Median formula for continuous data

In the video session “Computing median from histogram” , professor says the exact median cannot be determined if the individual values are not known but the median class can be evaluated. The mid point of the interval would be an approximation for the median.

But in statistics book, there is formula given for continuous data where frequencies are given and not the actual data points which goes by

Median = L+[h/f *(N/2-c)]

Where ‘L’ is the lower limit of the median class
(The median class is one whose cumulative Freq is just greater than N/2)

‘h’ is the class width of the median class
'f ’ is the Freq of median class
‘c’ is the cumulative Freq of the class preceding the median class.

Can this formula not be used. Please clarify

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The specified formula is the one used to estimate the median value from the given distribution for continuous data. Surely, it can be applied to compute median for continuous data.

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Thanks for the help. Can I get an explanation as to how this estimation can be equated to the median…the logic behind the estimation