To solve the problem of comparing the mean and median of the fundraiser totals over the last five years, let's follow a systematic approach:
### Step 1: List the Yearly Totals
Here are the given totals:
- Year 1: [tex]$896
- Year 2: $[/tex]925
- Year 3: [tex]$880
- Year 4: $[/tex]963
- Year 5: [tex]$914
### Step 2: Calculate the Mean
The mean (average) is calculated by summing all the totals and then dividing by the number of years.
Sum of the totals:
$[/tex][tex]$ 896 + 925 + 880 + 963 + 914 = 4578 $[/tex][tex]$
Number of years:
$[/tex][tex]$ 5 $[/tex][tex]$
Mean:
$[/tex][tex]$ \text{Mean} = \frac{4578}{5} = 915.6 $[/tex][tex]$
### Step 3: Calculate the Median
The median is the middle number when the totals are arranged in ascending order. Let's first sort the totals:
Sorted totals:
$[/tex][tex]$ [880, 896, 914, 925, 963] $[/tex][tex]$
The median is the middle value in this list. Since there are 5 numbers (an odd number of observations), the median is the 3rd number in the sorted list:
Median:
$[/tex][tex]$ \text{Median} = 914 $[/tex][tex]$
### Step 4: Compare the Mean and Median
Next, we need to calculate the difference between the mean and the median:
Difference:
$[/tex][tex]$ \text{Difference} = \text{Mean} - \text{Median} = 915.6 - 914 = 1.6 $[/tex][tex]$
### Step 5: Interpretation of the Difference
We find that the mean is $[/tex]1.60 greater than the median.
Therefore, the correct conclusion is:
The mean is [tex]$\$[/tex]1.60$ greater than the median.
