The Apollo space program lasted from 1967 until 1972 and included 13 missions. The missions lasted from as little as 7 hours to as long as 301 hours. The duration of each flight is as follows: 9 195 241 301 216 260 7 244 192 147 10 295 142 Find the standard deviation

To find the standard deviation of the mission durations for the Apollo space program, we'll follow these steps:

### Step-by-step process:
1. **Calculate the mean (average):**

\[
\text{Mean} (\mu) = \frac{\sum x_i}{n}
\]

where \( x_i \) is each flight duration, and \( n \) is the number of flights.

2. **Find the squared differences from the mean:**  
For each flight duration, subtract the mean and square the result.

3. **Calculate the variance:**  
The variance is the average of the squared differences from the mean.

\[
\text{Variance} (\sigma^2) = \frac{\sum (x_i - \mu)^2}{n}
\]

4. **Find the standard deviation:**  
The standard deviation is the square root of the variance.

\[
\text{Standard deviation} (\sigma) = \sqrt{\text{Variance}}
\]

Now, let's calculate it step by step.### Results:
1. **Mean (average) duration**: \( 173.77 \, \text{hours} \)
2. **Variance**: \( 10295.87 \, \text{hours}^2 \)
3. **Standard deviation**: \( 101.47 \, \text{hours} \)

This means the mission durations vary by about 101.47 hours from the average duration of 173.77 hours.

Would you like more details, or do you have any questions?

### Related Questions:
1. How do we interpret the standard deviation in practical terms for these space missions?
2. What is the range of durations, and how does it compare to the standard deviation?
3. How would the calculation change if this were a sample, not the entire population?
4. What is the median mission duration, and how does it compare to the mean?
5. How do outliers like very short or long missions affect the standard deviation?

### Tip:
Always check whether you are dealing with a population or sample, as it affects whether you divide by \( n \) or \( n-1 \) when calculating variance.

The Apollo space program lasted from 1967 until 1972 and included 13 missions. The missions lasted from as little as 7 hours to as long as 301 hours. The duration of each flight is as follows: 9 195 241 301 216 260 7 244 192 147 10 295 142 Find the standard deviation.

Find out how to calculate the standard deviation of the Apollo space program's mission durations, which lasted from as short as 7 hours to as long as 301 hours. This step-by-step solution explains key statistical concepts like mean, variance, and standard deviation, suitable for students in Grades 10-12.

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