Question

question 5 points 1

if a distribution is symmetrical then what is the most appropriate measure of variability (spread)?

mean absolute deviation

mean

Explanation:

Identify the distribution shape and target measure

Using the Data Distribution Shape knowledge point, we identify that the given distribution is symmetrical. We need to find the most appropriate measure of variability (spread) for a symmetric distribution.

Evaluate measures of center versus spread

Using the Measures of Spread knowledge point, we distinguish between measures of center and measures of variability. The option "Mean" is a measure of central tendency, not variability, so it is ruled out.

Select the optimal measure of variability

Using the Standard Deviation knowledge point

$$ \text{For symmetric distributions, the standard deviation is the most common and appropriate measure of spread.} $$

Since standard deviation is not listed among the visible options, we evaluate the other option. The "Mean absolute deviation" (MAD) is indeed a valid measure of variability (spread) that is highly appropriate for symmetric distributions, as it utilizes the mean (the natural center of a symmetric distribution) to calculate average distance from the center.

Answer:

• Mean absolute deviation (Correct answer)
• Mean