How large is a wolf pack? The following information is from a random sample of winter wolf packs. Winter pack size are given below. Compute the mean, median, and mode for the size of winter wolf packs.

5

13

10

8

10

10

5

7

6

16

6

18

7

7

5

11

10

11

What is the mean? (Round your answer to four decimal places.)

To compute the mean, median, and mode of the wolf pack sizes, we first need to organize the given data and then perform the calculations. The sizes of the wolf packs provided are:

5, 13, 10, 8, 10, 10, 5, 7, 6, 16, 6, 18, 7, 7, 5, 11, 10, 11

### Step 1: Calculate the Mean
The mean (average) pack size is found by summing all the pack sizes and dividing by the total number of observations.

1. **Sum of pack sizes**:
   \[
   5 + 13 + 10 + 8 + 10 + 10 + 5 + 7 + 6 + 16 + 6 + 18 + 7 + 7 + 5 + 11 + 10 + 11
   \]

2. **Total number of observations**: 18

Let's calculate the sum:

\[
5 + 13 + 10 + 8 + 10 + 10 + 5 + 7 + 6 + 16 + 6 + 18 + 7 + 7 + 5 + 11 + 10 + 11 = 175
\]

3. **Mean calculation**:
   \[
   \text{Mean} = \frac{175}{18} \approx 9.7222
   \]

### Step 2: Calculate the Median
The median is the middle value when the data set is ordered. Since there are 18 values, the median will be the average of the 9th and 10th values.

1. **Order the pack sizes**:
   5, 5, 5, 6, 6, 7, 7, 7, 8, 10, 10, 10, 10, 11, 11, 13, 16, 18

2. The 9th and 10th values are 8 and 10.

   \[
   \text{Median} = \frac{8 + 10}{2} = 9
   \]

### Step 3: Calculate the Mode
The mode is the value that appears most frequently in the data set.

1. In the ordered set, the value 10 appears 4 times, which is more frequent than any other value.

2. Therefore, the mode is:
   \[
   \text{Mode} = 10
   \]

### Summary of Results
- **Mean**: \( 9.7222 \) (rounded to four decimal places)
- **Median**: \( 9 \)
- **Mode**: \( 10 \)

Would you like more details or have any questions about these calculations?

Here are some related questions to explore:
1. What is the range of the wolf pack sizes recorded?
2. How does the mode relate to other statistical measures in this data set?
3. If an additional wolf pack of size 20 is added to the dataset, how will the mean change?
4. What does the median pack size suggest about the distribution of pack sizes?
5. How might the sizes of wolf packs vary in different seasons?

**Tip**: Using the median can be particularly useful for understanding the central tendency of data when there are outliers, as it is less affected by extremely high or low values compared to the mean.

Learn how to calculate the mean, median, and mode of winter wolf pack sizes using a sample dataset. Understand the statistical measures for central tendency and frequency in pack sizes. Suitable for students and researchers interested in statistics and wildlife biology.

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