Definition of the Five-Number Summary:

The five-number summary provides a concise description of a dataset using five specific values:

1. Minimum (low value): The smallest data point.
2. Lower Quartile (Q1): The median of the lower half of the data.
3. Median (Q2): The middle value when data is ordered.
4. Upper Quartile (Q3): The median of the upper half of the data.
5. Maximum (high value): The largest data point.

Visual Representation with a Boxplot:

A boxplot (or box-and-whisker plot) visually summarizes the five-number summary:

1. Box: The central part of the plot spans from Q1 to Q3, representing the interquartile range (IQR).
2. Line within the Box: Represents the median (Q2).
3. Whiskers: Extend from the box to the minimum and maximum values (excluding outliers).
4. Outliers (if any): Shown as individual points beyond the whiskers.

The boxplot provides a quick view of data distribution, variability, and potential outliers.

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Correct Answer:

B. low​ value, lower​ quartile, median, upper​ quartile, and high value

Additional Questions:

1. How does the interquartile range (IQR) relate to the boxplot?
2. What are outliers, and how are they determined in a boxplot?
3. How do you compute the quartiles for a given dataset?
4. Why is the median used instead of the mean in the five-number summary?
5. What advantages does a boxplot offer over a histogram for data visualization?

Tip:

When creating a boxplot, ensure your dataset is sorted, as this makes calculating quartiles and identifying outliers much easier.