In the question provided, we are given an ordered sample of dataIn the question provided, we are given an ordered sample of

$0, 1, 2, ?, 8, ?, 12, 12, 13, 29$

where the "?" symbols represent missing values. The goal is to determine the most appropriate measure of dispersion for this data.

Step-by-Step Explanation:

1. Missing Values: The presence of missing values complicates the calculation of typical measures of dispersion, such as the standard deviation or variance. Without knowing what those missing values are, traditional methods may not work well.

2. Possible Measures of Dispersion:

   • Range: This is the difference between the maximum and minimum values. In this case, it would be $29 - 0 = 29$, but it ignores the distribution of the other values.
   • Variance/Standard Deviation: These measures take into account how spread out the values are but require all values to be known.
   • Interquartile Range (IQR): This is the range of the middle 50% of the data, calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The IQR is more robust in the presence of outliers or missing values, making it a suitable choice.

3. Conclusion: Since there are missing values and we are concerned with a robust measure of dispersion that doesn't heavily depend on knowing all the values, the interquartile range (IQR) is likely the most appropriate measure of dispersion for this data.

Would you like more details on calculating the IQR, or do you have any other questions?

Related Questions:

1. How do we calculate the interquartile range (IQR) step by step?
2. What happens if the missing values are replaced with reasonable estimates? How would the standard deviation change?
3. How does the range compare to the interquartile range in terms of measuring dispersion?
4. What methods can we use to estimate missing data points in statistical samples?
5. Why is the IQR considered a robust measure of dispersion in statistics?

Tip:

The IQR is often used to measure variability when the data has outliers or is not symmetrically distributed, as it focuses on the central portion of the data and ignores extreme values.