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Compare the median and mean of the data set with and without the outlier.
With the outlier, the median increased by $ __________.
With the outlier, the mean increased by $ __________.
So, the effect of the outlier on the mean was __________ the effect of the outlier on the median.
To effectively compare the median and mean with and without an outlier, let’s first explain how to find these statistics:
1. Identify the data set: First, you need the original data and the outlier’s value.
2. Calculate the median: The median is the middle number when your data is ordered. If there’s an outlier, compare the median of the original data set to the median after adding the outlier.
3. Calculate the mean: The mean is calculated by summing all values and dividing by the number of values. Again, calculate this before and after adding the outlier.
4. Determine the increases: Subtract the median/mean without the outlier from the median/mean with the outlier to find how much they increased.
Once you have those calculations, you can fill in the blanks as follows:
1. “With the outlier, the median increased by $ _____.” (this is the difference you calculated).
2. “With the outlier, the mean increased by $ _____.” (this is the difference you calculated).
Finally, the last part: “So, the effect of the outlier on the mean was _____ the effect of the outlier on the median.” This comparison can be described as “greater than,” “less than,” or “equal to,” depending on the results of your calculations.
If you share the specific data, I can guide you through the calculations!