What statistical metric can be used to summarize a set of closed-ended responses?

The correct choice indicates that all listed metrics can be utilized to summarize a set of closed-ended responses. Closed-ended responses, which typically include options like "yes/no" or rate on a scale (1-5, for instance), can be effectively summarized using various statistical metrics.

The mean provides an average score of responses, making it useful for understanding the central tendency of the data. For example, if respondents rate a product on a scale from 1 to 5, calculating the mean can provide a quick summary of overall satisfaction.

The standard deviation measures the dispersion of responses around the mean. It tells us how varied respondents' answers are. A low standard deviation indicates that responses are clustered closely around the mean, while a high standard deviation indicates more variability among responses.

The interquartile range focuses on the middle 50% of responses, providing insights into the distribution and separation of the lower and upper quartiles. This metric helps in understanding the spread of the data, which is useful when there are outliers or when the data is skewed.

Since each of these metrics offers different insights into the data, they can all be effectively used to summarize closed-ended responses, making the choice encompassing all of them the most comprehensive and accurate.