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. 9 4 6 6 4 1 5 3 4 2 0 1 4 4 6 0 9 7 1 7 4 8 9 5 6 7 0 8 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

0, 0, 0, 1, 1, 1, 2, 3, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9

Step2: Calculate position of Q2

The position of the median (Q2) for \(n = 28\) data - points is \(i=\frac{n + 1}{2}=\frac{28+1}{2}=14.5\). So, \(Q2=\frac{4 + 5}{2}=4.5\).

Step3: Split data into lower and upper - halves

The lower - half of the data is 0, 0, 0, 1, 1, 1, 2, 3, 4, 4, 4, 4, 4, 4. The upper - half of the data is 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9.

Step4: Calculate position of Q1

For the lower - half (\(n_1 = 14\) data - points), \(i_1=\frac{n_1+1}{2}=\frac{14 + 1}{2}=7.5\). So, \(Q1=\frac{2+3}{2}=2.5\).

Step5: Calculate position of Q3

For the upper - half (\(n_2 = 14\) data - points), \(i_2=\frac{n_2+1}{2}=\frac{14 + 1}{2}=7.5\). So, \(Q3=\frac{6+7}{2}=6.5\).

Answer:

Q1 = 2.5
Q2 = 4.5
Q3 = 6.5