Consider a bar graph with a bar for each of the classes of data. Then f₁ is the height of

the bar of the model class, f₀ is the height of the bar on the left of it, and f₂ is the height t.

the bar on the right of it.

The quantity f₁ - f₀ measures how far the modal class bar sticks up above the bar on

its left. The quantity f₁ - f₂ measures how far the modal class bar sticks up above the 

bar on its right.

Now, observe that

    (f₁ - f₀ )/(2f₁ - f₀ - f₂ ) + (f₁ - f₂ )/(2f1−f0−f2) 

= (f₁ - f₀ )/{(f₁ - f₀ ) + (f₁ - f₂ )} +  (f₁ - f₀ )/{(f₁ - f₀ ) + (f₁ - f₂ )} = 1

So if we want to divide an interval of width h into two pieces, where the ratio of sizes of 

those two pieces is (f₁ - f₀ ) : (f₁ - f₂ ), the first piece will have width (f₁ - f₀ ) *h /{

(2f₁ - f₀ - f₂ )} 

This is what the formula for estimating the mode does. It splits the width of the modal bar

into two pieces whose ratio of widths is (f₁ - f₀ ) : (f₁ - f₂ ), and it says the mode is at the

line separating those two pieces, that is, at a distance

(f₁ - f₀ ) *h /{(2f₁ - f₀ - f₂ )} from the left edge of that bar, l.

Hence,

Mode = l + (f₁ - f₀ ) *h /{(2f₁ - f₀ - f₂ )}