Question

(interpreting data displays mc)
determine the best measure of variability. justify your answer.
box plot image with number line 1-10
options:
iqr, because the data distribution is skewed
range, because the data distribution is skewed
iqr, because the data distribution is symmetric
range, because the data distribution is symmetric

Explanation:

1. Recall the concepts of measure of variability and data distribution:

• The interquartile range (IQR) is a measure of variability that is resistant to outliers and is used when the data distribution is skewed. The range is the difference between the maximum and minimum values and is affected by outliers.
• A box - plot can be used to determine the skewness of the data. If the box in the box - plot is not centered (the median is not in the middle of the box) or the whiskers are of different lengths, the data is skewed. In a symmetric distribution, the box is centered and the whiskers are approximately equal in length.
• For a skewed data distribution, IQR is a better measure of variability than the range because the range is affected by extreme values (outliers) which are more likely to occur in a skewed distribution.
• Looking at the box - plot, we can see that the data distribution is skewed (the box is not centered and the whiskers seem to be of different lengths). So we should use IQR as the measure of variability.

Answer:

A. IQR, because the data distribution is skewed