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.

\

$$\begin{matrix} 6 & 2 & 4 & 4 & 4 & 9 & 1 & 1 & 9 \\\\ 6 & 0 & 9 & 2 & 4 & 1 & 9 & 9 & 4 \\\\ 1 & 9 & 3 & 8 & 0 & 4 & 1 & 0 & 4 \\\\ 7 & & & & & & & & \\end{matrix}$$

a. find the data sets first, second, and third quartiles.

\\(q_1 = \\)
\\(q_2 = \\)
\\(q_3 = \\)

(type integers or decimals. do not round.)

Explanation:

Sort the dataset

Using the Percentiles and Quantiles knowledge point

$$ \text{Raw data (28 values): } 6, 2, 4, 4, 4, 9, 1, 1, 9, 6, 0, 9, 2, 4, 1, 9, 9, 4, 1, 9, 3, 8, 0, 4, 1, 0, 4, 7 $$

$$ \text{Sorted data: } 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 7, 8, 9, 9, 9, 9, 9, 9 $$

Let's recount the sorted values to ensure we have exactly 28:

• 0s: 3
• 1s: 5
• 2s: 2
• 3s: 1
• 4s: 8
• 6s: 2
• 7s: 1
• 8s: 1
• 9s: 6

Total count: \(3 + 5 + 2 + 1 + 8 + 2 + 1 + 1 + 6 = 29\).
Let's recount the raw data in the image:
Row 1: 6, 2, 4, 4, 4, 9, 1, 1, 9 (9 values)
Row 2: 6, 0, 9, 2, 4, 1, 9, 9, 4 (9 values)
Row 3: 1, 9, 3, 8, 0, 4, 1, 0, 4 (9 values)
Row 4: 7 (1 value)
Total: \(9 + 9 + 9 + 1 = 28\) values.
Let's re-verify the counts from the image:

• 0s: Row 2 has one (0), Row 3 has two (0, 0). Total = 3. Correct.
• 1s: Row 1 has two (1, 1), Row 2 has one (1), Row 3 has two (1, 1). Total = 5. Correct.
• 2s: Row 1 has one (2), Row 2 has one (2). Total = 2. Correct.
• 3s: Row 3 has one (3). Total = 1. Correct.
• 4s: Row 1 has three (4, 4, 4), Row 2 has two (4, 4), Row 3 has two (4, 4). Total = 7. Let's recount:

Row 1: 4, 4, 4 (three)
Row 2: 4, 4 (two)
Row 3: 4, 4 (two)
Total 4s = 7. (My previous count of 8 was incorrect).

• 6s: Row 1 has one (6), Row 2 has one (6). Total = 2. Correct.
• 7s: Row 4 has one (7). Total = 1. Correct.
• 8s: Row 3 has one (8). Total = 1. Correct.
• 9s: Row 1 has two (9, 9), Row 2 has three (9, 9, 9), Row 3 has one (9). Total = 6. Correct.

Corrected sorted list of 28 values:

$$ 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 6, 6, 7, 8, 9, 9, 9, 9, 9, 9 $$

Calculate the second quartile

Using the Percentiles and Quantiles knowledge point

$$
LATEXBLOCK0
$$

Calculate the first quartile

Using the Percentiles and Quantiles knowledge point

$$
LATEXBLOCK1
$$

Calculate the third quartile

Using the Percentiles and Quantiles knowledge point

$$
LATEXBLOCK2
$$

Answer:

a. Find the data set's first, second, and third quartiles.

\(Q_1 =\) <blank>1</blank>
\(Q_2 =\) <blank>4</blank>
\(Q_3 =\) <blank>8.5</blank>