Question

if the distribution is bell shaped which measure of center and measure of variability makes sense to use? mean and mad median and iqr median and mad mean and iqr

Explanation:

For a bell - shaped (normal) distribution, the mean is the best measure of center as the data is symmetrically distributed around it. The standard deviation (or equivalently, variance) is a common measure of variability. Among the given options, the mean and the inter - quartile range (IQR) are not the best combination for a normal distribution. The median and IQR are more appropriate for skewed distributions. The median and MAD (median absolute deviation) are also more suitable for non - normal distributions. The mean and MAD is not the typical combination for a normal distribution. The best combination for a bell - shaped distribution among the options is the mean and the standard deviation (or variance). Since MAD and IQR are not standard for normal distributions and median is not the best measure of center for normal distributions, the most appropriate is mean and standard deviation - related measures.

Answer:

The measure of center is the mean and the measure of variability is the standard deviation (or variance). Among the given options, the closest is mean and MAD (though standard deviation is more common than MAD for normal distributions). But if we assume MAD as a proxy for a measure related to variability for normal - like symmetric distributions, the answer is mean and MAD.