we can eliminate options A and B:
A. The new mean is the same as the original mean. (Incorrect. Removing an outlier will change the mean.)
B. The new mean is the same as the median. (Incorrect. The median is a measure of central tendency that is not affected by outliers, but it is not guaranteed to be the same as the new mean.)
Now, let's consider the remaining options:
C. The new mean is greater than the original mean.
D. The new mean is less than the original mean.
Since the outlier value is smaller than the original mean, removing it is likely to increase the mean. Therefore, the correct answer is:
C. The new mean is greater than the original mean.