Question

determine the best measure of variability. justify your answer. standard deviation, because the data distribution is skewed iqr, because the data distribution is skewed iqr, because the data distribution is symmetric standard deviation, because the data distribution is symmetric

Explanation:

To determine the best measure of variability, we analyze the box - plot. A box - plot shows the distribution of data. If the data distribution is skewed, the Inter - Quartile Range (IQR) is a better measure of variability. The IQR is less affected by extreme values (outliers) and skewed data compared to the standard deviation. The standard deviation is more appropriate for symmetric distributions as it takes into account all the data points (including those in the tails), but in skewed distributions, the mean (and thus the standard deviation which is based on the mean) can be pulled in the direction of the skew. From the box - plot (even with the partial view), we can infer the distribution's skewness. So, when the data distribution is skewed, IQR is the best measure of variability.

Answer:

IQR, because the data distribution is skewed