It looks like you're working on a statistics problem involving measures of spread. Let’s clarify each part before solving:

• Part b: You are adding 3 to each measurement and then recalculating the range, variance (s²), and standard deviation (s).
• Range: The difference between the maximum and minimum values in a data set.
• Variance (s²): The average squared deviation from the mean.
• Standard deviation (s): The square root of the variance.

Adding a constant (like 3) to each value does not change the range, variance, or standard deviation. This is because these measures depend on the spread of the data, not the location.

Answers:

• Range: The range remains the same as before.
• Variance (s²): The variance remains the same as before (rounded to one decimal place).
• Standard deviation (s): The standard deviation remains the same as before (rounded to two decimal places).

Would you like me to verify calculations for a specific data set?

Related Questions:

1. How does multiplying all data values by a constant affect variance and standard deviation?
2. Why does adding a constant to data not change its spread?
3. What is the formula for sample variance and how is it derived?
4. How do outliers affect variance and standard deviation?
5. What are real-life examples where variance and standard deviation are useful?

Tip: When working with variance and standard deviation, always check whether you're using a sample or population formula.