Answer:
[tex]Q_1 = 7[/tex]
[tex]Q_2 = 10[/tex]
[tex]Q_3 = 13.5[/tex]
Step-by-step explanation:
Given
5, 7, 7, 8, 10, 11, 12, 15, 17.
Required
Determine Q1, Q2 and Q3
The number of data is 9
Calculating Q1:
Q1 is calculated as:
[tex]Q_1 = \frac{1}{4}(N + 1)[/tex]
Substitute 9 for N
[tex]Q_1 = \frac{1}{4}(9 + 1)[/tex]
[tex]Q_1 = \frac{1}{4}*10[/tex]
[tex]Q_1 = 2.5th\ item[/tex]
This means that the Q1 is the mean of the 2nd and 3rd data.
So:
[tex]Q_1 = \frac{1}{2}(7+7)[/tex]
[tex]Q_1 = \frac{1}{2}*14[/tex]
[tex]Q_1 = 7[/tex]
Calculating Q2:
Q2 is calculated as:
[tex]Q_2 = \frac{1}{2}(N + 1)[/tex]
Substitute 9 for N
[tex]Q_2 = \frac{1}{2}(9 + 1)[/tex]
[tex]Q_2 = \frac{1}{2}*10[/tex]
[tex]Q_2 = 5th\ item[/tex]
[tex]Q_2 = 10[/tex]
Calculating Q3:
Q3 is calculated as:
[tex]Q_3 = \frac{3}{4}(N + 1)[/tex]
Substitute 9 for N
[tex]Q_3 = \frac{3}{4}(9 + 1)[/tex]
[tex]Q_3 = \frac{3}{4}*10[/tex]
[tex]Q_3 = 7.5th\ item[/tex]
This means that the Q3 is the mean of the 7th and 8th data.
So:
[tex]Q_3 = \frac{1}{2}(12+15)[/tex]
[tex]Q_3 = \frac{1}{2}*27[/tex]
[tex]Q_3 = 13.5[/tex]
