Question

a scout leader counted how many badges each scout had earned. badges earned 4 0 5 6 8 9 9 10 4 10 5 which box plot represents the data? badges earned badges earned

Explanation:

Step1: Order the data

First, we order the data set: \(4, 4, 5, 5, 6, 8, 9, 9, 9, 10, 10\)

Step2: Find the minimum, Q1, median, Q3, maximum

• Minimum: The smallest value is \(4\).
• Q1 (First Quartile): The median of the lower half (\(4, 4, 5, 5, 6\)). The median of this set is \(5\).
• Median (Second Quartile): The middle value of the ordered data. Since there are 11 values, the 6th value is \(8\).
• Q3 (Third Quartile): The median of the upper half (\(9, 9, 9, 10, 10\)). The median of this set is \(9\).
• Maximum: The largest value is \(10\).

Now, let's analyze the box - plots:

• The box in a box - plot is defined by Q1 (left end), median (line inside the box), and Q3 (right end). The whiskers extend from the minimum to Q1 and from Q3 to the maximum.
• For the first box - plot: Let's assume the left end of the box (Q1) is around \(5\), the median line is around \(7\) (incorrect as our median is \(8\)), and the right end of the box (Q3) is around \(9\).
• For the second box - plot: The left end of the box (Q1) is around \(5\), the median line is around \(8\) (matches our median), and the right end of the box (Q3) is around \(9\). Also, the minimum is \(4\) and the maximum is \(10\) which matches our calculated values.

Answer:

The second box - plot (the one with the box starting around \(5\), median line at \(8\), and box ending around \(9\) with whiskers from \(4\) to \(10\)) represents the data.