the data show the number of hours of television watched per day by a sample of 28 people. use technology to…
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 0 5 0 3 1 8 1 7 4 4 9 7 5 6 6 5 5 8 2 1 3 2 9 3 8 3 7 a. find the data sets first, second, and third quartiles. q1 = q2 = q3 = (type integers or decimals. do not round.)
Answer
Explanation:
Step1: Sort the data set
First, sort the data set in ascending - order: 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9.
Step2: Calculate the position of Q2
The second - quartile (Q2) is the median. Since (n = 28) (an even number), the median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+1))th ordered values. (\frac{n}{2}=14) and (\frac{n}{2}+1 = 15). The 14th value is 5 and the 15th value is 5, so (Q2=\frac{5 + 5}{2}=5).
Step3: Calculate the position of Q1
The first - quartile (Q1) is the median of the lower half of the data. The lower half of the data consists of the first 14 values. Since (n_1 = 14) (an even number), the median of the lower half is the average of the (\frac{14}{2})th and ((\frac{14}{2}+1))th ordered values in the lower - half. The 7th value is 2 and the 8th value is 3, so (Q1=\frac{2+3}{2}=2.5).
Step4: Calculate the position of Q3
The third - quartile (Q3) is the median of the upper half of the data. The upper half of the data consists of the last 14 values. Since (n_2 = 14) (an even number), the median of the upper half is the average of the (\frac{14}{2})th and ((\frac{14}{2}+1))th ordered values in the upper - half. The 7th value in the upper - half (counting from the 15th value of the whole data set) is 7 and the 8th value is 7, so (Q3=\frac{7 + 7}{2}=7).
Answer:
(Q1 = 2.5) (Q2 = 5) (Q3 = 7)