The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest:

1212; 1717; 1818; 2020; 2020; 2121; 2323; 2424; 2525; 2525; 2525; 2626; 2626; 2626; 2727; 2727; 2828; 2929; 2929; 3232; 3333; 3333; 3434; 3535; 3737; 3939; 4444

Calculate the mean.

Round your answer to two decimal places.

Identify the median.

Enter the exact answer.

Identify the mode.

The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;62;4;6 or x+1;x−1x+1;x−1). The order of the list does not matter.

### Step 1: Calculate the Mean

The mean (average) is calculated by adding up all the numbers in the dataset and then dividing by the number of values.

Given data### Step 1: Calculate the Mean

The mean (average) is calculated by adding up all the numbers in the dataset and then dividing by the number of values.

Given  
\( 12, 17, 18, 20, 20, 21, 23, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 29, 29, 32, 33, 33, 34, 35, 37, 39, 44 \)

There are 27 data points.

#### Sum of the data### Step 1: Calculate the Mean

The mean (average) is calculated by adding up all the numbers in the dataset and then dividing by the number of values.

Given  
\( 12, 17, 18, 20, 20, 21, 23, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 29, 29, 32, 33, 33, 34, 35, 37, 39, 44 \)

There are 27 data points.

#### Sum of the 
\[
12 + 17 + 18 + 20 + 20 + 21 + 23 + 24 + 25 + 25 + 25 + 26 + 26 + 26 + 27 + 27 + 28 + 29 + 29 + 32 + 33 + 33 + 34 + 35 + 37 + 39 + 44 = 730
\]

#### Mean:
\[
\text{Mean} = \frac{730}{27} \approx 27.04
\]

So, the mean is \( \mathbf{27.04} \).

### Step 2: Identify the Median

The median is the middle value in the ordered list. If the number of data points is odd, the median is the middle number. If it’s even, the median is the average of the two middle numbers.

Since there are 27 data points (odd number), the median is the 14th number in the ordered list.

Looking at the data, the 14th number is \( 26 \).

So, the median is \( \mathbf{26} \).

### Step 3: Identify the Mode

The mode is the number that appears most frequently in the dataset.

By examining the data### Step 1: Calculate the Mean

The mean (average) is calculated by adding up all the numbers in the dataset and then dividing by the number of values.

Given  
\( 12, 17, 18, 20, 20, 21, 23, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 29, 29, 32, 33, 33, 34, 35, 37, 39, 44 \)

There are 27 data points.

#### Sum of the 
\[
12 + 17 + 18 + 20 + 20 + 21 + 23 + 24 + 25 + 25 + 25 + 26 + 26 + 26 + 27 + 27 + 28 + 29 + 29 + 32 + 33 + 33 + 34 + 35 + 37 + 39 + 44 = 730
\]

#### Mean:
\[
\text{Mean} = \frac{730}{27} \approx 27.04
\]

So, the mean is \( \mathbf{27.04} \).

### Step 2: Identify the Median

The median is the middle value in the ordered list. If the number of data points is odd, the median is the middle number. If it’s even, the median is the average of the two middle numbers.

Since there are 27 data points (odd number), the median is the 14th number in the ordered list.

Looking at the data, the 14th number is \( 26 \).

So, the median is \( \mathbf{26} \).

### Step 3: Identify the Mode

The mode is the number that appears most frequently in the dataset.

By examining the 
- \(25\) appears 3 times.
- \(26\) appears 3 times.

Both \(25\) and \(26\) are the most frequent values.

So, the mode is \( \mathbf{25; 26} \).

### Summary:
- **Mean**: \( 27.04 \)
- **Median**: \( 26 \)
- **Mode**: \( 25; 26 \)

Would you like any further details or have any questions? 

Here are five related questions to expand on this topic:
1. How would the mean change if another boat with a length of 50 was added to the data?
2. How do you calculate the median for an even number of data points?
3. What is the difference between mean, median, and mode?
4. Can a dataset have more than one mode?
5. How would removing the smallest and largest values affect the mean and median?

**Tip**: In a symmetrical distribution, the mean, median, and mode are all the same.

Learn how to calculate the mean, median, and mode from a dataset of boat lengths. This problem involves applying statistical concepts to ordered data points and understanding measures of central tendency. Suitable for students in Grades 9-12.

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