Which of the following best describes the effect of outliers on the $\mathrm{mean}$ of a data set?

• A. Outliers have no effect on the $\mathrm{mean}$ and only affect the $\mathrm{median}$.
• B. Outliers make the $\mathrm{mean}$ equal to the $\mathrm{mode}$.
• C. Outliers can significantly increase or decrease the $\mathrm{mean}$, making it less representative of the central tendency of the data.
• D. Outliers always decrease the $\mathrm{mean}$, regardless of their value.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand what an outlier is — an outlier is a data point that is significantly different from the other observations in the data set, either much larger or much smaller.
2. Step 2: Recall the definition of the mean — the mean is the sum of all data values divided by the number of values, expressed as \(\text{mean} = \frac{\sum x_i}{n}\).
3. Step 3: Consider how adding an outlier affects the sum — since the mean depends on the total sum, an extremely large or small outlier will increase or decrease the sum substantially.
4. Step 4: Recognize that because the mean is sensitive to every value, outliers can pull the mean toward themselves, making it less representative of the typical data point.
5. Step 5: Contrast this with the median, which is the middle value and less affected by extreme values, explaining why outliers impact the mean more than the median.