Sure, let's find the median and mean of the given data set step-by-step.
The given data set is:
[tex]\[ 0, 41, 7, 38 \][/tex]
### Step 1: Arranging the Data
To find the median, the first step is to arrange the data in ascending order:
[tex]\[ 0, 7, 38, 41 \][/tex]
### Step 2: Calculating the Median
The median is the middle value of a data set. Since our data set contains an even number of values (4 values), the median is calculated by finding the average of the two middle values.
The two middle values in our sorted data set are 7 and 38. So, the median is:
[tex]\[ \text{Median} = \frac{7 + 38}{2} = \frac{45}{2} = 22.5 \][/tex]
### Step 3: Calculating the Mean
The mean (or average) is calculated by summing all the values in the data set and then dividing by the total number of values.
Sum of the data set:
[tex]\[ 0 + 7 + 38 + 41 = 86 \][/tex]
Number of values in the data set: [tex]\( 4 \)[/tex]
So, the mean is:
[tex]\[ \text{Mean} = \frac{86}{4} = 21.5 \][/tex]
### Final Answer
So, the median of the data set is [tex]\( 22.5 \)[/tex] and the mean is [tex]\( 21.5 \)[/tex].
[tex]\[
\boxed{\text{Median} = 22.5 \quad \text{Mean} = 21.5}
\][/tex]
