Question
In the data set below, what is the lower quartile?
Ask by Rowe Adkins. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The lower quartile is 1.
Solution
-
First, arrange the data in ascending order (if not already sorted). The data set is already sorted:
-
Determine the number of data points,
. Here, . -
Since
is even, split the data into two halves. The lower half consists of the first values: -
Find the median of the lower half to obtain the lower quartile (first quartile,
).
The median of the lower half is the middle value of, which is .
Thus, the lower quartile is
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Simplify this solution The Deep Dive
To find the lower quartile (Q1), first, order the data set, which is already sorted:
Another way to think about quartiles is that they split the sorted data into four equal parts. The lower quartile represents the value below which 25% of the data points fall. In this case, with most of the numbers clustered around 1, it’s easy to see why the lower quartile would reflect that, making it intuitive as well as mathematically precise!
