Answer:
The median price is $32.50
Explanation:
I attached a picture of a boxplot that represents the data and I'll use this explanation to explain the five parts of a boxplot, which includes:
- the minimum (i.e., lowest data point),
- Q1,
- the median (i.e., the middle data point),
- Q3,
- and the maximum (i.e., the highest data point).
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Identifying the minimum and maximum:
- 20.00 is the smallest data point, so it's the minimum.
- 50.00 is the largest data point, so it's the maximum.
Finding the median:
- We need to find the median (i.e., the middle data point) before we can both Q1 and Q3.
First we need to arrange the data in order from least to greatest:
20.00, 24.00, 25.50, 32.00, 32.50, 38.50, 45.00, 45.00, 50.00
Since there an odd number of data points (9), there will be four data points to the left and to the right of the median.
Since there are four data points to the left and to the right of 32.50, it's the median.
Finding Q1:
- About 25% of the data lies below Q1.
- To find it, we find the middle value of the four data points to the left of the median (i.e,. 20.00, 24.00, 25.50, and 32.00).
Because there are four data points and both 24.00 and 25.50 lie in the middle, we find Q1 by averaging these two data points:
Q1 = (24.00 + 25.50) / 2
Q1 = 49.50 / 2
Q1 = 24.75
Thus, Q1 is 24.75
Finding Q3:
- About 25% of the data lies above Q3.
- To find it, we find the middle value of the four data points to the right of the median (i.e., 38.50, 45.00, 45.00, 50.00)
Because there are four data points and both 45.00 and 45.00 lie in the middle, we find Q3 by averaging these two data points:
Q3 = (45.00 + 45.00) / 2
Q3 = 90.00 / 2
Q3 = 45.00
Thus, Q3 is 45.00.