Respuesta :
Answer:
The lower quartile is [tex]Q_1=33[/tex] thousand dollars.
The median quartile is [tex]Q_2=39[/tex] thousand dollars.
The upper quartile is [tex]Q_3=45[/tex] thousand dollars.
Step-by-step explanation:
The lower quartile is the median value of the lower half of a data set at the 25th percentile of a distribution.
The median quartile is the median value of a data set at the 50th percentile of a distribution.
The upper quartile is the median value of the upper half of a data set at the 75th percentile of a distribution.
To locate each quartile in a data set, we follow four steps:
Step 1: Put the numbers in order: 23, 25, 33, 34, 39, 39, 44, 45, 48, 55
Step 2: The median is given by [tex]\frac{n+1}{2}[/tex] where n is all scores in the data set.
Because n = 10, the median position is [tex]\frac{10+1}{2}=5.5[/tex]
The median is the average of the fifth and sixth positioned scores
[tex]Q_2=\frac{39+39}{2} =39[/tex]
Step 3: Compute [tex]\frac{n+1}{2}[/tex] where n is all scores below [tex]Q_2[/tex].
For scores below [tex]Q_2[/tex], use only 23, 25, 33, 34, 39.
Because n = 5, the median position is [tex]\frac{5+1}{2}=3[/tex]
The median is the third positioned score: [tex]Q_1=33[/tex]
Step 4: Compute [tex]\frac{n+1}{2}[/tex] where n is all scores above [tex]Q_2[/tex].
For scores above [tex]Q_2[/tex], use only 39, 44, 45, 48, 55
Because n = 5, the median position is [tex]\frac{5+1}{2}=3[/tex]
The median is the third positioned score: [tex]Q_3=45[/tex]
