Math Problem Statement

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 0.79 0.52 0.48 0.63 0.31

0.72 0.57 0.49 0.44 0.29

0.58 0.32 0.53 0.41 0.73

0.48 0.40 0.34 0.36 0.41

Solution

Let's calculate the mean, median, and mode of the given dataLet's calculate the mean, median, and mode of the given

Data:

0.79, 0.52, 0.48, 0.63, 0.31,
0.72, 0.57, 0.49, 0.44, 0.29,
0.58, 0.32, 0.53, 0.41, 0.73,
0.48, 0.40, 0.34, 0.36, 0.41

1. Mean:

The mean is the average of the numbers, calculated as:

Mean=data valuesnumber of data values\text{Mean} = \frac{\sum \text{data values}}{\text{number of data values}}

2. Median:

The median is the middle value when the data is ordered in increasing order. If there's an even number of values, the median is the average of the two middle numbers.

3. Mode:

The mode is the value that appears most frequently in the data set.

Let me calculate these values.### Results:

  1. Mean: 0.490.49 (rounded to two decimal places)
  2. Median: 0.480.48
  3. Mode: 0.410.41 (appears most frequently)

Would you like more details on these calculations, or have any other questions?

Here are 5 related questions you might find useful:

  1. How does the mean compare to the median in this dataset?
  2. Can you have more than one mode in a dataset?
  3. What happens if all values in the dataset are different? Is there still a mode?
  4. Why is the median preferred in skewed data over the mean?
  5. How does adding an outlier affect the mean and median?

Tip: The median is often more resistant to extreme values compared to the mean, making it a good measure for skewed distributions.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics

Formulas

Mean = (Sum of values) / (Number of values)
Median = Middle value of an ordered dataset
Mode = Most frequently occurring value

Theorems

Central Tendency Theorem

Suitable Grade Level

Grades 8-10