Whether calculations can be performed on distributions with open-ended classes depends on the specific calculation and the assumptions one is willing to make.

• Measures of Central Tendency:
  • Mean: Calculating the mean is problematic with open-ended classes because the midpoint of the open interval is undefined. You would need to make an assumption about the value to assign to the open end, which introduces potential inaccuracies.
  • Median: The median can often be determined even with an open-ended class, provided that the median falls within a closed interval. You need the cumulative frequency distribution to determine the interval containing the median.
  • Mode: The mode can be identified if the modal class is a closed interval. If the open-ended class has the highest frequency, then the mode cannot be precisely determined.
• Measures of Dispersion:
  • Range: The range cannot be determined with open-ended classes since the maximum value is undefined.
  • Variance and Standard Deviation: These are generally difficult to calculate accurately with open-ended classes because they depend on knowing (or estimating) the values of individual data points or class midpoints. Estimating the open-ended interval's contribution to the variance can introduce significant error.
  • Interquartile Range (IQR): The IQR can often be calculated, similar to the median, as long as the first and third quartiles fall within closed intervals.

In summary, while some calculations like the median and IQR *can* sometimes be performed with open-ended classes (provided the relevant quartiles fall within defined intervals), other calculations like the mean, standard deviation, and range are problematic and require assumptions or estimations that can impact accuracy. The feasibility depends heavily on the specific dataset and the desired level of precision.