To calculate the mean, median, mode, and range for the winning bids, we first need to list the bids clearly:
Bids: $4.00, $5.00, $6.00, $4.00, $7.00, $5.00$
1. Range
The range is calculated as the difference between the highest and lowest values in the data set.
- Highest bid: $7.00
- Lowest bid: $4.00
Range = Highest - Lowest
Range = $7.00 - $4.00 = $3.00
2. Mean
The mean is the average of the bids.
Mean = (Sum of all bids) / (Number of bids)
Sum of bids = $4.00 + $5.00 + $6.00 + $4.00 + $7.00 + $5.00$
Sum = $31.00
Number of bids = 6
Mean = $31.00 / 6 ≈ $5.17 (rounded to two decimal places)
3. Median
The median is the middle value when the data is organized in ascending order.
First, arrange the bids in ascending order: $4.00, $4.00, $5.00, $5.00, $6.00, $7.00$
Since there are 6 bids (an even number), the median will be the average of the two middle values (3rd and 4th).
3rd and 4th values: $5.00$ and $5.00$
Median = ($5.00 + $5.00) / 2 = $5.00
4. Mode
The mode is the value that appears most frequently in the data set.
In the list of bids:
- $4.00$ appears 2 times
- $5.00$ appears 2 times
- $6.00$ appears 1 time
- $7.00$ appears 1 time
Since $4.00$ and $5.00$ both appear the most frequently (twice), there are two modes in this data set.
Modes: $4.00$ and $5.00$
Summary
- Range: $3.00
- Mean: $5.17
- Median: $5.00
- Modes: $4.00 and $5.00