When you group data into intervals, information is lost. So assumptions are made in order to make reasonable estimates of the sample mean, median, etc.

The assumption of this formula for estimating the median from grouped data is that the data are spread roughly uniformly throughout the interval. Clearly, this assumption is not met in your situation because all ten of the 's lie at the lower endpoint of the interval. The idea of the formula is to estimate the median by interpolation, putting the estimate somewhere within the interval. In your case the estimated value is in the middle of the 'median interval' (the interval known to contain the median).

If you were trying to contrive a situation in which the estimate is even farther from the truth, you could put your ten 's at the left end of an interval With no other data, your estimate of the median would then be

There is nothing wrong with the formula, provided the assumption of data spread evenly throughout the interval is close to the truth. But any formula for estimating the median from grouped data will have to depend on assumptions. All that can be said for sure is the the median lies somewhere in the median interval. You have to recognize that the information lost in grouping data into intervals cannot be precisely recovered (unless the original data are saved and used).

Note: By contrast, the assumption usually made when trying to estimate the sample mean from grouped data is that each observation lies precisely at the midpoint of the interval that contains it. This idea gives rise to the formula $\bar X \approx \frac 1 n \sum_{i=1}^k f_jm_j,$ where there are intervals (usually of equal width), with midpoints and frequencies

Because this is essentially a duplicate, I address a few issues that are do not explicitly overlap the related question or answer:

If a class has cumulative frequency .5, then the median is at the boundary of that class and the next larger one.

If is large (really the only case where this method is generally successful), there is little difference between and in the formula. All references I checked use .

Before computers were widely available, large datasets were customarily reduced to categories (classes) and plotted as histograms. Then the histograms were used to approximate the mean, variance, median, and other descriptive measures. Nowadays, it is best just to use a statistical computer package to find exact values of all measures.

One remaining application is to try to re-claim the descriptive measures from grouped data or from a histogram published in a journal. These are cases in which the original data are no longer available.

This procedure to approximate the sample median from grouped data $assumes$ that data are distributed in roughly a uniform fashion throughout the median interval. Then it uses interpolation to approximate the median. (By contrast, methods to approximate the sample mean and sample variance from grouped data one assumes that all obseervations are concentrated at their class midpoints.)