The results in the table represent a random sample of 50 observations.
 
Rate of Fatal Alcohol Impaired Car Crashes per 100 Million Vehicle Miles of Travel
0.45	0.53	0.32	0.70	0.50	0.63	0.77	0.73	0.68	0.32
0.56	0.56	0.41	0.32	0.52	0.59	0.30	0.33	0.41	0.33
0.36	0.78	0.59	0.44	0.65	0.58	0.66	0.40	0.57	0.61
0.47	0.37	0.49	0.49	0.50	0.53	0.55	0.66	0.45	0.52
0.74	0.34	0.40	0.59	0.47	0.64	0.45	0.33	0.42	0.55
 
Find the requested summary statistics. Round your answers to three decimal places.

To calculate the requested summary statistics for the given dataset, I will find the following:

1. **Mean (Average)**:
   The mean is the sum of all the values divided by the number of values.

2. **Median**:
   The median is the middle value when the data is arranged in ascending order. If the number of observations is even, the median is the average of the two middle values.

3. **Mode**:
   The mode is the value that appears most frequently in the dataset.

4. **Range**:
   The range is the difference between the maximum and minimum values.

5. **Variance**:
   Variance is the average of the squared differences from the mean.

6. **Standard Deviation**:
   The standard deviation is the square root of the variance.

7. **Min and Max**:
   The minimum and maximum values of the dataset.

Let me calculate these values for you.

### The dataset:
\[
\text{Data} = \{0.45, 0.53, 0.32, 0.70, 0.50, 0.63, 0.77, 0.73, 0.68, 0.32, 0.56, 0.56, 0.41, 0.32, 0.52, 0.59, 0.30, 0.33, 0.41, 0.33, 0.36, 0.78, 0.59, 0.44, 0.65, 0.58, 0.66, 0.40, 0.57, 0.61, 0.47, 0.37, 0.49, 0.49, 0.50, 0.53, 0.55, 0.66, 0.45, 0.52, 0.74, 0.34, 0.40, 0.59, 0.47, 0.64, 0.45, 0.33, 0.42, 0.55\}
\]

I'll now perform the calculations.Here are the requested summary statistics for the given dataset:

1. **Mean**: 0.511
2. **Median**: 0.510
3. **Mode**: 0.320
4. **Range**: 0.480 (Max: 0.780 - Min: 0.300)
5. **Variance**: 0.017
6. **Standard Deviation**: 0.131
7. **Minimum**: 0.300
8. **Maximum**: 0.780

Would you like further details or clarification on any of the calculations?

Here are 5 related questions:
1. How is the variance different from the standard deviation?
2. How would you interpret the mean value in the context of this data?
3. Why might the mode be important in this dataset?
4. What is the significance of the range in understanding data spread?
5. How would removing the highest or lowest value impact the summary statistics?

**Tip**: The standard deviation is a useful measure to understand how spread out the values are around the mean. A lower standard deviation indicates that data points are closer to the mean.

The results in the table represent a random sample of 50 observations. Find the requested summary statistics. Round your answers to three decimal places.

Find the mean, median, mode, range, variance, and standard deviation for a dataset representing the rate of fatal alcohol-impaired car crashes per 100 million vehicle miles. This example demonstrates the core concepts of descriptive statistics, ideal for Grades 9-12.

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