Answer: The number of degrees of freedom in estimating the population variance with the sample variance is equal to the sample size minus one

## Explanation Let's analyze each statement: **Statement A: "The range shows how the data are distributed"** - This is **incorrect**. The range only shows the difference between the maximum and minimum values, but it does not provide information about how the data are distributed within that range. The range is a measure of spread, but it doesn't show the distribution pattern. **Statement B: "The variance is expressed in the same unit of measurement as the observations"** - This is **incorrect**. Variance is expressed in the square of the units of the original observations. For example, if the data are in meters, variance is in square meters. The standard deviation (which is the square root of variance) is expressed in the same units as the observations. **Statement C: "The number of degrees of freedom in estimating the population variance with the sample variance is equal to the sample size minus one"** - This is **correct**. When estimating population variance using sample variance, we use (n-1) degrees of freedom, not n. This is because we lose one degree of freedom when we estimate the population mean using the sample mean. The formula for sample variance is: $$s^2 = \frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}$$ where n-1 represents the degrees of freedom. **Key Concepts:** 1. **Range**: Maximum value minus minimum value - simple but sensitive to outliers. 2. **Variance**: Average of squared deviations from the mean - expressed in squared units. 3. **Degrees of Freedom**: Number of independent pieces of information available for estimation. For sample variance, it's n-1 because one parameter (the mean) has been estimated from the data. Therefore, statement C is the most accurate among the three options.

Author: LeetQuiz .