Why is the $standard deviation$ generally considered a better measure of variation than the $range$?

• A. Because the $standard deviation$ uses all data values and reflects how each value deviates from the $mean$, while the $range$ only considers the largest and smallest values.
• B. Because the $standard deviation$ is always smaller than the $range$ for any data set.
• C. Because the $standard deviation$ ignores outliers, while the $range$ is affected by them.
• D. Because the $standard deviation$ is easier to calculate than the $range$.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand what the range measures. The range is the difference between the largest and smallest values in a data set, calculated as \(\text{Range} = \text{Max} - \text{Min}\). It only considers two data points and ignores all others.
2. Step 2: Understand what the standard deviation measures. The standard deviation quantifies the average amount by which each data value deviates from the mean of the data set. It uses all data points, not just the extremes.
3. Step 3: Recognize that because the standard deviation incorporates every data value, it provides a more comprehensive measure of variability, reflecting the overall spread of the data around the mean.
4. Step 4: Note that the range can be heavily influenced by outliers (extremely high or low values), which may not represent the typical variation in the data, whereas the standard deviation accounts for all values and their distances from the mean, giving a balanced view.
5. Step 5: Conclude that the standard deviation is generally preferred over the range as a measure of variation because it uses all data points and better reflects the distribution of the data, while the range only considers the two extreme values.