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.

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

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
The sample size is \(n = 28\). We first arrange the 28 data values 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 second quartile (Median, Q2)

Using the Percentiles and Quantiles knowledge point
Since \(n = 28\) is even, the median \(Q_2\) is the average of the \(14^{\text{th}}\) and \(15^{\text{th}}\) values:

$$
LATEXBLOCK0
$$

Calculate the first quartile (Q1)

Using the Percentiles and Quantiles knowledge point
The lower half consists of the first 14 values:

$$ 0, 1, 1, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6 $$

Since there are 14 values, \(Q_1\) is the average of the \(7^{\text{th}}\) and \(8^{\text{th}}\) values of this lower half:

$$
LATEXBLOCK1
$$

Calculate the third quartile (Q3)

Using the Percentiles and Quantiles knowledge point
The upper half consists of the last 14 values:

$$ 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9 $$

Since there are 14 values, \(Q_3\) is the average of the \(7^{\text{th}}\) and \(8^{\text{th}}\) values of this upper half:

$$
LATEXBLOCK2
$$

Answer:

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

\(Q_1 =\) <blank>\(3.5\)</blank>
\(Q_2 =\) <blank>\(6\)</blank>
\(Q_3 =\) <blank>\(7\)</blank>

(Type integers or decimals. Do not round.)