To calculate the mean, median, mode, and range of the weights of the care packages, we first need to organize the data. The weights provided are:
- 9 pounds
- 6 pounds
- 8 pounds
- 8 pounds
- 5 pounds
- 6 pounds
Step 1: List the weights from least to greatest
Arranging the weights in ascending order gives us:
5 pounds, 6 pounds, 6 pounds, 8 pounds, 8 pounds, 9 pounds
Step 2: Calculate the Mean
The mean is calculated by adding all the values and dividing by the number of values.
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]
Summing the weights: \[ 5 + 6 + 6 + 8 + 8 + 9 = 42 \text{ pounds} \]
There are 6 packages, so:
\[ \text{Mean} = \frac{42}{6} = 7 \text{ pounds} \]
Step 3: Calculate the Median
The median is the middle value. Since there are 6 numbers (an even amount), the median will be the average of the two middle numbers.
The middle numbers (3rd and 4th) are: 6 pounds and 8 pounds
\[ \text{Median} = \frac{6 + 8}{2} = \frac{14}{2} = 7 \text{ pounds} \]
Step 4: Calculate the Mode
The mode is the number that appears most frequently in the dataset.
6 pounds appears 2 times, and 8 pounds appears 2 times, while all other numbers appear only once.
Thus, the modes are:
- 6 pounds
- 8 pounds
Step 5: Calculate the Range
The range is the difference between the maximum and minimum values.
Highest weight = 9 pounds
Lowest weight = 5 pounds
\[ \text{Range} = 9 - 5 = 4 \text{ pounds} \]
Summary of Results
- Mean: 7 pounds
- Median: 7 pounds
- Mode: 6 pounds and 8 pounds (bimodal)
- Range: 4 pounds
Final Weights from Least to Greatest
5 pounds, 6 pounds, 6 pounds, 8 pounds, 8 pounds, 9 pounds