Question

which box plot best represents data that are skewed to the right?

Explanation:

Step1: Recall Right Skewness in Box Plots

Right - skewed (positively skewed) data in a box plot has the following characteristics: The median is closer to the lower quartile (Q1), the upper whisker is longer than the lower whisker, and the upper half of the data (from median to maximum) is more spread out than the lower half (from minimum to median).

Step2: Analyze Each Box Plot

• For a right - skewed distribution, we look at the position of the median within the box and the lengths of the whiskers. The box represents the inter - quartile range (IQR = Q3 - Q1), with Q1 (lower quartile) at the left end of the box, the median (M) inside the box, and Q3 (upper quartile) at the right end of the box. The whiskers extend from the box to the minimum and maximum values.
• In a right - skewed distribution, the median is closer to Q1 (left side of the box), and the upper whisker (from Q3 to maximum) is longer than the lower whisker (from minimum to Q1).
• Looking at the four box plots:
• The fourth box plot (the one in the bottom - right) has the median closer to the left side of the box (Q1), and the upper whisker (from Q3 to maximum) is longer than the lower whisker (from minimum to Q1). This matches the characteristics of a right - skewed distribution.
• The first box plot: The median is more centered, and the whiskers do not show a long upper whisker relative to the lower one.
• The second box plot: The median is more centered, and the whiskers do not show a long upper whisker relative to the lower one.
• The third box plot: The median is closer to the right side of the box, which would be characteristic of a left - skewed distribution.

Answer:

The box plot in the bottom - right (with minimum around 1, Q1 around 5 - 6, median around 6 - 7, Q3 around 11 - 12, and maximum around 19 - 20) best represents data skewed to the right. (If we assume the box plots are labeled as follows: Top - left (1), Top - right (2), Bottom - left (3), Bottom - right (4), then the answer is 4. The box plot with the median closer to the left of the box and a long upper whisker.)