Which measure describes how dispersed individual observations are from the mean?

Which measure describes how dispersed individual observations are from the mean?

• A. Range
• B. Variance
• C. Standard Deviation
• D. Interquartile Range

Answer: (C)

The measure that describes how dispersed individual observations are from the mean is the standard deviation. It quantifies how far, on average, each data point lies from the average value and puts that spread in the same units as the data, making it easy to interpret. Variance is related but uses squared distances, which can be harder to grasp; standard deviation is just the square root of variance, returning the spread to the original units. The range looks at only the distance between the extreme values (max and min) and can be heavily affected by outliers, giving a crude sense of spread. The interquartile range focuses on the middle 50% of the data around the median, which describes spread in a way that's robust to outliers but centers on the median, not the mean. So for describing dispersion around the mean, standard deviation is the best choice.

The measure that describes how dispersed individual observations are from the mean is the standard deviation. It quantifies how far, on average, each data point lies from the average value and puts that spread in the same units as the data, making it easy to interpret. Variance is related but uses squared distances, which can be harder to grasp; standard deviation is just the square root of variance, returning the spread to the original units. The range looks at only the distance between the extreme values (max and min) and can be heavily affected by outliers, giving a crude sense of spread. The interquartile range focuses on the middle 50% of the data around the median, which describes spread in a way that's robust to outliers but centers on the median, not the mean. So for describing dispersion around the mean, standard deviation is the best choice.