Final Answer:
The five-number summary for the given data set {5, 14, 17, 10, 7, 13, 16, 10, 5} is as follows: Minimum = 5, First Quartile (Q1) = 7.5, Median = 10, Third Quartile (Q3) = 14.5, Maximum = 17. The boxplot visually represents this summary, providing insights into the distribution and central tendency of the data.
Explanation:
To obtain the five-number summary, we first need to arrange the data in ascending order: {5, 5, 7, 10, 10, 13, 14, 16, 17}. The minimum value is 5, the maximum is 17, and the median is the middle value, which is 10. To find the first and third quartiles, we divide the data into two halves at the median. For Q1, we take the median of the lower half, resulting in 7.5, and for Q3, we take the median of the upper half, yielding 14.5.
The boxplot is a graphical representation of the five-number summary. It consists of a rectangular box that spans from Q1 to Q3, with a line inside marking the median. The "whiskers" extend from the box to the minimum and maximum values. Outliers, if any, are represented as individual points beyond the whiskers. In this case, the boxplot would visually show the spread of the data, the central tendency, and the presence of any outliers.
In conclusion, the five-number summary and the boxplot provide a concise and informative summary of the data's distribution, central tendency, and potential outliers. They serve as valuable tools for understanding the characteristics of a dataset in a visual and quantitative manner.