Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. The two most frequently used measures of central tendency are the mean and median. Compare these two measures for the following characteristics: Take every score into account? Affected by extreme scores? Advantages.
Mean takes every score into account and is more effected by extreme scores.
With this knowledge, what advantages for each do you note?
To compare the mean and median for the characteristics of taking every score into account, being affected by extreme scores, and their advantages, we can observe the following:
1. Take every score into account:
- The mean considers every score in the dataset when calculating the central tendency. Each score contributes equally to the mean.
- On the other hand, the median only considers the middle value in the dataset. It does not take into account every score.
2. Affected by extreme scores:
- The mean is highly influenced by extreme scores since it incorporates all the values. Even a single extreme score can significantly impact the mean.
- In contrast, the median is not significantly affected by extreme scores. It only considers the middle value and is less influenced by outliers.
3. Advantages:
- The mean provides a comprehensive summary of the data since it considers all the values. It is useful when the dataset is normally distributed and has no extreme outliers.
- The median is advantageous when the dataset has extreme values or a skewed distribution. It is a more robust measure of central tendency compared to the mean, as it is not heavily influenced by outliers.
In summary, the mean takes every score into account but is sensitive to extreme values, while the median only considers the middle value and is less affected by outliers. The advantage of the mean lies in its inclusivity of all data points, while the advantage of the median lies in its resilience to extreme scores.