Answer:
The lower quartile is
thousand dollars.
The median quartile is
thousand dollars.
The upper quartile is
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
where n is all scores in the data set.
Because n = 10, the median position is ![\frac{10+1}{2}=5.5](https://tex.z-dn.net/?f=%5Cfrac%7B10%2B1%7D%7B2%7D%3D5.5)
The median is the average of the fifth and sixth positioned scores
![Q_2=\frac{39+39}{2} =39](https://tex.z-dn.net/?f=Q_2%3D%5Cfrac%7B39%2B39%7D%7B2%7D%20%3D39)
Step 3: Compute
where n is all scores below
.
For scores below
, use only 23, 25, 33, 34, 39.
Because n = 5, the median position is ![\frac{5+1}{2}=3](https://tex.z-dn.net/?f=%5Cfrac%7B5%2B1%7D%7B2%7D%3D3)
The median is the third positioned score: ![Q_1=33](https://tex.z-dn.net/?f=Q_1%3D33)
Step 4: Compute
where n is all scores above
.
For scores above
, use only 39, 44, 45, 48, 55
Because n = 5, the median position is ![\frac{5+1}{2}=3](https://tex.z-dn.net/?f=%5Cfrac%7B5%2B1%7D%7B2%7D%3D3)
The median is the third positioned score: ![Q_3=45](https://tex.z-dn.net/?f=Q_3%3D45)