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 2 6 3 3 0 2 5 0 0 4 7 2 4 1 8 6 1 2 4 0 9 3 7 7 4 9 6 a. find the data sets first, second, and third quartiles. q1 = q2 = q3 = (type integers or decimals. do not round.)

Explanation:

Step1: Sort the data

First, sort the data set in ascending order: 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 9, 9.

Step2: Calculate the position of Q2 (median)

The formula to find the position of the median for a data - set of size $n$ is $i=\frac{n + 1}{2}$. Here, $n = 28$, so $i=\frac{28+1}{2}=14.5$. The median $Q_2$ is the average of the 14th and 15th ordered data values. The 14th value is 4 and the 15th value is 4, so $Q_2=\frac{4 + 4}{2}=4$.

Step3: Calculate the position of Q1

The lower half of the data set has $n_1 = 14$ values. The formula to find the position of the median of the lower - half (which is $Q_1$) is $i_1=\frac{14 + 1}{2}=7.5$. So $Q_1$ is the average of the 7th and 8th ordered data values in the lower half. The 7th value is 2 and the 8th value is 2, so $Q_1=\frac{2+2}{2}=2$.

Step4: Calculate the position of Q3

The upper half of the data set has $n_2 = 14$ values. The formula to find the position of the median of the upper - half (which is $Q_3$) is $i_2=\frac{14 + 1}{2}=7.5$. So $Q_3$ is the average of the 7th and 8th ordered data values in the upper half. The 7th value in the upper half is 6 and the 8th value is 7, so $Q_3=\frac{6 + 7}{2}=6.5$.

Answer:

$Q_1 = 2$
$Q_2 = 4$
$Q_3 = 6.5$