Let's evaluate each statement:
i. "It is okay to use the median to estimate the mean since both are a measure of the center of a distribution."
- False: The median and mean are different measures of central tendency, and they can diverge significantly, especially in skewed distributions. Using the median to estimate the mean is not generally advisable.
ii. "It is okay to use the standard deviation to estimate the IQR since both are measures of variability."
- False: The standard deviation and interquartile range (IQR) measure variability in different ways. The standard deviation is sensitive to outliers and assumes a normal distribution, while the IQR focuses on the range of the middle 50% of the data and is robust to outliers. Therefore, using one to estimate the other is not appropriate.
iii. "Point estimates based on a sample are sometimes far from a parameter's value."
- True: Point estimates, such as sample means or proportions, can differ from population parameters due to sampling error. This is a recognized issue in statistics, and the variability is often quantified using confidence intervals.
Based on this evaluation:
- Statement i is false.
- Statement ii is false.
- Statement iii is true.
Thus, the correct answer is C. iii only.
1 answer