To calculate the mean and median of the given data set, follow these steps:
Step 1: Listing the Data
First, list the given pounds of trash data:
[tex]\[ 3.25, 3.25, 3.66, 3.83, 4.57, 4.52, 4.74, 4.69, 4.44 \][/tex]
Step 2: Calculating the Mean
The mean (average) is calculated by adding all the data values together and dividing by the number of values.
[tex]\[ \text{Mean} = \frac{\sum \text{data values}}{\text{number of values}} \][/tex]
Adding the values:
[tex]\[ 3.25 + 3.25 + 3.66 + 3.83 + 4.57 + 4.52 + 4.74 + 4.69 + 4.44 = 36.95 \][/tex]
The number of data values is 9.
So, the mean is:
[tex]\[ \text{Mean} = \frac{36.95}{9} \approx 4.11 \][/tex]
Step 3: Calculating the Median
To find the median, list the numbers in ascending order:
[tex]\[ 3.25, 3.25, 3.66, 3.83, 4.44, 4.52, 4.57, 4.69, 4.74 \][/tex]
Since there are 9 data points (an odd number), the median is the middle value, which is the fifth value in this ordered list:
The fifth value is:
[tex]\[ 4.44 \][/tex]
Final Step: Rounding (if necessary)
The mean and median are already rounded to two decimal places.
Therefore, the median is:
[tex]\[ \text{Median} = 4.44 \][/tex]
And the mean is:
[tex]\[ \text{Mean} = 4.11 \][/tex]
So:
Median \(= 4.44\)
Mean [tex]\(= 4.11\)[/tex]
