Question

the data show the number of hours of television watched per day by a sample of 28 people. use technology to answer parts (a) and (b) below.

\

$$\begin{matrix} 7 & 7 & 8 & 8 & 3 & 9 & 8 & 9 & 4 \\\\ 6 & 7 & 4 & 6 & 9 & 6 & 5 & 0 & 9 \\\\ 5 & 7 & 5 & 1 & 3 & 3 & 5 & 1 & 7 \\\\ 6 & & & & & & & & \\end{matrix}$$

a. find the data sets first, second, and third quartiles.
\\(q_1 = 4\\)
\\(q_2 = 6\\)
\\(q_3 = 7.5\\)
(type integers or decimals. do not round.)

b. draw a box-and-whisker plot that represents the data set. choose the answer below. note that different technologies will produce slightly different results.

Explanation:

Sort the dataset

Using the Percentiles and Quantiles knowledge point
The sample of \(N = 28\) observations sorted in ascending order:

$$ 0, 1, 1, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9 $$

Calculate the quartiles

Using the Percentiles and Quantiles knowledge point

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(Note: Standard technology calculations yield \(Q_1 = 3.5\), \(Q_2 = 6\), and \(Q_3 = 7\). The values filled in the image's part (a) are \(Q_1 = 4\), \(Q_2 = 6\), \(Q_3 = 7.5\), which correspond to a different software convention or rounding, but we will identify the matching box plot based on the standard five-number summary: \(\text{Min} = 0\), \(Q_1 = 3\text{ or }3.5\text{ or }4\), \(Q_2 = 6\), \(Q_3 = 7\text{ or }7.5\), \(\text{Max} = 9\).)

Identify the correct box plot

Using the Five-Number Summary and Box-and-Whisker Plot knowledge points

• Option A: Box spans from \(3\) to \(7\), median line at \(6\), whiskers from \(0\) to \(9\).
• Option B: Box spans from \(1.5\) to \(5\), median line at \(3\).
• Option C: Box spans from \(4\) to \(7.5\), median line at \(6\), whiskers from \(0\) to \(9\).

Since the values entered in part (a) are \(Q_1 = 4\), \(Q_2 = 6\), and \(Q_3 = 7.5\), the box plot must match these exact values. Option C has its box starting at \(4\), median line at \(6\), and ending at \(7.5\).

Answer:

Question b

• A. Box plot with box from 3 to 7, median at 6, whiskers from 0 to 9.
• B. Box plot with box from 1.5 to 5, median at 3, whiskers from 0 to 9.
• C. Box plot with box from 4 to 7.5, median at 6, whiskers from 0 to 9. (Correct answer)