Question

HELP ASAP!

Question
When comparing two populations, when should you use the mean and the MAD? the median and the IQR?

A. When comparing two populations, use the mean and the MAD when each distribution is skewed toward the beginning of the data. Use the median and the IQR when each distribution is skewed toward the end of the data.

B. When comparing two populations, use the mean and the MAD when each distribution contains fewer than 10 items. Use the median and the IQR when each distribution contains 10 or more items.

C. When comparing two populations, use the mean and the MAD when either one or both distributions are skewed. Use the median and the IQR when each distribution is symmetric.

D. When comparing two populations, use the mean and the MAD when each distribution is symmetric. Use the median and the IQR when either one or both distributions are skewed.

Answer 1

D

Step-by-step explanation:

Use the mean and the (MAD) methods to compare two populations when both distributions are symmetric Use the median and the i (IQR) when either one or both distributions are skewed

Answer 2

Use the mean and MAD for symmetric distributions, and the median and IQR for skewed distributions; skewness affects the mean, making the median a better central tendency measure for skewed data.

Step-by-step explanation:

When comparing two populations, the choice between using the mean and the mean absolute deviation (MAD), or the median and the interquartile range (IQR), depends on the shape of the distributions. For symmetric distributions where the data values are evenly spread around the center, the mean and MAD are appropriate. This is because the mean is an accurate measure of central tendency when each side of the distribution is a mirror image of the other, and the MAD provides a measure of variability that is not affected by extreme values.

However, when distributions are skewed (either positively or negatively), the median and IQR are preferred. Skewness causes the mean to be pulled in the direction of the tail, which may not represent the center of the data accurately. In such cases, the median is a better measure of central tendency because it is less affected by extreme values. Similarly, the IQR, which measures the range between the first and third quartiles, provides a clearer picture of the spread of the middle 50 percent of the data without being influenced by outliers.