How to Calculate Statistics for Open-Ended Frequency Distribution
If you had a frequency distribution something like the below (and did not have the raw data), how would you calculate statistics without being able to determine the midpoint of the final range (595+).
I have considered taking a sample of the dataset (0-9 to 520-594) and approximating it as a Normal Distribution with the Central Limit Theorem, then estimating the "effective" maximum (99%) for the range. However, this seems very approximate and not a true representation.
How should I estimate the midpoint of the 595+ range in the example below for calculating statistics such as the Average, Standard Deviation, etc?
$$ \begin{array}{c|lcr} Value & \text{Occurrences} \\ \hline 0-9 & 150 \\ 10-24 & 146 \\ 25-44 & 211 \\ 45-69 & 205 \\ 70-99 & 175 \\ 100-134 & 195 \\ 135-174 & 435 \\ 175-219 & 369 \\ 220-269 & 279 \\ 270-324 & 210 \\ 325-384 & 144 \\ 385-449 & 138 \\ 450-519 & 130 \\ 520-594 & 97 \\ 595+ & 14 \end{array} $$
Please note: Values are made up, and are a lot more "pretty" than they are in the actual dataset.
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