Think carefully before you do this. You have no idea what the underlying height distribution is. Here are four possibilities.
If you were building a regression model, each of these sets of height data would be interpreted differently. However, if replaced by your ordinal variable, they all look numerically equivalent. If you use this variable as a continuous variable, you are assuming a level of precision and information not present in the data.
Keep your ordinal variable as an ordinal variable. It may even be advantageous to bin this variable into fewer categories (for example "low", "low-middle", "middle", "middle-high", "high"). There are two reasons to do this.
- This is a variable that has a unique value for each observation, which may lead to it looking disproportionately important. When you bin it like this, you remove that problem.
- Think about future data that your model will be used to evaluate. Will those height classes in the new data reference the original classes? What if the new set has 100 observations? Now the new data has a range larger than what the model originally considered. Binning this variable is equivalent to normalizing a continuous variable.
Ultimately, your choice should be based on the performance of your regression model. If it behaves better with the variable as a continuous numerical variable, then do that. If the model behaves better with the variable as an ordinal variable in bins, do that.