Final Answer:
The 5-number summary for the given data set {8, 15, 12, 10, 6, 7, 4, 10} is as follows: Minimum = 4, Q1 = 6.75, Median = 9, Q3 = 11.75, Maximum = 15. The interquartile range (IQR) is Q3 - Q1 = 11.75 - 6.75 = 5, and the box and whisker plot visually represents the distribution of the data, showcasing the median, quartiles, and any outliers.
Step-by-step explanation:
To find the 5-number summary, we start by ordering the data set in ascending order: {4, 6, 7, 8, 10, 10, 12, 15}. The minimum is the first value (4), Q1 is the average of the two middle values (6 + 7) / 2 = 6.75, the median is the middle value (10), Q3 is the average of the two middle values in the upper half (12 + 15) / 2 = 13.5, and the maximum is the last value (15).
The interquartile range (IQR) is calculated as the difference between Q3 and Q1: IQR = Q3 - Q1 = 13.5 - 6.75 = 5.
The box and whisker plot is constructed by drawing a number line and marking points for the minimum, Q1, median, Q3, and maximum. A box is then drawn from Q1 to Q3, with a line inside representing the median. Whiskers extend from the box to the minimum and maximum values. In this case, the plot provides a visual representation of the data's spread and central tendency.
In summary, the 5-number summary and the interquartile range offer insights into the central tendency and variability of the data, and the box and whisker plot provides a graphical representation of these statistical measures.