*see attachment for the data set given
Answer:
[tex] Q_1 = 2.5 [/tex]
[tex] Q_2 = 5.5 [/tex]
[tex] Q_3 = 8 [/tex]
The box plot is shown in the attachment below.
Step-by-step Explanation:
a. To find Q1, Q2 (median), and Q3, first order the data from the least to the largest. We would have:
0, 1, 1,1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9
Q2 which is also the median, is the middle value that divides the data set into two equal parts. In the data set given, Q2 is the data value between the 14th and 15th data value. The average of the 14th and the 15th data value would give us Q2.
0, 1, 1,1, 2, 2, 2, 3, 4, 5, 5, 5, 5, [5,Q2, 6], 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9
They are 5 and 6. Average = [tex] \frac{5+6}{2} = 5.5 [/tex]
Q1 is the middle value of the lower part of the data set from Q2 down to your left.
0, 1, 1,1, 2, 2, [2, Q1, 3,] 4, 5, 5, 5, 5, 5, Q2, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9
Q1 = average of the 7th and 8th value = [tex] \frac{2+3}{2} = 2.5 [/tex]
Q3 = [tex] \frac{8+8}{2} = 8 [/tex]
0, 1, 1,1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 5,Q2, 6, 6, 7, 7, 7, 8, [8, Q3, 8], 8, 9, 9, 9, 9, 9.