Question

HH.1 Calculate mean, median, mode, and range
U2A
Natalie assembled and shipped some care packages to friends who were away at college. The 6 packages weighed:
9 pounds6 pounds8 pounds8 pounds5 pounds6 pounds
What was the mean weight?

pounds
list from leasteet to greatest

Answer 1

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

Answer 2

HH.1 Calculate mean, median, mode, and range
U2A
What is the mean?
336109665