To solve this:

1. Range: The range is calculated as the difference between the maximum and minimum values in the data set.

   Range = $\text{Maximum value} - \text{Minimum value}$

2. Sample Standard Deviation: This is calculated using the formula: $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$ where:

   • $x_i$ = each data value
   • $\bar{x}$ = sample mean
   • $n$ = sample size
   • $s$ = sample standard deviation

I will now calculate these values. numpy as np

Data set

data = np.array([102.1, 91, 89.2, 116, 124.2, 124.2, 124.2, 106.2, 92.8, 106.8])

Calculating the range

data_range = np.max(data) - np.min(data)

Calculating the sample standard deviation

sample_std_dev = np.std(data, ddof=1) # ddof=1 for sample standard deviation

data_range, round(sample_std_dev, 4)### Results:

1. Range: $35.0$
2. Sample Standard Deviation: $13.9968$

The standard deviation has been rounded to match the precision (2 decimal places more than the original data): 13.997.

Let me know if you'd like detailed steps, or have any questions! Here are some related queries:

1. What is the mean of this data set?
2. How does the sample standard deviation differ from the population standard deviation?
3. What does the range tell us about this data set?
4. How would the results change if one outlier was removed?
5. Can we visualize this data on a number line?

Tip: Always check the dataset for outliers as they can significantly affect both range and standard deviation!