Find the mean, median, and mode of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

Rate of Fatal Alcohol Impaired Car Crashes per 100
Million Vehicle Miles of Travel
0.31
0.38
0.37
0.43
0.37
0.53
0.61
0.38
0.78
0.31
0.50
0.55
0.36
0.39
0.80
0.79
0.51
0.52
0.32
0.54

To find the mean, median, and mode of the given data set, we'll first sort the data, then calculate each statistic step by step.

### 1. **Organize the Data:**
The given rates of fatal alcohol-impaired car crashes per 100 million vehicle miles of travel are:

\[ 0.31, 0.38, 0.37, 0.43, 0.37, 0.53, 0.61, 0.38, 0.78, 0.31, 0.50, 0.55, 0.36, 0.39, 0.80, 0.79, 0.51, 0.52, 0.32, 0.54 \]

First, let's sort this data in ascending order:

\[ 0.31, 0.31, 0.32, 0.36, 0.37, 0.37, 0.38, 0.38, 0.39, 0.43, 0.50, 0.51, 0.52, 0.53, 0.54, 0.55, 0.61, 0.78, 0.79, 0.80 \]

### 2. **Calculate the Mean:**
The mean (average) is calculated by summing all the values and then dividing by the total number of values.

\[
\text{Mean} = \frac{\sum \text{values}}{\text{number of values}}
\]

Let's compute the sum of all values and then divide by the total count (20).

### 3. **Calculate the Median:**
The median is the middle value of a sorted list. If the number of observations (n) is odd, the median is the middle value; if n is even, it is the average of the two middle values.

Since we have 20 data points (an even number), the median will be the average of the 10th and 11th values in the sorted list.

### 4. **Calculate the Mode:**
The mode is the value(s) that appear most frequently in the data set.

Now, I'll compute these statistics.Here are the calculated statistics for the given data set:

1. **Mean (Average):** 0.4875
2. **Median:** 0.465 (rounded to three decimal places)
3. **Mode:** 0.31

### Explanation:
- **Mean** is the average of all values.
- **Median** is the middle value in the sorted data set. Since there are 20 values, it's the average of the 10th and 11th values.
- **Mode** is the most frequently occurring value in the data set, which is 0.31.

Would you like to see more details or have any questions?

### Related Questions:
1. How do you calculate the range of a data set?
2. What is the impact of outliers on the mean, median, and mode?
3. How can the standard deviation of this data set be calculated?
4. What are the differences between the mean, median, and mode?
5. How would the calculations change if a new value were added to the data set?

**Tip:** Knowing the mean, median, and mode helps in understanding the distribution and central tendency of your data set!

Find the mean, median, and mode of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Rate of Fatal Alcohol Impaired Car Crashes per 100 Million Vehicle Miles of Travel: 0.31, 0.38, 0.37, 0.43, 0.37, 0.53, 0.61, 0.38, 0.78, 0.31, 0.50, 0.55, 0.36, 0.39, 0.80, 0.79, 0.51, 0.52, 0.32, 0.54

Learn how to calculate the mean, median, and mode of a dataset representing the rate of fatal alcohol-impaired car crashes per 100 million vehicle miles of travel. This example covers key statistical concepts and is suitable for students in Grades 8-10.

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