Question
Two soccer teams tracked the number of goals they score per game. Which summary statistics should be used to compare the two data sets, and why? Responses The mean and the standard deviation because the data sets are normally distributed. The mean and the standard deviation because the data sets are normally distributed. The median and the interquartile range because the data sets are normally distributed. The median and the interquartile range because the data sets are normally distributed. The median and the interquartile range because the data sets are skewed. The median and the interquartile range because the data sets are skewed. The mean and the standard deviation because the data sets are skewed.
Answers
GPT-4o mini
To determine which summary statistics to use for comparing the goal data sets of the two soccer teams, first consider the distribution of the data. If the data sets are normally distributed, the best summary stats are the mean and standard deviation. However, if the data sets are skewed, the median and interquartile range (IQR) are more appropriate because they are more robust to outliers and provide a better representation of the central tendency and spread of the data.
Here are the options summarized:
1. **The mean and the standard deviation** because the data sets are normally distributed.
2. **The mean and the standard deviation** because the data sets are normally distributed. *(This option is repeated.)*
3. **The median and the interquartile range** because the data sets are normally distributed.
4. **The median and the interquartile range** because the data sets are normally distributed. *(This option is repeated.)*
5. **The median and the interquartile range** because the data sets are skewed.
6. **The median and the interquartile range** because the data sets are skewed. *(This option is repeated.)*
7. **The mean and the standard deviation** because the data sets are skewed.
Based on this, if you know that the data sets are skewed, the correct response would be:
**The median and the interquartile range because the data sets are skewed.**
If you had established that the data is normally distributed, then you would select the mean and standard deviation. The key here is understanding the shape of the data distribution which informs the choice of summary statistics.
Here are the options summarized:
1. **The mean and the standard deviation** because the data sets are normally distributed.
2. **The mean and the standard deviation** because the data sets are normally distributed. *(This option is repeated.)*
3. **The median and the interquartile range** because the data sets are normally distributed.
4. **The median and the interquartile range** because the data sets are normally distributed. *(This option is repeated.)*
5. **The median and the interquartile range** because the data sets are skewed.
6. **The median and the interquartile range** because the data sets are skewed. *(This option is repeated.)*
7. **The mean and the standard deviation** because the data sets are skewed.
Based on this, if you know that the data sets are skewed, the correct response would be:
**The median and the interquartile range because the data sets are skewed.**
If you had established that the data is normally distributed, then you would select the mean and standard deviation. The key here is understanding the shape of the data distribution which informs the choice of summary statistics.