\begin{tabular}{|c|c|}
\hline Year & Pounds of Trash \\
\hline 1970 & 3.25 \\
\hline 1975 & 3.25 \\
\hline 1980 & 3.66 \\
\hline 1985 & 3.83 \\
\hline 1990 & 4.57 \\
\hline 1995 & 4.52 \\
\hline 2000 & 4.74 \\
\hline 2005 & 4.69 \\
\hline 2010 & 4.44 \\
\hline
\end{tabular}

The table shows the average number of pounds of trash generated per person per day in the United States from 1970 to 2010. Use a statistics calculator to calculate the mean and median. Round the answers to the nearest hundredth.

Median [tex]$=$[/tex] [tex]$\square$[/tex]

Mean [tex]$=$[/tex] [tex]$\square$[/tex]



Answer :

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]