Questions: Q. Here is a skewed distribution where the mode is not in the middle but to one side of the distribution. This distribution has a mode of 3, a median of 4, and a mean of 4.8. Take a moment to think about which measure of central tendency would give the best description of the center of the distribution. Do extreme scores impact the calculation of the mean? In other words, does including a very high or very low value change the mean in any way? What about the median? Is there one measure of central tendency that is less affected by extreme scores, thus making it a better estimate of central tendency when we have these scores present?

Solution Steps

Extreme scores have a significant impact on the mean. If a very high score is added to the distribution, the mean will increase. If a very low score is added, the mean will decrease.

The median is less affected by extreme scores. The median represents the middle value when the data is ordered. Adding an extreme value will shift the middle position slightly, but not as drastically as the mean shifts.

For skewed distributions, the median is generally the best measure of central tendency because it is less sensitive to extreme scores. In this case, where the mode is 3, the median is 4, and the mean is 4.8, the mean is pulled higher by the scores on the right tail of the distribution. The median is a better representation of the "center" in this scenario.

Final Answer