The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). According to the safety requirement, the hic measurement should be less than 1000 hic.

774  649  1210  546  431  612
 
Mean: Answer 1 Question 10 hic.

Median: Answer 2 Question 10 hic.

Mode: Answer 3 Question 10  7746491210546431612No mode hic.

Midrange

To solve this problem, let's compute the mean, median, mode, and midrange of the given data set:

### Given Data Set
\[
774, 649, 1210, 546, 431, 612
\]

### 1. Mean

The **mean** (average) is calculated by summing all the values and dividing by the number of values.

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

\[
\text{Mean} = \frac{774 + 649 + 1210 + 546 + 431 + 612}{6}
\]

\[
\text{Mean} = \frac{4222}{6} \approx 703.67 \, \text{hic}
\]

### 2. Median

The **median** is the middle value of a sorted data set. If there is an even number of values, it is the average of the two middle values.

First, let's sort the dataTo solve this problem, let's compute the mean, median, mode, and midrange of the given data set:

### Given Data Set
\[
774, 649, 1210, 546, 431, 612
\]

### 1. Mean

The **mean** (average) is calculated by summing all the values and dividing by the number of values.

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

\[
\text{Mean} = \frac{774 + 649 + 1210 + 546 + 431 + 612}{6}
\]

\[
\text{Mean} = \frac{4222}{6} \approx 703.67 \, \text{hic}
\]

### 2. Median

The **median** is the middle value of a sorted data set. If there is an even number of values, it is the average of the two middle values.

First, let's sort the 

\[
431, 546, 612, 649, 774, 1210
\]

There are 6 values, so the median will be the average of the 3rd and 4th values:

\[
\text{Median} = \frac{612 + 649}{2} = \frac{1261}{2} = 630.5 \, \text{hic}
\]

### 3. Mode

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

In this case, each value appears exactly once. Therefore, there is **no mode**.

### 4. Midrange

The **midrange** is calculated by taking the average of the maximum and minimum values in the data set.

\[
\text{Midrange} = \frac{\text{Max value} + \text{Min value}}{2}
\]

\[
\text{Max value} = 1210, \quad \text{Min value} = 431
\]

\[
\text{Midrange} = \frac{1210 + 431}{2} = \frac{1641}{2} = 820.5 \, \text{hic}
\]

### Summary of Answers:

- **Mean**: \(703.67 \, \text{hic}\)
- **Median**: \(630.5 \, \text{hic}\)
- **Mode**: No mode
- **Midrange**: \(820.5 \, \text{hic}\)

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

### Related Questions:

1. What is the range of the given data set?
2. How does the mean compare to the median in terms of data skewness?
3. How would the mean change if an additional test result of 900 hic was included?
4. What is the standard deviation of the given data set?
5. How many of the test results exceed the safety requirement of 1000 hic?

**Tip:** When analyzing a data set, it's important to consider not just the mean, but also the median, mode, and range to get a full picture of the data's distribution.

Learn how to calculate the mean, median, mode, and midrange of child booster seat crash test results conducted by the National Highway Traffic Safety Administration. Detailed step-by-step solution provided. Suitable for statistics enthusiasts and students in Grades 9-12.

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