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Mr. Walker is looking at the fundraiser totals for the last five years.

Yearly Fundraiser Totals

\begin{tabular}{|c|c|}
\hline
Year & Total \\
\hline
1 & [tex]$\$[/tex] 896[tex]$ \\
\hline
2 & $[/tex]\[tex]$ 925$[/tex] \\
\hline
3 & [tex]$\$[/tex] 880[tex]$ \\
\hline
4 & $[/tex]\[tex]$ 963$[/tex] \\
\hline
5 & [tex]$\$[/tex] 914[tex]$ \\
\hline
\end{tabular}

How does the mean of the totals compare to the median?

A. The median is $[/tex]\[tex]$ 1.60$[/tex] greater than the mean.

B. The mean is [tex]$\$[/tex] 1.60[tex]$ greater than the median.

C. The median is $[/tex]\[tex]$ 2.82$[/tex] greater than the mean.

D. The mean is [tex]$\$[/tex] 282$ greater than the median.


Sagot :

Sure, let's go through the process step by step to understand how the mean and median of the fundraiser totals for the last five years compare.

1. Listing the Yearly Totals:
- Year 1: \[tex]$896 - Year 2: \$[/tex]925
- Year 3: \[tex]$880 - Year 4: \$[/tex]963
- Year 5: \[tex]$914 2. Calculate the Mean: The mean (average) is calculated by adding all the totals together and then dividing by the number of years. \[ \text{Mean} = \frac{896 + 925 + 880 + 963 + 914}{5} = \frac{4578}{5} = 915.6 \] 3. Calculate the Median: To find the median, we need to arrange the totals in ascending order and then find the middle value. Arranging in ascending order: \[ 880, \ 896, \ 914, \ 925, \ 963 \] The median is the middle number in the ordered list: \[ \text{Median} = 914.0 \] 4. Compare the Mean and the Median: We now compare the mean and the median by finding the difference between them: \[ \text{Difference} = \text{Median} - \text{Mean} = 914.0 - 915.6 = -1.6 \] A negative difference indicates that the mean is greater than the median. Specifically: \[ \text{The mean ( } 915.6 \text{) is \$[/tex]1.60 greater than the median ( } 914.0 \text{).}
\]

5. Conclusion:
Comparing the calculated values:
- The mean of the totals is \[tex]$915.6. - The median of the totals is \$[/tex]914.0.
- The mean is \[tex]$1.60 greater than the median. Thus, the correct answer is: \[ \boxed{\text{The mean is \$[/tex]1.60 greater than the median.}}
\]