1. Range:

The range of a data set is calculated by subtracting the smallest value from the largest value.

• Smallest value: 0
• Largest value: 17

$\text{Range} = 17 - 0 = 17 \text{ hours}$

2. Standard Deviation:

To calculate the standard deviation, we first find the mean, then calculate the variance, and finally take the square root of the variance.

1. Find the mean ($\mu$):

$\mu = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{6 + 8 + 0 + 2 + 16 + 5 + 13 + 16 + 10 + 10 + 7 + 10 + 6 + 4 + 5 + 5 + 4 + 12 + 11 + 13 + 16 + 15 + 17 + 9 + 14 + 15 + 9 + 9 + 6 + 3 + 0 + 16 + 3 + 12 + 13 + 6 + 17 + 13}{38}$

$\mu = \frac{359}{38} \approx 9.45$

2. Find the variance ($\sigma^2$):

$\sigma^2 = \frac{\sum (x - \mu)^2}{n}$

$\sigma^2 = \frac{(6-9.45)^2 + (8-9.45)^2 + \ldots + (13-9.45)^2}{38}$

3. Find the standard deviation ($\sigma$):

$\sigma = \sqrt{\sigma^2}$

Let's calculate this.

3. Five-Number Summary:

The five-number summary consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

1. Minimum (Min): 0
2. First Quartile (Q1): The 25th percentile value
3. Median (Q2): The 50th percentile value
4. Third Quartile (Q3): The 75th percentile value
5. Maximum (Max): 17

I will calculate the exact values for the standard deviation and the five-number summary.### Results:

1. Range: $17 \text{ hours}$

2. Standard Deviation: $\sigma \approx 4.9 \text{ hours}$

3. Five-Number Summary:

   • Minimum (Min): 0
   • First Quartile (Q1): 5.25
   • Median (Q2): 9.5
   • Third Quartile (Q3): 13.0
   • Maximum (Max): 17

Would you like more details or have any questions?

Related Questions:

1. How is the standard deviation useful in understanding the spread of data?
2. What do the quartiles represent in the context of this data set?
3. How would the range change if we exclude outliers?
4. Can we determine the skewness of the data using these results?
5. What is the interquartile range (IQR) and what does it tell us?

Tip: The standard deviation provides insight into the variability of the data—how spread out the values are from the mean.