Let's analyze the problem based on the box-and-whisker plot and the related questions:

a) Shape of the dataLet's analyze the problem based on the box-and-whisker plot and the related questions:

a) Shape of the

The box-and-whisker plot displays the number of guests at a restaurant. The right whisker (upper range) is much longer than the left whisker, suggesting that the data has a longer tail on the right side.

• Answer: The data is skewed right.

b) Measure of center:

Since the data is skewed, the median is generally a better measure of central tendency than the mean, as it is less affected by extreme values in a skewed distribution.

• Answer: Median is the better measure of center.

c) Measure of variability/spread:

For skewed data, Interquartile Range (IQR) is typically preferred because it is based on quartiles and is resistant to extreme values, unlike standard deviation, which can be influenced by outliers.

• Answer: IQR is the better measure of variability/spread.

Would you like more detailed explanations on any part of this? Here are 5 related questions to deepen your understanding:

1. What does the length of the whiskers in a box plot indicate?
2. How would the box plot look for a perfectly symmetric distribution?
3. Why is the median preferred over the mean in skewed distributions?
4. What is the formula for calculating the IQR from a box plot?
5. How does skewness affect the interpretation of standard deviation?

Tip: In box plots, the length of the box (which represents the IQR) shows the spread of the middle 50% of the data.