Question

1. the number of songs fifteen students have on their mp3 players is: 120, 124, 132, 145, 200, 255, 260, 292, 308, 314, 342, 407, 421, 435, 452 state the values of the minimum, 1st quartile, median, 3rd quartile, and maximum. using these values, construct a box-and-whisker plot using an appropriate scale on the line below.

Explanation:

Step1: Order the data

First, we confirm the data is already ordered: \(120, 124, 132, 145, 200, 255, 260, 292, 308, 314, 342, 407, 421, 435, 452\) (n = 15).

Step2: Find Minimum and Maximum

Minimum is the smallest value: \(120\).
Maximum is the largest value: \(452\).

Step3: Find Median (2nd Quartile)

For \(n = 15\) (odd), the median is the \(\frac{n + 1}{2}=8\)-th term.
8th term: \(292\).

Step4: Find 1st Quartile (\(Q_1\))

\(Q_1\) is the median of the lower half (first 7 terms: \(120, 124, 132, 145, 200, 255, 260\)).
For \(n = 7\) (odd), median is the \(\frac{7 + 1}{2}=4\)-th term: \(145\).

Step5: Find 3rd Quartile (\(Q_3\))

\(Q_3\) is the median of the upper half (last 7 terms: \(308, 314, 342, 407, 421, 435, 452\)).
For \(n = 7\) (odd), median is the \(\frac{7 + 1}{2}=4\)-th term: \(407\).

Answer:

• Minimum: \(120\)
• 1st Quartile (\(Q_1\)): \(145\)
• Median: \(292\)
• 3rd Quartile (\(Q_3\)): \(407\)
• Maximum: \(452\)

To construct the box - and - whisker plot:

1. Draw a number line that covers the range from \(120\) to \(452\).
2. Plot the minimum (\(120\)) and maximum (\(452\)) as the endpoints of the whiskers.
3. Draw a box from \(Q_1 = 145\) to \(Q_3=407\). Inside the box, draw a vertical line at the median (\(292\)).