This question asks about appropriate measures of center and spread based on the box plot shown.

Analyzing the Box Plot:

• Center (median or mean): The box plot shows the median (the line inside the box), which is a good measure of central tendency, especially when there are outliers or the data is skewed, as seen here with the whiskers being unequal in length.

• Spread (standard deviation or interquartile range, IQR): The interquartile range (IQR) is a better measure for spread in box plots because it describes the middle 50% of the data, represented by the length of the box. The IQR is resistant to outliers, unlike the standard deviation.

Answer:

• Center: The better measure of center is the median (Option A).
• Spread: The better measure of spread is the IQR (Option C).

Would you like further clarification?

Here are 5 related questions to deepen your understanding:

1. What conditions make the median a better measure than the mean?
2. How do outliers affect the choice between standard deviation and IQR?
3. Can you explain how to calculate the IQR from a box plot?
4. What situations would make the mean and standard deviation better choices?
5. How does the shape of the box plot (e.g., skewed, symmetrical) influence the choice of center and spread measures?

Tip: The median is often better for skewed distributions or when outliers are present, while the mean is more suitable for symmetrical distributions.