Question

bruce helps answer mail for the mayor of pineville. after the mayor visited his towns middle school last week, he received lots of letters from students. bruce kept track of how many student letters he answered every day. letters from students 4 6 11 8 3 7 3 5 8 4 6 which box plot represents the data? letters from students letters from students

Explanation:

Step1: Order the data

First, we order the data set: \(3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 11\)

Step2: Find the median (Q2)

The number of data points \(n = 11\) (odd). The median is the middle value, which is the \(\frac{11 + 1}{2}=6^{\text{th}}\) value. So the median (Q2) is \(6\).

Step3: Find Q1 (median of lower half)

The lower half of the data (excluding the median) is \(3, 3, 4, 4, 5\). The median of this set (with \(n = 5\)) is the \(3^{\text{rd}}\) value, so \(Q1 = 4\).

Step4: Find Q3 (median of upper half)

The upper half of the data (excluding the median) is \(6, 7, 8, 8, 11\). The median of this set (with \(n = 5\)) is the \(3^{\text{rd}}\) value, so \(Q3 = 8\).

Step5: Find the minimum and maximum

The minimum value is \(3\) and the maximum value is \(11\).

Now, let's analyze the box - plots:

• The box in a box - plot has Q1 (left end), median (line inside the box), and Q3 (right end). The whiskers extend to the minimum and maximum.
• For our data, Q1 = 4, median = 6, Q3 = 8, min = 3, max = 11.

Looking at the two box - plots:

• In the first box - plot, the left end of the box (Q1) should be at 4, the median line at 6, and the right end (Q3) at 8. The whiskers should go from 3 (min) to 11 (max).
• In the second box - plot, the left end of the box is not at 4 (it seems to be at a value less than 4), so it does not match our calculated Q1.

So the first box - plot (the one with the box starting at 4, median at 6, and ending at 8, with whiskers from 3 to 11) represents the data.

Answer:

The first box - plot (the one where the left end of the box is at 4, the median line is at 6, the right end of the box is at 8, and the whiskers extend from 3 to 11) represents the data. (Assuming the first box - plot is the one with the box starting at 4 as per the calculation of Q1 = 4)