Answered

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



Yearly Fundraiser Totals




Year		Total

1		\$896

2		\$925

3		\$880

4		\$963

5		\$914






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


AThe median is \$1.60 greater than the mean.
BThe mean is \$1.60 greater than the median.
CThe median is \$2.82 greater than the mean.
DThe mean is \$2.82 greater than the median.

Verified Answer :

  • Calculate the mean: \(\frac{896 + 925 + 880 + 963 + 914}{5} = \$915.60\).
  • Identify the median by ordering the set: \(\{880, 896, 914, 925, 963\}\), so the median is \(\$914.00\).
  • Find the difference: \(\$915.60 - \$914.00 = \$1.60\).
  • Conclude the mean is \(\$1.60\) greater than the median: \(\boxed{\text{The mean is } \$1.60 \text{ greater than the median.}}\)

Explanation

  1. Analyze the problem and data set

To compare the mean and median of the fundraiser totals, we first identify the data set. The totals for the five years are: \(\$896\), \(\$925\), \(\$880\), \(\$963\), and \(\$914\). We are comparing the arithmetic mean to the median of these five values.

  1. Calculate the mean of the totals

The mean (\(\mu\)) is the sum of all values divided by the number of observations (\(n = 5\)).
Sum = \(896 + 925 + 880 + 963 + 914 = 4578\).
Mean \(\mu = \frac{4578}{5} = \$915.60\).

  1. Find the median of the totals

To find the median, we first arrange the data set in ascending order:
Ordered set: \(880, 896, 914, 925, 963\).
Since there are 5 values, the median is the value in the middle position (the 3rd position).
Median = \(\$914.00\).

  1. Compare the mean and the median

We now compare the mean and the median:
Mean = \(\$915.60\)
Median = \(\$914.00\)
Difference = \(915.60 - 914.00 = \$1.60\).
Since the mean is greater than the median by \(\$1.60\), we conclude that the mean is \(\$1.60\) greater than the median.

Examples

Understanding the mean and median is essential in financial analysis. For example, if a charity wants to understand their "typical" fundraising year, they might look at the median to avoid being skewed by an exceptionally high or low year, whereas the mean provides an average that includes all data points equally. Comparing the two helps identify if the data is distributed symmetrically or skewed.