I am studying in 10 th grade. In statistics chapter they gave formulas of mean,mode,median for grouped data. I could derive formula for mean easily but I can't for others. My textbook also didn't gave derivation, they blindly put them in textbooks and make students to mug them. I am curious to know how these formulas came.
For median, it follows more or less directly from the assumption that within each group, the data are entirely evenly distributed. Basically the same assumption leads you to the calculation for the mean, so it shouldn't be too much of a stretch.
I don't really know about mode. I don't even know whether it makes that much sense to talk about mode for grouped data. With mean and median, you can at least have a decent idea of which group it's in. Not so much with mode. And I'm not entirely certain about the formula. But it does seem to choose a mode closer to the preceeding class if $f_0$ and $f_1$ are close, and a mode closer to the succeeding class if $f_1$ and $f_2$ are closer. Which is reasonable.
