Answer:
[tex]\%Pr =71.43 \%[/tex]
Step-by-step explanation:
Given
[tex]S = \{8, 7, 3, 8, 14, 15, 20\}[/tex]
[tex]n(S) = 7[/tex]
Required
Percentage of values between Q1 and Q3
We have:
[tex]S = \{8, 7, 3, 8, 14, 15, 20\}[/tex]
Sort
[tex]Sorted = \{3, 7, 8, 8, 14, 15, 20\}[/tex]
Q1 is calculated as:
[tex]Q_1 = \frac{n+1}{4}th[/tex]
[tex]Q_1 = \frac{7+1}{4}th[/tex]
[tex]Q_1 = \frac{8}{4}th[/tex]
[tex]Q_1 = 2nd[/tex]
The second element is: 7; So:
[tex]Q_1 = 7[/tex]
Q3 is calculated as:
[tex]Q_3 = 3*\frac{n+1}{4}th[/tex]
[tex]Q_3 = 3*\frac{7+1}{4}th[/tex]
[tex]Q_3 = 3*\frac{8}{4}th[/tex]
[tex]Q_3 = 3*2th[/tex]
[tex]Q_3 = 6th[/tex]
The sixth element is: 15; So:
[tex]Q_3 = 15[/tex]
From the sorted dataset, the data between Q1 and Q3 is:
[tex]Q_3&Q_1 = \{7, 8, 8, 14, 15\}[/tex]
[tex]n(Q_3&Q_1) = 5[/tex]
The percentage is:
[tex]\%Pr =\frac{n(Q_3&Q_1)}{n(S)} * 100\%[/tex]
[tex]\%Pr =\frac{5}{7} * 100\%[/tex]
[tex]\%Pr =\frac{5* 100}{7} \%[/tex]
[tex]\%Pr =\frac{500}{7} \%[/tex]
[tex]\%Pr =71.43 \%[/tex]
