Which of the following is a measure of variability?Choose one of the following answers. Third quartile Maximum Mode Standard Deviation

Break Down the Problem

1. Identify the options given and classify them according to their characteristics.
2. Determine which of the options specifically measures variability in data sets.

Relevant Concepts

• Third Quartile (Q3): A value that separates the highest 25% of a data set from the rest, not a direct measure of variability.
• Maximum: The highest value in a data set, which does not reflect variability by itself.
• Mode: The value that appears most frequently in a data set, which does not measure spread or variability.
• Standard Deviation: A statistic that quantifies the amount of variation or dispersion in a set of values.

Analysis and Detail

1. Third Quartile (Q3): Useful for understanding data distribution but does not provide variability.
2. Maximum: Indicates the highest point but no insight into how spread out the data is.
3. Mode: Indicates the most common value but not how close or spread out values are.
4. Standard Deviation: Measures how much individual values in a set differ from the mean, thus effectively capturing the variability.

Verify and Summarize

The only option that directly measures variability in a data set is standard deviation. It gives a clear indication of how much the values deviate from the average.

Final Answer

Standard Deviation is the correct answer as it is a measure of variability.